Learn on ChickenFryBytes Studios

Potential Dividers

Sat, 28 Feb 2026 15:50:31 -0400

A potential divider is used to divide an input voltage into a smaller output voltage. Consider a circuit where the input voltage, $V$ is applied across two resistors, $R_1$ and $R_2$ in series:

The current flowing from the battery depends on the input voltage and the total resistance: $$ \begin{equation}\begin{aligned} I&=\frac{V}{R_T}\\ \end{aligned}\end{equation} $$

Because the resistors are in series, the same current flows through $R_1$, with a potential difference of $V_1$ across its ends: $$ \begin{equation}\begin{aligned} I&=\frac{V_1}{R_1}\\ \end{aligned}\end{equation} $$

Volume of Revolution

Thu, 19 Feb 2026 06:22:45 -0500

Recall that the area bounded by a curve, the x-axis, and the two lines $x=a$ and $x=b$, is given by:

$$ \begin{equation}\begin{aligned} A=\int_a^bf(x)dx\\ \end{aligned}\end{equation} $$

If we were to take this area and rotate $360\degree$, the volume of the solid shape generated by this rotation would be given by:

$$ \begin{equation}\begin{aligned} V=\pi\int_a^b[f(x)]^2dx\\ \end{aligned}\end{equation} $$

Note the two changes:

We multiply by pi ($\pi$)
We integrate the square of the function instead of just the function

Example

FInd the volume of revolution when the area bounded by the curve $y=x+3$, and the lines $x=1$ and $x=3$, and the x-axis, is rotated about the x-axis.

Definite Integrals and Area Bounded by a Curve

Thu, 19 Feb 2026 06:22:33 -0500

Consider the area that is bounded vertically by a curve $y=f(x)$ and the x-axis, and horizontally by the lines $x=a$ and $x=b$:

This enclosed area is given by the definite integral: $$ \begin{equation}\begin{aligned} A=\int_a^bf(x)dx\\ \end{aligned}\end{equation} $$

The definite integral is the result of evaluation the integral considering two boundaries, in this case the lines $x=a$ and $x=b$.

Area trapped between two curves

In order to find the area, we need to determine the boundaries by finding the intersection of the curves. We then find, in the case of area relative to the x-axis, the integral of the difference between the upper curve and the lower curve.

Integration

Thu, 19 Feb 2026 06:21:45 -0500

Whereas differentiation is used to find the rate of change of one variable with respect to another, integration does the opposite. When we integrate, we find the area under the graph. That is, we find the product of the function on the y-axis and infinitely thin sections of the x-axis variable.

The anti-derivative

This is the opposite of the derivative of a function. It is not the same as the integral as it does not include the constant of integration. The constant of integration represents the information lost when differentiation occurs.

Kirchhoff's Laws

Sat, 14 Feb 2026 08:35:21 -0500

These laws govern the general behaviour of current ($I$) and voltage ($V$) in circuits.

Kirchhoff’s Current Law

The algebraic sum of currents entering and leaving a node is zero: $$ \begin{equation}\begin{aligned} I_T&=I_1+I_2+I_3\\ \end{aligned}\end{equation} $$

Kirchhoff’s Voltage Law

The algebraic sum of e.m.f.’s and p.d.’s in a loop is zero: $$ \begin{equation}\begin{aligned} E-(V_1+V_2+V_3)&=0\\ \end{aligned}\end{equation} $$

Note that there does not have to be any source of power for a loop to be analyzed in a circuit. We simply consider the total e.m.f. to be zero ($0$).

Internal Resistance

Sat, 14 Feb 2026 08:34:54 -0500

Rates of Change

Mon, 09 Feb 2026 06:31:04 -0500

We must acknowledge that so far we have always been working with the rate of change. By differentiating $y$ with respect to $x$, we get the derivative of $y$ with respect to $x$: $$ \begin{equation}\begin{aligned} \frac{d}{dx}(y)&=\frac{dy}{dx}\\ \end{aligned}\end{equation} $$

This is also referred to as the rate of change of $y$ with respect to $x$. Read the following rates of change:

$\frac{du}{d\theta}$
$\frac{dv}{dx}$
$\frac{d\theta}{dx}$
$\frac{du}{dt}$
$\frac{ds}{dt}$

When the rate of change of a variable is with respect to time, we do not have to mention that it is with respect to time e.g. $\frac{du}{dt}$ can be simply read as the rate of change of $u$.

Resistance

Sat, 07 Feb 2026 09:02:16 -0500

Electric resistance, $R$ is the tendency of a material to resist the flow of an electric current, $I$. The SI unit of resistance is the Ohm ($\Omega$).

Ohm’s Law

The current flowing through a conductor is directly proportional to the voltage across its end, given that temperature is constant: $$ \begin{equation}\begin{aligned} V&=IR\\ \end{aligned}\end{equation} $$

Electric resistance is thus the ratio of the voltage applied to a conductor to the electric current that results from this voltage:

Electric Current

Sat, 07 Feb 2026 08:29:32 -0500

Electricity is the presence or flow of charged particles. There are two ($2$) types of electricity:

Static electricity - this is associated with an excess or lack of charged particles e.g. too many electrons or missing electrons
Current electricity - this is associated with the movement of charged particles

Current

This is the charge transferred per unit time: $$ \begin{equation}\begin{aligned} I&=\frac{Q}{t}\\ \end{aligned}\end{equation} $$

Thus charge is the product of current and time: $$ \begin{equation}\begin{aligned} Q&=It\\ \end{aligned}\end{equation} $$

Waves

Sat, 31 Jan 2026 09:02:42 -0500

A wave is a disturbance that transfers energy from one point to another, without the net displacement of matter. There are three ($3$) types of waves:

Mechanical waves
Electromagnetic waves
Matter waves

Matter waves are associated with wave-particle duality. We know that light can sometimes behave as a wave and other times as a particle. By that logic, it is thus possible that other particles of matter can behave as waves.

Young's Modulus

Sat, 24 Jan 2026 10:13:44 -0500

It is important that we have means for determining the strength of a material. Young’s Modulus is the ratio of the tensile stress ($\sigma$) to the tensile strain ($\epsilon$): $$ \begin{equation}\begin{aligned} E&=\frac{\sigma}{\epsilon}\\ \end{aligned}\end{equation} $$

The stress is the force per unit area and the strain is the percentage change in length: $$ \begin{equation}\begin{aligned} &=\frac{F/A}{\Delta l/l}\\ \end{aligned}\end{equation} $$

The SI unit for stress is the $Pa$: $$ \begin{equation}\begin{aligned} \sigma&=\frac{F}{A}\\ &\rightarrow\frac{N}{m^2}\\ &=Pa\\ \end{aligned}\end{equation} $$

Deformation

Sat, 24 Jan 2026 08:40:13 -0500

We know that forces can cause changes in motion, size and shape. When we consider the shape/size changing aspect of forces, we are talking about deformation. Deformation is a change in the size or shape of a body or system e.g. stretching a rubber band, hitting a nail into a wooden board or having something hit your car and dent it.

Types of deformation

There are two ($2$) types of deformation:

Discrete Random Variables

Fri, 23 Jan 2026 06:50:13 -0500

These are variables that can take on a countable set of discrete values. The sum of the probabilities of each possible outcome is always $1$.

Expected value

The expected value (the mean) of a discrete random variable is given by the formula $$ \begin{equation}\begin{aligned} E(X)&=\sum{xP(X=x)}\\ \end{aligned}\end{equation} $$

where $X$ is the variable e.g. the face obtained from rolling a fair die and $x$ is a particular outcome e.g. $1$, $2$, etc.

Creating a Main Menu

Thu, 22 Jan 2026 12:00:11 -0500

The main() function is the entry point to our program. As such, we try our best not to clutter this function with much code. Instead, it is better to place the main menu here and call other functions from this main menu. Here is a possible implementation for the main menu:

#include <stdio.h>
#include <stdlib.h>

void clear_stdin() {
 int ch;
 while ((ch = getchar()) != '\n' && ch != EOF)
 ;
}

void feature_1() { printf("Using feature 1...\n"); }

void feature_2() { printf("Using feature 2...\n"); }

void feature_3() { printf("Using feature 3...\n"); }

int main() {
 int choice;

 // label to be used with 'goto' statement
present_choice:
 printf("\n📝 MAIN MENU 📝\n");
 printf("------------------------\n");
 printf("📌 1 - Use feature 1\n");
 printf("📌 2 - Use feature 2\n");
 printf("📌 3 - Use feature 3\n\n");

 printf("Please enter a choice: ");
 scanf("%d", &choice);

 switch (choice) {
 case 1:
 feature_1();
 break;
 case 2:
 feature_2();
 break;
 case 3:
 feature_3();
 break;
 default:
 printf("\n❌ Option does not exist! Please enter a valid option!\n");
 }

 // remove any characters left in stdin
 clear_stdin();
 goto present_choice;
 return 0;
}

menu.c

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Clearing standard input

The standard input (stdin) buffer will contain extra characters not handled by scanf. Leaving these characters in buffer will cause future calls to scanf to use the characters as if the user had input them into these newer calls. Thus we write a function to clear this buffer:

Stationary Points

Thu, 22 Jan 2026 06:57:41 -0500

A stationary point is a point on a curve where the gradient is zero ($0$). This means that the derivative will be $0$: $$ \begin{equation}\begin{aligned} \frac{dy}{dx}=0\\ \end{aligned}\end{equation} $$

To find the stationary points, we simply find $dy/dx$ and equate it to $0$. We then solve this equation to get the $x$ value(s) that satisfy it. The $y$ values can be found by substituting these $x$ values into the original equation of the curve.

Searching Algorithms

Tue, 20 Jan 2026 13:18:03 -0500

The purpose of sorting is to reorder data whereas the purpose of search is to find the desired data. Sorting thus serves to prepare a dataset for more efficient searching. Two basic search algorithms are:

Linear or sequential search
Binary

Linear/sequential search

This algorithm iterates through the entire list of items one by one until the data is found. It is a very naive searching algorithm as finding an element could require searching the entire list.

#include <stdio.h>

int linear_search(int *list, int key, int n) {
 for (int i = 0; i < n; i++) {
 if (list[i] == key) {
 return i;
 }
 }
 return -1;
}

int main() {
 int list[] = {1, 2, 45, -2, 13, 12};
 int key = 45;
 int n = sizeof(list) / sizeof(list[0]);
 int i = linear_search(list, key, n);
 if (i == -1) {
 printf("Did not find element\n");
 return -1;
 }
 printf("Found element %d at index %d\n", key, i);
 return 0;
}

linear-search.c

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Sorting Algorithms

Tue, 20 Jan 2026 13:17:55 -0500

Sorting is used to reorder data in a structure. For example, we may want to reorder the books on a desk by order of the dates they were published, in chronological order. Some common sorting algorithms are:

Bubble sort
Selection sort
Insertion sort
Merge sort
Quick sort

Sorting is not limited to alphabetical order or chronological order. Some languages designers provide an interface by which we can specify the condition to be used to determine if two elements should be swapped e.g. swap two persons if the first person’s height and the second person’s weight is greater than that of the other person.

Sorting and Searching

Tue, 20 Jan 2026 13:17:40 -0500

Queues

Tue, 20 Jan 2026 13:17:00 -0500

Stacks

Tue, 20 Jan 2026 13:16:53 -0500

Tangents and Normals

Tue, 20 Jan 2026 06:24:11 -0500

Recall that the gradient function tells us the gradient of a curve at any point, given the $x$ value (or any other required inputs).

The gradient at a point on the curve is the same as the gradient of the tangent to the curve at that point. Therefore the gradient function is used to find the gradient of the tangent at any given point on a curve.

Example

Find the equation of the tangent to the curve $y=x^2+5x+6$ at the point $(1,12)$.

Higher Order Derivatives

Mon, 19 Jan 2026 06:33:45 -0500

We can differentiate a function many times. The $nth$ derivative is represented by the notation: $$ \begin{equation}\begin{aligned} \frac{d^ny}{dx^n} \text{ OR }f^{(n)}(x)\\ \end{aligned}\end{equation} $$

For example, the second derivative is written as $$ \begin{equation}\begin{aligned} \frac{d^2y}{dx^2}\\ \end{aligned}\end{equation} $$

Example Find the third derivative of the function $y=\cos{3x}$

Solution The first derivative is $$ \begin{equation}\begin{aligned} \frac{dy}{dx}&=-\sin{3x}\times 3\\ &=-3\sin{3x}\\ \end{aligned}\end{equation} $$

The second derivative is $$ \begin{equation}\begin{aligned} \frac{d^2y}{dx^2}&=-3\cos{3x}\times 3\\ &=-9\cos{3x}\\ \end{aligned}\end{equation} $$

The third order derivative is $$ \begin{equation}\begin{aligned} \frac{d^3y}{dx^3}&=9\sin{3x}\times 3\\ &=27\sin{3x}\\ \end{aligned}\end{equation} $$

Rules for Differentiation

Tue, 13 Jan 2026 06:03:32 -0500

We now know how to differentiate basic algebraic and trigonometric functions but how we differentiate the compositions, products and quotients of these functions?

Chain rule

Given the composition of two functions, $$ \begin{equation}\begin{aligned} y=f(u)\text{ where } u=g(x)\\ \end{aligned}\end{equation} $$

The derivative will be $$ \begin{equation}\begin{aligned} \frac{dy}{dx}=\frac{dy}{du}\times \frac{du}{dx}\\ \end{aligned}\end{equation} $$

Example 1

For example, consider the function $$ \begin{equation}\begin{aligned} y=\sin(x+1)\\ \end{aligned}\end{equation} $$ This function can be achieved by substituting $x+1$ into $\sin{x}$. Thus, it is a composition of two functions. We can let the inner function $x+1$ be $u$: $$ \begin{equation}\begin{aligned} u&=x+1\\ \therefore y&=\sin{u}\\ \end{aligned}\end{equation} $$

Differentiation

Mon, 12 Jan 2026 06:11:08 -0500

Consider the formula for gradient: $$ \begin{equation}\begin{aligned} m&=\frac{y_2-y_1}{x_2-x_1}\\ &=\frac{\Delta y}{\Delta x}\\ \end{aligned}\end{equation} $$

This formula caters for an average rate of change from one point, $(x_1,y_1)$ to another, $(x_2,y_2)$. For differentiation, we find the instantaneous rate of change: $$ \begin{equation}\begin{aligned} m=\frac{dy}{dx}\\ \end{aligned}\end{equation} $$

This is referred to as the gradient function because it produces the gradient of the curve when provided with the $x$ value.

$\Delta$ means an average change whereas $d$ represents an infinitesimally small change - a change so small it is virtually zero ($0$).

Power

Sat, 10 Jan 2026 12:39:47 -0500

Power is the rate of transfer/conversion of energy. Due to energy being the ability to do work, power can also be defined as the work done per unit time: $$ \begin{equation}\begin{aligned} P=\frac{E}{t}\\ \end{aligned}\end{equation} $$

The SI unit is the Watt ($W$), equivalent to a Joule per second: $$ \begin{equation}\begin{aligned} P&=\frac{E}{t}\\ &\rightarrow \frac{J}{s}\\ &=W\\ \end{aligned}\end{equation} $$

The kilowatt-hour

Because energy is the product of power and time, the kilowatt-hour is a unit of energy: $$ \begin{equation}\begin{aligned} E&=Pt\\ &=1 kW\times h\\ 1kWh&=1000 W\times 3600 s\\ &=3,600,000 J\\ &=3.6MJ\\ \end{aligned}\end{equation} $$

Energy Conservation

Sat, 10 Jan 2026 08:50:52 -0500

Energy is the ability to do work. The SI unit of energy is the Joule ($J$).

Work

Work is given by the dot product of the force and the displacement: $$ \begin{equation}\begin{aligned} Work=\vec{F}\cdot \vec{s}\\ \end{aligned}\end{equation} $$

Recall that the dot product of two vectors is the sum of the products of the corresponding components. Given the vectors $\vec{a}$ and $\vec{b}$: $$ \begin{equation}\begin{aligned} \vec{a}&=\begin{pmatrix}x_1\\ y_1\\ \end{pmatrix}\\ \vec{b}&=\begin{pmatrix}x_2\\ y_2\\ \end{pmatrix}\\ \end{aligned}\end{equation} $$ The dot product is $$\vec{a}\cdot \vec{b}=x_1x_2+y_1y_2$$

Channels

Fri, 19 Dec 2025 20:29:13 -0500

We can use channels in order to send information among concurrent goroutines. They can be thought of as pipes in which we pass data around. A new channel is created using the syntax:


make(chan <dataType>)
// e.g. a channel for passing strings
myChannel := make(chan string)

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We can then send values through the channel using the syntax:

Permutations

Thu, 27 Nov 2025 06:16:50 -0500

These are also called arrangements because the order in which the elements are selected matters.

Permute $r$ out of $n$ objects

Given $n$ objects, the number of arrangements of $r$ objects is: $$ \begin{equation}\begin{aligned} {}^n P_r =\frac{n!}{(n-r)!}\\ \end{aligned}\end{equation} $$

Example: Your mom bought $6$ toys for you but you only have $3$ boxes. How many ways can you arrange the toys into the $3$ boxes?

Solution: $$ \begin{equation}\begin{aligned} {}^6 P_3&=\frac{6!}{(6-3)!}\\ &=\frac{6!}{3!}\\ &=120\\ \end{aligned}\end{equation} $$

Geometric Progressions

Tue, 25 Nov 2025 07:16:00 -0500

A geometric progression is a series in which each successive term is generated by multiplying the term before it by a fixed value called the common ratio. Given that the first term is $a$ and the common ratio is $r$, the $nth$ term of a GP is: $$ \begin{equation}\begin{aligned} u_n=ar^{n-1}\\ \end{aligned}\end{equation} $$

The sum up to the $nth$ term is: $$ \begin{equation}\begin{aligned} S_n&=\frac{a(r^{n}-1)}{r-1},r>1\\ \end{aligned}\end{equation} $$

For fractional and negative values of $r$, we use a variation of this formula: $$ \begin{equation}\begin{aligned} S_n&=\frac{a(1-r^{n})}{1-r},r<1\\ \end{aligned}\end{equation} $$

Arithmetic Progressions

Tue, 25 Nov 2025 06:22:37 -0500

An arithmetic progression is a series in which each successive term is generated by adding the term before it to a fixed value called the common difference. Given the first term of an arithmetic progression $a$, and a common difference (the difference between each consecutive term) $d$, the $nth$ term is:

$$ \begin{equation}\begin{aligned} u_n=a+(n-1)d\\ \end{aligned}\end{equation} $$

The sum up to the $nth$ term is: $$ \begin{equation}\begin{aligned} S_n=\frac{n}{2}[2a+(n-1)d]\\ \end{aligned}\end{equation} $$

Deriving the formula for the sum of the first $n$ terms in an AP

Consider that the sum up to the $nth$ term is: $$ \begin{equation}\begin{aligned} S_n&=u_1+u_2+...+u_{n-1}+u_n\\ &=[a]+[a+d]+...+[a+(n-2)d]+[a+(n-1)d]\\ \end{aligned}\end{equation} $$

Pressure

Sat, 22 Nov 2025 10:40:04 -0500

Pressure ($P$) is the force ($F$) per unit area ($A$): $$ \begin{equation}\begin{aligned} P=\frac{F}{A}\\ \end{aligned}\end{equation} $$

The SI unit is: $$ \begin{equation}\begin{aligned} P&=\frac{F}{A}\\ &\rightarrow \frac{N}{m^2}\\ &=Nm^{-2}\\ \end{aligned}\end{equation} $$

Example: Find the pressure exerted by a $5kg$ block placed on a surface. The area of the block in contact with the surface is $2m^2$.

Solution: $$ \begin{equation}\begin{aligned} P&=\frac{F}{A}\\ &=\frac{5kg\times 9.81 ms^{-2}}{2m^2}\\ &=24.5Nm^{-2}\\ \end{aligned}\end{equation} $$

Fluid pressure

Given a fluid of density $\rho$ and an object submerged at a depth of $h$, the pressure exerted by the fluid on the object is: $$ \begin{equation}\begin{aligned} P=\rho gh\\ \end{aligned}\end{equation} $$

Density

Sat, 22 Nov 2025 10:19:23 -0500

Density ($\rho$) is the mass per unit volume:

$$ \begin{equation}\begin{aligned} \rho&=\frac{mass}{volume}\\ &=\frac{m}{V}\\ \end{aligned}\end{equation} $$

Thus the SI unit is:

$$ \begin{equation}\begin{aligned} \rho&=\frac{m}{V}\\ &\rightarrow \frac{kg}{m^3}\\ &=kgm^{-3}\\ \end{aligned}\end{equation} $$

Example: Find the density of a material whose volume is $4m^3$ and mass is $7kg$.

Solution: $$ \begin{equation}\begin{aligned} \rho &= \frac{m}{V}\\ &=\frac{7kg}{4m^3}\\ &=1.75kgm^{-3}\\ \end{aligned}\end{equation} $$

Relative density

This is the ratio of the density of a substance relative to the density of a standard, usually water: $$ \begin{equation}\begin{aligned} \rho_{rel}&=\frac{\rho_{substance}}{\rho_{standard}}\\ \end{aligned}\end{equation} $$

Moments

Sat, 22 Nov 2025 08:27:53 -0500

The moment is the turning effect of a force. It is the product of the force ($F$) and the perpendicular distance between the pivot and the line of action of the force ($d$):

$$ \begin{equation}\begin{aligned} \text{moment} =F\times d\\ \end{aligned}\end{equation} $$

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Image Credits: Physics - I Can

Business and Funding

Mon, 17 Nov 2025 19:27:54 -0500

It is a fatal flaw of many technical persons within the animation and game industries to focus solely on their craft instead of nurturing the business aspects of the company. This is the advantage of working for a larger company where there is dedicated staff to handle sales and marketing.

The benefits of a smaller team, be in the production of an indie game or an animation passion will always be high velocity. Information exchange and decision-making are often slow in larger organizations so a small team can avoid the “middle men” and make the important decisions quickly.

Drag Force

Sat, 15 Nov 2025 09:17:21 -0500

The drag force ($F_d$) on an object in a fluid is given by: $$ \begin{equation}\begin{aligned} F_d=\frac12 \rho v^2 C_d A\\ \end{aligned}\end{equation} $$

Where $\rho$ is the density of the fluid, $v^2$ is the flow velocity relative to the object, $A$ is the reference area and $C_d$ is the drag coefficient.

A simpler format for this is: $$ \begin{equation}\begin{aligned} F_d=kv^2\\ \end{aligned}\end{equation} $$

Where $k$ is a placeholder for the other factors.

Energy and Work

Sat, 15 Nov 2025 07:48:13 -0500

Energy is the ability to do work. The SI unit for energy is the Joule ($J$).

Types of energy

There are many types of energy:

Light (electromagnetic) energy
Sound energy
Thermal (heat) energy
Mechanical energy (potential and kinetic energy)

Kinetic energy

This is the energy a body possesses by virtue of its motion. The kinetic energy of a body with mass $m$ and velocity $v$ is given as: $$ \begin{equation}\begin{aligned} KE=\frac12 mv^2\\ \end{aligned}\end{equation} $$

Connected Particles

Sat, 15 Nov 2025 07:47:52 -0500

Points of Intersection

Fri, 14 Nov 2025 09:38:35 +0000

In order to find the points of intersection of two curves/lines, it is necessary to solve the equations of the curves/lines simultaneously.

The discriminant

Whenever we use the equations of two curves/lines to generate a quadratic equation, the discriminant of this quadratic equation tells us the nature of the intersection:

$b^2-4ac=0$ means that the two graphs intersect at exactly one point
$b^2-4ac>0$ means that the two graphs intersect at more than one points
$b^2-4ac<0$ means that the two graphs do not intersect

Many times we do have sufficient information to narrow down the solution to get the exact points but we can get a range of values for which the discriminant has a certain value.

Normal Distribution

Thu, 13 Nov 2025 06:12:20 -0500

A normal distribution is a distribution whereby the mean, mode and median are all the same. We represent a normal distribution with mean $\mu$ and standard deviation $\sigma$ as: $$ \begin{equation}\begin{aligned} X\sim N(\mu,\sigma^2)\\ \end{aligned}\end{equation} $$

The graph is symmetric about the mean and the total area under the graph is $1$.

For example, if the masses of cows is normally distributed, with a mean of $55kg$, and a standard deviation of $3kg$, the distribution of the masses is represented as: $$ \begin{equation}\begin{aligned} X\sim N(55kg,9kg^2)\\ \end{aligned}\end{equation} $$

Friction

Sat, 08 Nov 2025 09:58:51 -0500

Friction is a resistive force. It opposes the motion of objects. There are two kinds of friction:

Static friction - the friction that resists any force serving to move any object from rest
Kinetic friction - the friction that causes any object already in motion to slow down

The maximum force of friction is dependent on the force pressing the two surfaces together and a coefficient of friction, unique to the pair of surfaces:

Colour Theory

Tue, 04 Nov 2025 18:01:33 -0500

Visual Design

Tue, 04 Nov 2025 18:00:50 -0500

Principles for creating a visual design

Designing Interactions for Games and Animations

Tue, 04 Nov 2025 18:00:27 -0500

Interactive Design

Tue, 04 Nov 2025 17:57:41 -0500

Interactive design (IxD) is a field of study that focuses on creating products and services that facilitate meaningful communication between people and technology. It is very user-focused (a.k.a. user-centric). It addresses both the physical and emotional aspects of the dialogue between person and machine.

Interactive design might be a misnomer as it deals with the design of interactions between user and product/service. The term could be mistakenly interpreted as a design which involves interaction. The term interaction design is more fitting and is actually used as a synonym.

Game Genres

Tue, 04 Nov 2025 17:55:41 -0500

There are many genres of games. The primary way in which we may classify games is by the game mechanics they involve and the various genres corresponding to the dominant mechanics observed in each game.

Arcade

Action

Adventure

Puzzle

Role-playing game (RPG)

Strategy

Simulation

Board game

Sports

Relative Density Lab

Tue, 04 Nov 2025 09:26:32 -0500

Theory

Density($\rho$) is the mass ($m$) per unit volume ($V$) of a substance:

$$ \begin{equation}\begin{aligned} \rho=\frac{m}{V}\\ \end{aligned}\end{equation} $$

The relative density is the ratio of the density of the substance to the density of a standard (usually water):

$$ \begin{equation}\begin{aligned} \rho_{rel}=\frac{\rho_{substance}}{\rho_{water}}\\ \end{aligned}\end{equation} $$

The relative density of an irregular solid can thus be determined by finding the density of the solid and dividing it by the density of water. The relative density can also be found by taking the ratio of the masses of equal volumes of the solid and the water:

Relative Density

Tue, 04 Nov 2025 09:26:25 -0500

Density ($\rho$) is the mass per unit volume of a substance: $$ \begin{equation}\begin{aligned} density &= \frac{mass}{volume}\\ \rho &= \frac{m}{V}\\ \end{aligned}\end{equation} $$

The SI unit for density is thus the kilogram per cubic metre: $$ \begin{equation}\begin{aligned} \rho &= \frac{m}{V}\\ &\rightarrow \frac{kg}{m^3}\\ &= kgm^{-3}\\ \end{aligned}\end{equation} $$

Defining relative density

The relative density of the substance is the ratio of the density of the substance to the density of a standard (normally we use water): $$ \begin{equation}\begin{aligned} \rho_{rel} &= \frac{\rho_{substance}}{\rho_{standard}}\\ &= \frac{\rho_{substance}}{\rho_{water}}\\ \end{aligned}\end{equation} $$

Center of Gravity Lab

Mon, 03 Nov 2025 17:29:21 +0000

This lab experiment is based on the fact that when an object is allowed to pivot about a point, the force of gravity will be exerted through the center of gravity of the object so as to rotate the object such that the center of gravity will always be vertically aligned within the pivot. Only when this alignment is complete does the moment due to gravity about the pivot become zero ($0$).

Newton's Laws of Motion

Mon, 03 Nov 2025 06:08:09 -0500

There are three ($3$) laws of motion.

First law

An object in uniform motion, or at rest, will remain in its state of uniform motion, or rest, given that no external unbalanced forces are acting.

Second law

The rate of change of momentum of a body is directly proportional to the force applied and takes place in the direction of the applied force.

Given that the object has initial velocity $u$ and final velocity $v$, the initial momentum and final momentum will be $mu$ and $mv$ respectively. Thus: $$ \begin{equation}\begin{aligned} F_{net}&\propto \frac{mv-mu}{t}\\ F_{net}&=k (\frac{mv-mu}{t})\\ F_{net}&=\frac{mv-mu}{t}\\ F_{net}&=\frac{m(v-u)}{t}\\ F_{net}&=ma\\ \end{aligned}\end{equation} $$

Projectile Motion

Sat, 01 Nov 2025 10:19:19 -0400

Projectile motion is the motion of an object which is being influenced by gravity after being launched. The values which do not change for a projectile are:

$u_x=u\cos{\theta}$
$u_y=u\sin{\theta}$
$a_x=0$ (no horizontal forces)
$a_y=-g$ (the force of gravity acts vertically downwards, downwards being negative)

Applying the horizontal direction to the equation, $v=u+at$: $$ \begin{equation}\begin{aligned} v&=u+at\\ v_x&=u_x+a_xt\\ v_x&=u\cos{\theta}+(0)t\\ v_x&=u\cos{\theta}\\ v_x&=u_x\\ \end{aligned}\end{equation} $$

Applying the vertical direction to the equation, $v=u+at$: $$ \begin{equation}\begin{aligned} v&=u+at\\ v_y&=u_y+a_yt\\ v_y&=u\sin{\theta}+(-g)t\\ v_y&=u\sin{\theta}-gt\\ \end{aligned}\end{equation} $$

Linear Momentum

Sat, 01 Nov 2025 08:49:22 -0400

Linear momentum is the product of the mass and velocity of an object:

$$ \begin{equation}\begin{aligned} momentum &= mass \times velocity\\ p &= m \times v\\ \end{aligned}\end{equation} $$

The SI unit for linear momentum is: $$ \begin{equation}\begin{aligned} p &= m \times v\\ &\rightarrow kg\times ms^{-1}\\ &=kgms^{-1}\\ \end{aligned}\end{equation} $$

Example

Find the momentum of a car of mass $1000kg$ moving at a velocity of $4 ms^{-1}$ north. $$ \begin{equation}\begin{aligned} p &= m \times v\\ &= 1000kg \times 4ms^{-1}\\ &= 4000kgms^{-1}\\ \end{aligned}\end{equation} $$

Linked List

Tue, 28 Oct 2025 09:33:04 -0400

In C, we have to implement the Abstract Data Types (ADTs) ourselves. Implementations of these ADTs would be very limited if we had to base the underlying memory off of arrays in C. This is because C arrays, as we know, are fixed length.

The solution to this issue is to use dynamic memory allocation in order to request chunks of memory during runtime as needed. We ask the computer for these chunks (called nodes) and connect/link them using pointers. This is the idea of a linked list.

Abstract Data Types

Tue, 28 Oct 2025 09:32:51 -0400

We know that C has many primitive data types. These include integers, characters, floats, doubles, arrays, etc. Primitive data types are built-in data types provided by the language. They are used to store and manipulate data in a program and are modelled that way because of the physical constraints imposed by the machine implementing them.

They are limited in that they are more concerned with the device used to run the program than the information that the programmer desires to represent in the program. Imagine if we had primitive data types like humans and pets instead of numbers and characters. Instead of a program assuming that data should be modelled in terms of numbers and characters, it would require that everything be expressed in terms of humans and pets.

The Equation of a Circle

Tue, 28 Oct 2025 05:40:46 -0400

We have seen that the gradient and the y-intercept of a straight line are what make it special. In order to represent circles, we need to acknowledge that the following make one circle different from another:

the center (two circles can have the same size but a different offset)
the radius (concentric circles have the same center but different radius)

The standard form

Given that a circle has a center $(a,b)$ and radius $r$ units, the standard form of the equation of the circle is: $$ \begin{equation}\begin{aligned} (x-a)^2+(y-b)^2=r^2\\ \end{aligned}\end{equation} $$

WHERE

Mon, 27 Oct 2025 18:34:57 -0400

We can use the WHERE clause to filter information down to the rows that satisfy a certain condition(s). Run the following:


SELECT name,gender FROM biodata WHERE gender = 'Male';

Copy

Here only the rows that have the gender being exactly the word “Male” will be returned. By using !=, we can ask for the rows that do not match a certain condition, in this case the records with gender “Female”:

Archimedes' Principle

Mon, 27 Oct 2025 13:14:04 -0400

This principle states that the upthrust experienced by a body which is wholly/partially immersed/submerged in a fluid is equal to the weight of the fluid displaced.

Pressure

Mon, 27 Oct 2025 13:14:03 -0400

Pressure ($P$) is the force exerted per unit area:

$$ \begin{equation}\begin{aligned} P&=\frac{F}{A}\\ \end{aligned}\end{equation} $$

The SI unit is the Pascal($Pa$), equivalent to the pressure exerted by applying a one Newton ($1 N$) force over an area of one square-metre ($m^2$):

$$ \begin{equation}\begin{aligned} P&=\frac{F}{A}\\ &\rightarrow \frac{1N}{1 m^2}\\ &=1 Pa\\ \end{aligned}\end{equation} $$

Pressure in a fluid

In a fluid, pressure increases with depth. The pressure is also directly proportional to the density, $\rho$ of the fluid as well as acceleration due to gravity, $g$. For a closed vessel (one not exposed to the atmosphere), the pressure is given by

Components and Resultants

Mon, 27 Oct 2025 07:08:02 -0400

Any vector can be resolved into two ($2$) perpendicular components. This means that we can replace a vector with $2$ other vectors without the system showing any differences.

Forces

Mon, 27 Oct 2025 07:07:49 -0400

A force is an action that can cause a change in shape, size or motion. This means that a force that cause an object to deform and/or cause it to speed up or slow down.

SELECT and FROM

Sun, 26 Oct 2025 15:52:10 -0400

The SELECT clause is the most basic of the commands associated with data manipulation. We need some data first so we select the database:


USE mydatabase;

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Then we create the table:

Introduction to SQL

Sun, 26 Oct 2025 15:32:11 -0400

SQL is the standard for managing structured data in industry. There is a debate as to whether SQL or NoSQL databases are better but it is wise to be able to work with both. SQL serves as:

a Data Definition Language (DDL) - used to define and manage the structure of database objects
a Data Manipulation Language (DML) - used to manage the data living within database objects

Creating a database

We can have multiple databases in SQL. You can think about each database as corresponding to a different app. For example, we can have $5$ databases if we are working with $5$ separate web apps. The value in this is that we can isolate the information to be managed by an app to the app’s own database.

The Constant Acceleration Equations of Motion

Sat, 25 Oct 2025 06:52:05 -0400

The constant acceleration equations of motion are:

$v=u+at$ (no $s$)
$s=(\frac{u+v}{2})t$ (no $a$)
$s=ut+\frac{1}{2}at^2$ (no $v$)
$s=vt-\frac{1}{2}at^2$ (no $u$)
$v^2=u^2+2as$ (no $t$)

Where $s$ is displacement, $u$ is initial velocity, $v$ is final velocity, $a$ is acceleration and $t$ is time. Time is the only scalar thus we apply the sign convention to the other physical quantities.

Deriving the equations of motion

Starting with the defining equation for acceleration (the rate of change of velocity with respect to time): $$ \begin{equation}\begin{aligned} a=\frac{v-u}{t}\\ \end{aligned}\end{equation} $$

Graphs Depicting Motion

Sat, 25 Oct 2025 06:50:01 -0400

Displacement-time graphs

Velocity-time graphs

Measuring Motion

Sat, 25 Oct 2025 06:49:47 -0400

Distance vs. Displacement

Displacement is the distance traveled in a particular direction. It has direction.

Speed vs. Velocity

Acceleration

This is the rate of change of velocity with respect to time: $$ \begin{equation}\begin{aligned} a=\frac{v-u}{t}\\ \end{aligned}\end{equation} $$

Research Questions

You will be competent enough to answer the following:

What is the difference between distance and displacement?
What is the difference between speed and velocity?
What is the significance of the gradient of a displacement-time graph?
What is the significance of the gradient of a velocity-time graph?
What is the significance of the area under a velocity-time graph?
What are the constant acceleration equations of motion?

The Equation of a Straight Line

Sat, 25 Oct 2025 06:02:11 -0400

The form $y=mx+c$ is the known as the slope-intercept form of the equation of a straight line. This is because we can clearly read the gradient/slope ($m$) and the $y$ coordinate of the y-intercept ($c$) from this form.

The general form of the equation of a straight line is $ax+by+c=0$. It is not as easy to tell the gradient and y-intercept from this form as it requires some transposition to be done.

Transformations of Functions

Tue, 21 Oct 2025 17:23:43 -0400

Translation along the x axis

Given the function $$ \begin{equation}\begin{aligned} f(x)\\ \end{aligned}\end{equation} $$

A translation of this function along the $x$ axis can be represented by $$ \begin{equation}\begin{aligned} f(x+a)\\ \end{aligned}\end{equation} $$

Here the function’s graph is left-shifted by $a$ units. When we have the form: $$ \begin{equation}\begin{aligned} f(x-a)\\ \end{aligned}\end{equation} $$

This represents a right-shift of the graph of the function by $a$ units.

Hold a focus!

Q1: The function $g(x)=\sin(x+3)$ is translation of the function $f(x)=\sin x$ along the $x$ axis in the positive (right) direction by $3$ units.

Representing Data Using Diagrams

Fri, 10 Oct 2025 18:37:35 -0400

Data can be discrete, having distinct separate values with no possibility of in-between values e.g. eye colour and favourite movie or continuous, having intermediate values e.g. heights and weights.

Discrete data

Discrete data can be quantitative (having countable, numerical values) e.g. number of students writing math or categorical data (having distinct categories) e.g. favourite colour. Categorical data itself can be:

Nominal - having categories with no order or ranking e.g. eye colour and favourite snack
Ordinal - having categories that can be ordered or ranked e.g. T-shirt sizes (S, M, L, XL) and final grade for a course (A, B, etc.)

Continuous data

Continuous data is also known as scale data because the data is often retrieve from the scales (the continuous, graduated sections) of measuring instruments. Continuous data can be classified as:

Descriptive Statistics

Thu, 09 Oct 2025 19:53:54 -0400

When we have a dataset, we often will want to describe the dataset to others without having to show them all of the individual values which make up the dataset. This is especially true for very large datasets.

Measures of location/central tendency

These values tell us where the data is centered around/located at. They include:

Mean ($\bar{x}$) - the average of all of the data points. It is affected by the outliers (extreme values)
Median ($Q2$) - the middle value. It is not affected by outliers
Mode - the most frequent value

Measures of spread

These values tell us how far the data is spread out. They are important because the measures of location are often insufficient in describing how far apart the data points are. The measures of spread are:

Composition of Functions

Tue, 07 Oct 2025 13:50:22 -0400

Sometimes we want to take the output of one function and use it as the input of another function. This is the idea of composing functions - we chain them together. Consider the notation: $$ \begin{equation}\begin{aligned} f\circ g(x)\\ \end{aligned}\end{equation} $$

This means that we substitute the function on the right, $g(x)$ into the function on the left, $f(x)$. That is, wherever we see $x$ in $f(x)$, we place $g(x)$: $$ \begin{equation}\begin{aligned} f\circ g(x)=f[g(x)]\\ \end{aligned}\end{equation} $$

Inverse of a Function

Tue, 07 Oct 2025 13:50:02 -0400

The inverse of a function does the opposite of the original function. If the function takes an input $a$ and produces an output $b$, the inverse function will take $b$ and produces $a$: $$ \begin{equation}\begin{aligned} f(a)&=b\\ f^{-1}(b)&=a\\ \end{aligned}\end{equation} $$

Only bijective functions (those which are both injective and surjective) have inverses.

The inverse of the inverse is the original function

Consider the functions $f(x)$ and $$ \begin{equation}\begin{aligned} g(x)=f^{-1}(x)\\ \end{aligned}\end{equation} $$

Types of Functions

Tue, 07 Oct 2025 13:49:27 -0400

There are three ($3$) types of functions that we study at this level:

Injective functions
Surjective functions
Bijective functions

Injective (one-to-one) functions

For a function to be injective, every $x$ value must have exactly one ($1$) $y$ value. In other words, every output has a unique input. Injective functions can be referred to as injections.

The algebraic method of determining injectivity

Given a function $f(x)$, we let $$ \begin{equation}\begin{aligned} f(a)=f(b)\\ \end{aligned}\end{equation} $$ If we can prove exactly that $$ \begin{equation}\begin{aligned} a=b\\ \end{aligned}\end{equation} $$ Then the function $f(x)$ is injective. Note that a variation such as $a=\pm b$ will disqualify the function from being injective. We must be able to show exactly that $a=b$.

Scalars and Vectors

Tue, 07 Oct 2025 07:12:42 -0400

A scalar is a physical quantity that has a magnitude. A vector quantity has both magnitude and direction.

Examples

Some scalars are:

distance
speed
mass

Some vectors are:

displacement
velocity
acceleration
force

Classifications of vectors

Vectors can be described in terms of their direction:

Horizontal
Vertical
Oblique

Vectors can also be classified relative to each other:

Parallel
Anti-parallel
Perpendicular

Research Questions

What is a scalar quantity?
What are some examples of scalar quantities?
What is a vector quantity?
What are some examples of vector quantities?
What are horizontal, vertical and oblique vectors?
What does it mean for vectors to be parallel, perpendicular or anti-parallel?
What does it mean to resolve a vector?
What is the role of resolving vectors when combining multiple vectors into a single resultant vector?
What is a resultant vector?
Is the adjacent component of a vector always $R\cos{\theta}$ if the vector has a magnitude of $R$ and angle $\theta$?

Functions

Mon, 06 Oct 2025 07:43:46 -0400

A relation is a relationship between two sets. Relations can be:

one-to-one e.g. each student in a class receiving one fruit
one-to-many e.g. one drummer playing for many bands (he’s free this Saturday btw)
many-to-one e.g. many persons following an artist (they all claim Kes is their husband)
many-to-many e.g. citizens reading many newspapers to find a consensus on what is true

The set of all inputs (x values) is referred to as the domain. The set of all outputs (y values) is called the co-domain.

Errors and Uncertainties

Sun, 28 Sep 2025 09:00:24 -0400

Errors are an inherent part of the scientific process. Every measurement has an associated error, no matter how small. Because the measurement of physical quantities are central to science, scientists need to care about errors.

Types of errors

There are three ($3$) types of errors:

Systematic errors - consistent errors which occur due to the system being used to conduct the experiment. This system consists of the environment (e.g. temperature not being intentionally controlled), observation (e.g. parallax errors and flawed apparatus setup) and instruments (e.g. a metre rule can only distinguish as small as a millimeter)
Random errors - happen in an unpredictable manner due to factors outside of the scope of the scientific experiment e.g. wind, temperature variations, voltage fluctuations
Gross errors - these happen due to mistakes and oversights on the part of the experimenter (the person conducting the scientific experiment) e.g. writing down the wrong measurements or misreading a scale

Propagation of errors

When we add or subtract two values, we need to add their absolute errors.

Homogeneity of Equations

Sun, 28 Sep 2025 08:59:59 -0400

Using any unit

We do not need to use the SI units for the physical quantities involved in an equation in order to show that the equation is homogeneous. Consider the case of speed: $$ \begin{equation}\begin{aligned} speed=\frac{distance}{time}\\ \end{aligned}\end{equation} $$

We can use $m/s$, $m$ and $s$ respectively for the units of speed, distance and time: $$ \begin{equation}\begin{aligned} m/s&=\frac{m}{s}\\ m/s&=m/s\\ \end{aligned}\end{equation} $$

We can also use $km/h$, $km$ and $h$ respectively for the units of speed, distance and time: $$ \begin{equation}\begin{aligned} km/h&=\frac{km}{h}\\ km/h&=km/h\\ \end{aligned}\end{equation} $$

SI Units

Sun, 28 Sep 2025 08:59:46 -0400

The SI units are the standard units that we use to measure both fundamental and derived quantities.

Multiples and submultiples

Multiples help us to represent large numbers without having to write many digits.

**Table 1** *Table showing some common multiples*
Multiple prefix	Symbol	Value	Value expressed as a power of 10
Kilo-	k	1,000	$10^3$
Mega-	M	1,000,000	$10^6$
Giga-	G	1,000,000,000	$10^9$
Tera-	T	1,000,000,000,000	$10^{12}$

Notice that the prefixes are simply placeholders for positive (+ve) powers of 10.

Physical Quantities

Sun, 28 Sep 2025 08:59:37 -0400

These are the properties of solids, liquids and gases that can be measured/quantified. Examples include the volume of a gas, temperature of a cup of tea, height of a building, etc.

Fundamental quantities

These are the physical quantities from which all other physical quantities are derived. According to the International System of Units (SI), there are seven (7) fundamental quantities:

Quantity	Symbol	Unit	Abbreviation for unit
Mass	$m$	kilogram	$kg$
Length	$l$	metre	$m$
Time	$t$	second	$s$
Temperature	$T$	Kelvin	$K$
Amount of substance	$n$	mole	$mol$
Current	$I$	ampere	$A$
Luminous intensity	$I_v$	candela	$cd$

Derived quantities

These are combinations of the fundamental quantities. The following are examples of derived quantities. Note the fundamental quantities which are involved in each. $$ \begin{equation}\begin{aligned} area=length\times width\\ \end{aligned}\end{equation} $$ Width is a length measurement and is essentially Length disguised under another word. This would mean that height, breadth, distance, displacement, perimeter and circumference are also length measurements (they fall under the fundamental quantity Length). $$ \begin{equation}\begin{aligned} volume&=length\times width\times height\\ OR&\\ volume&=area\times height\\ \end{aligned}\end{equation} $$ Notice that area is a derived quantity. Thus volume can be seen as the product of three fundamental quantities (length, width and height) or as the product of a derived quantity (area) and a fundamental quantity (height).

Conditional Probability

Sun, 28 Sep 2025 08:56:08 -0400

When working with probabilities previously, we would have assumed that we are asked to state the probability of an event given that we are working with the entire universal set, $U$. Thus, for an event $A$, the probability is: $$ \begin{equation}\begin{aligned} P(A)=\frac{n(A)}{n(U)}\\ \end{aligned}\end{equation} $$

We can think of this as the conditional probability of $A$ given $U$: $$ \begin{equation}\begin{aligned} P(A|U)=\frac{n(A)}{n(U)}\\ \end{aligned}\end{equation} $$

What if we are given only the elements of the set $B$? The conditional probability of $A$ given $B$ would thus be: $$ \begin{equation}\begin{aligned} P(A|B)=\frac{n(A\cap B)}{n(B)}\\ \end{aligned}\end{equation} $$

Introduction to Probability

Sun, 28 Sep 2025 08:55:55 -0400

The probability of an event is the ratio of the number of outcomes associated with that event divided by the total number of possible outcomes:

$$ \begin{equation}\begin{aligned} P(A)=\frac{n(A)}{n(U)}\\ \end{aligned}\end{equation} $$

Consider the case of flipping an unbiased coin. There are $2$ possible outcomes:

landing a head or
landing a tail

There is only one outcome associated with getting a tail thus the probability of getting a tail is: $$ \begin{equation}\begin{aligned} P(T)&=\frac{n(T)}{n(U)}\\ &=\frac{1}{2}\\ \end{aligned}\end{equation} $$

Solving Quadratic Inequalities

Sun, 28 Sep 2025 08:55:29 -0400

When solving a quadratic inequality, we need to first determine the roots of the original quadratic equation. This will allow us to determine the x-values relative to which the region of solutions will be stated.

Solving and Sketching Quadratic Curves

Sun, 28 Sep 2025 08:55:00 -0400

In order to sketch quadratic curves, we need to ascertain some critical information about the curve:

the y-intercept, $(0,c)$ obtained from $ax^2+bx+c$
the x-intercepts (if any) obtained from solving $ax^2+bx+c=0$
the turning point $(-h,k)$ obtained from completing the square $a(x+h)^2+k$

Pointers

Tue, 23 Sep 2025 10:20:32 -0400

Pointers are variables used to store the locations of other variables.

The syntax for declaring a pointer is:


pointerType *pointerName;

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Consider the following code:

#include <stdio.h>

int main(void) {
 int age = 12;
 printf("The age is %d\n", age);
 printf("The variable age is located at %p\n", &age);

 int *myPointer;
 myPointer = &age;

 printf("The location stored using the pointer is %p\n", myPointer);
 printf("The value stored at this location is %d\n", *myPointer);

 return 0;
}

pointers.c

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Completing the Squares

Thu, 18 Sep 2025 23:18:34 +0000

A quadratic polynomial is a polynomial whose degree (the highest power of $x$) is $2$. The general form of a quadratic polynomial is:

$$ \begin{equation}\begin{aligned} y=ax^2+bx+c\\ \end{aligned}\end{equation} $$

The coefficient of $x^2$

The coefficient of $x^2$ tells us whether the curve is a maximum curve (a frown) or a minimum curve (a smile). In other words, it tells us the nature of the turning point.

When $a$ is positive we have a minimum curve (positive people like to smile). When $a$ is negative we have a maximum curve (negative people like to frown).

Introduction

Thu, 18 Sep 2025 22:25:01 +0000

The following topics are considered to be necessary before attempting to learn this content for this module of Cambridge AS Pure Mathematics.

Transposition

This is a fancy term which means changing the subject of the formula.

Laws of indices

Any number raised to the power of $1$ is itself: $$ \begin{equation}\begin{aligned} a^1&=a\\ \end{aligned}\end{equation} $$

Any number raised to the power of zero ($0$) is $1$: $$ \begin{equation}\begin{aligned} a^0&=1\\ \end{aligned}\end{equation} $$

Goroutines

Wed, 17 Sep 2025 14:01:39 -0400

A goroutine is a lightweight thread of execution. We can use them to execute instructions concurrently. Go uses the fork-join paradigm for concurrency. By utilizing primitives such as goroutines, channels and select, we can coordinate when the forking and joining happens.

The main() function in Go is executed within the context of a goroutine - the main goroutine. All other goroutines are spawned from it.

Spawning a goroutine

After defining the function, use the go keyword to tell Go to execute the function using the goroutine:

The Aesthetics of Play

Mon, 08 Sep 2025 19:22:34 -0400

Whereas game genres are defined by how we choose to categorize games, the aesthetics of play are the reasons we play games. When we take a mundane task and gamify it, we simply integrate one or more of the aesthetics of play into that activity.

Watch this video:

Click/tap here to load video

Credits: Extra Credits

What Is a Game?

Mon, 08 Sep 2025 19:21:38 -0400

A game is a form of structured play or activity governed by rules, roles, goals and challenges and taken by players for entertainment.

Characteristics of game

Games tend to have:

players - the person(s) participating in the game
rules - the constraints under which the game is executed
choices - the players have some degree of agency in which affecting the outcome of the game
outcomes - there is usually an end state in which we can conclude that the game has ended; outcomes can be losses, wins or ties
goals - the desirable achievements attainable by the players; goals can be achieved in the process of arriving at an outcome or they can be outcomes themselves

Game design vs. Game development

Game design is the process of creating the rules, roles, goals and challenges characteristic of the game. The final product of this process is usually a game design document.

What Is Animation?

Mon, 08 Sep 2025 19:21:26 -0400

Animation is the art of using multiple images to depict motion/create the illusion of movement. Whereas a painting or picture only shows a static image, an animation is a series of successive static images/drawings/models that convey information about movement in the scene.

Our eyes are only able to retain images for about $100$ milliseconds thus when presented with many successive images, the viewer’s brain processes these images to appear as a single moving image.

Errors

Fri, 05 Sep 2025 10:15:40 -0400

As opposed to other languages like Python and JavaScript that use a try-catch approach to error handling, Go encourages us to return a separate value that will indicate that the code did not perform in an ideal manner - an error.

This way of handling errors ensures that dealing with errors are part of the normal execution flow of the code, instead of having a structure that can be completely left out, as is the case of a try-catch.

Iterators

Sat, 30 Aug 2025 10:00:28 -0400

Iterators are functions with a special signature:


func (yield func(V) bool)

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Iterators yield one value at a time, allowing us to range over a queue of values instead of getting all values all at once.

Generics

Sat, 30 Aug 2025 09:00:01 -0400

Generics help us to avoid redundant declarations of functions by allowing us to specify type parameters for the data being passed to the function. Consider the following code:

package main

import "fmt"

func SumInts(m map[string]int64) int64 {
	var s int64
	for _, v := range m {
		s += v
	}
	return s
}

func SumFloats(m map[string]float64) float64 {
	var s float64
	for _, v := range m {
		s += v
	}
	return s
}

func main() {
	ints := map[string]int64{
		"first": 10,
		"second": 12,
	}
	floats := map[string]float64{
		"first": 12.34,
		"second": 15.52,
	}

	fmt.Println("sum of ints:", SumInts(ints))
	fmt.Println("sum of floats:", SumFloats(floats))
}

generics-1.go

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The functions SumInts and SumFloats are used to find the sum of the integers and floats respectively passed via maps into them. This might become even more redundant if we have to handle other numeric data types.

Struct Embedding

Fri, 15 Aug 2025 09:29:58 -0400

Go uses struct and interfaces to help developers achieve composition. We can embed structs within other structs and access the methods and variables of the child struct from the parent struct.

package main

import "fmt"

type bag struct {
	items []string
}

func (b *bag) listItems() {
	list := ""
	for _, item := range b.items {
		list += item + " "
	}
	fmt.Println("items in bag: ", list)
}

func (b *bag) addItem(itemName string) {
	b.items = append(b.items, itemName)
}

type Player struct {
	name string
	age int
	bag
}

func (p *Player) talk() {
	fmt.Printf("Hello my name is %s. I am %d years old.\n", p.name, p.age)
}

func main() {
	bookBag := bag{items: []string{}}
	me := Player{name: "Joash", age: 26, bag: bookBag}
	me.talk()
	me.bag.addItem("shovel")
	me.bag.addItem("pencil")
	me.bag.listItems()
	me.addItem("eraser")
	me.listItems()
}

struct-embedding.go

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The name of the struct bag serves as the field we use to access its methods and data (via me.bag). Please note that the declaration for Player is:

Enums

Fri, 15 Aug 2025 09:06:20 -0400

Enums (enumerated types) are sum types that have a fixed number of possible values, each with a distinct name. Golang enums are not a language specific feature but we can implement them using existing language idioms.

package main

import "fmt"

type PlayerState int

const (
	Idle PlayerState = iota
	Walking
	Running
	Jumping
)

var stateName = map[PlayerState]string{
	Idle: "idle",
	Walking: "Walking",
	Running: "running",
	Jumping: "jumping",
}

// implement fmt.Stringer interface
func (ps PlayerState) String() string {
	return stateName[ps]
}

func transition(ps PlayerState) PlayerState {
	switch ps {
	case Idle:
		return Walking
	case Walking, Running:
		return Jumping
	default:
		panic(fmt.Errorf("unknown state: %s", ps))
	}
}

func main() {
	ns := transition(Idle)
	fmt.Println(ns)

	ns2 := transition(ns)
	fmt.Println(ns2)

	ns3 := transition(ns2)
	fmt.Println(ns3)
}

enums.go

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The Stringer interface

The fmt.Stringer interface dictates how the fmt print commands will format the output when the item implementing the interface is passed as an argument to that print command:

Interfaces

Thu, 14 Aug 2025 07:32:15 -0400

These are named collections of method signatures (function signatures). Once a struct has the same method signatures as an interface, we say that the struct satisfies that interface - it serves as an implementation of the interface. Here is an example of two structs (rect and circle) which both satisfy a geometry interface:

package main

import (
	"fmt"
	"math"
)

type geometry interface {
	area() float64
	perimeter() float64
}

type rect struct {
	length, width float64
}

type circle struct {
	radius float64
}

func (r rect) area() float64 {
	return r.length * r.width
}

func (r rect) perimeter() float64 {
	return 2 * (r.length + r.width)
}

func (c circle) area() float64 {
	return math.Pi * c.radius * c.radius
}

func (c circle) perimeter() float64 {
	return 2 * math.Pi * c.radius
}

func measure(g geometry) {
	fmt.Println(g)
	fmt.Println(g.area())
	fmt.Println(g.perimeter())
}

func detectCircle(g geometry) {
	if c, ok := g.(circle); ok {
		fmt.Println("circle with radius", c.radius)
	}
}

func main() {
	r := rect{length: 3, width: 5}
	c := circle{radius: 4}

	measure(r)
	measure(c)

	detectCircle(r)
	detectCircle(c)
}

interfaces-geometry.go

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The function measure accepts an interface of type geometry which means it can operate on any struct that satisfies the interface - in this case both the rect and circle. We can call the methods in the interface (area() and perimeter())

Methods

Tue, 12 Aug 2025 11:20:59 -0400

In Go, we can attach methods (functions) onto structs to make them behave like objects in other languages.

Objects own data (they have variables) and perform actions (they have functions).

Each method has a receiver type which is the type of the struct:

package main

import "fmt"

type person struct {
	name string
	age int
	xPosition int
	yPosition int
}

func (p *person) describeYourself() {
	fmt.Printf("My name is %s. I am %d years old.\nYou can find me at coordinates (%d, %d).\n", p.name, p.age, p.xPosition, p.yPosition)
}

func (p *person) moveTo(x, y int) {
	p.xPosition = x
	p.yPosition = y
	fmt.Printf("Moving %s to (%d, %d)...\n", p.name, x, y)
}

func main() {
	me := person{name: "James", age: 34}
	me.describeYourself()

	me.moveTo(3, 4)
	me.describeYourself()
}

methods.go

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Pointer receiver type vs. normal receiver type

We can also use the normal receiver type person instead of the pointer receiver type *person:

Structs

Mon, 11 Aug 2025 09:32:02 -0400

These are typed collections of fields. We use structs in order to group related data together as records. Consider a struct with four ($4$) member variables:

package main

import "fmt"

type person struct {
	name string
	age int
	xPosition int
	yPosition int
}

func main() {
	// declaration by member variable order
	p := person{"John", 32, 0, 0}
	fmt.Println("person:", p)

	fmt.Println("name:", p.name)
	fmt.Println("age:", p.age)
	fmt.Println("x position:", p.xPosition)
	fmt.Println("y position:", p.yPosition)

	// declaration with named member variables
	p2 := person{name: "Mary", age: 5, xPosition: 2, yPosition: 9}
	fmt.Println("person 2:", p2)

	fmt.Println("name:", p2.name)
	fmt.Println("age:", p2.age)
	fmt.Println("x position:", p2.xPosition)
	fmt.Println("y position:", p2.yPosition)
}

struct-person.go

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For person p, we list the member variables in the order in which they are declared in the struct - name, age, xPosition, yPosition respectively. For person p2, we use the names of the member variables - these can be listed in any order. The latter form is more commonly used as the former is not very readable unless you know what the original struct declaration looks like and the specific order of the member variables/fields:

Pointers

Sun, 10 Aug 2025 10:24:39 -0400

We can work with variables using their identifiers but we can also work with the underlying memory in which we store those variables. Pointers allow us to do this. A pointer is a variable that stores the memory address of another variable.

Memory locations

We can get the memory location of a variable by using the ampersand & before the name of the variable:

package main

import "fmt"

func main() {
	myName := "John"
	fmt.Println("my name:", myName, ", memory address:", &myName)
}

print-memory-location.go

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Dereferencing a pointer

This is where we get the actual value being stored in the memory address that the pointer is referring to. We use the unary operator * to get the value stored at the location:

Range Over Built-in Types

Sat, 09 Aug 2025 11:59:02 -0400

The range keyword in Golang allows us to iterate over the elements in numerous built-in types. We can range over numbers, slices, etc., with a simple syntax.

Range over slice

We can range over the individual elements in a slice without using the index of each element - here we use the blank identifier _ where the index would be:

package main

import "fmt"

func main() {
	sum := 0
	nums := []int{1, 2, 3, 4, 5, 6}

	for _, num := range nums {
		sum += num
	}

	fmt.Println("sum:", sum)
}

range-over-slice.go

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Slice with index

We can also make use of the index if we so desire:

Recursion

Thu, 17 Jul 2025 14:50:11 -0400

We have seen that functions can call other functions. Recursion means that functions can call themselves. In each consecutive call, the computation done is dependent on the data produced by the previous call.

One good example of recursion is the factorial. Recall that $n!$ (n factorial) is simply the product of all numbers from $1$ to $n$: $$ \begin{equation}\begin{aligned} n!=1\times 2\times 3\times ... \times (n-1) \times n\\ \end{aligned}\end{equation} $$

We can write a function to find the factorial of a number:

package main

import "fmt"

func factorial(n int) int {
	// if the number becomes 1 then stop recursion by returning 1
	if n == 1 {
		return 1
	}
	// return the current number times the factorial of the number minus 1
	return n * factorial(n-1)
}

func main() {
	fmt.Println(factorial(1))
	fmt.Println(factorial(3))
	fmt.Println(factorial(5))
	fmt.Println(factorial(15))
}

factorial.go

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Closures

Sun, 13 Jul 2025 10:15:56 -0400

A closure is a function that stores (“closes over”) an environment (a set of captured variables) and another function that uses that environment. We can create closures using anonymous functions.

Anonymous functions are functions without an identifier (a name). They are useful when we may want to associate a set of steps with arguments and/or return values without having to refer to or call the function more than once.

Here is an example of a closure:

package main

import "fmt"

func intSeq() func() int {
	i := 0
	return func() int {
		fmt.Printf("address of i: %p\n", &i)
		i++
		return i
	}
}

func main() {
	nextInt := intSeq()
	fmt.Println(nextInt())
	fmt.Println(nextInt())
	fmt.Println(nextInt())
	fmt.Println(nextInt())
	fmt.Println(nextInt())

	newInt := intSeq()
	fmt.Println(newInt())
	fmt.Println(newInt())
	fmt.Println(newInt())
	fmt.Println(newInt())
	fmt.Println(newInt())

}

closure.go

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Variadic Functions

Sun, 13 Jul 2025 09:40:26 -0400

These are functions that can accept any number of arguments. We have already seen Println from the fmt package. It can accept many values and string them together to be outputted into the console. Here is a function that accepts any number of integers and returns their product:

package main

import "fmt"

func Product(numbers ...int) int {
	product := 1

	for _, number := range numbers {
		product *= number
	}
	return product
}

func main() {
	a := Product(4, 5, 2)
	b := Product(-1, 2, 5)
	fmt.Println("a:", a)
	fmt.Println("b:", b)
}

variadic-product.go

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Defining the function this way allows us to access the values in the numbers variable as if they were in a slice. In fact, we can pass a slice of integers into the function in the following manner and it will still work:

Functions

Mon, 30 Jun 2025 17:11:15 -0400

Functions basically accept values and return values. They are the basic unit of abstraction in Go.

Abstraction is the concept of hiding what happens in the background in order to simplify one’s view of a system. An abstraction is a simplified view of a system which omits unimportant details.

For example, we do not have to know how the Println function in the fmt package actually works to add characters to the console, in order to use Println. This means that the Println function is an abstraction (a simplified view) of the entire process that sends letters and other characters to the console.

Maps

Mon, 30 Jun 2025 17:11:06 -0400

Maps allow us to map items (keys) onto other items (values). We create a make using the syntax:


make(map[keyType]valueType)

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Here we create a map of strings onto integers, where the key is the name of the person and the value is their age:

package main

import "fmt"

func main() {
	// create map
	ages := make(map[string]int)

	// set values for keys "John" and "Mark"
	ages["John"] = 13
	ages["Mark"] = 41

	fmt.Println("The age map is:", ages)
	fmt.Println("John is", ages["John"], "years old")
	fmt.Println("Mark is", ages["Mark"], "years old")

	// edit value
	ages["Mark"] = 42
	fmt.Println("Mark is now", ages["Mark"], "years old")
}

age-map.go

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Notice how we use the format:

Slices

Tue, 24 Jun 2025 21:33:52 -0400

Slices are the hip alternative to arrays in Go. They can be resized and grow in capacity, without us having to do any memory management, as we append values to them. The zero value of a slice is nil and its length is $0$:

package main

import "fmt"

func main() {
	var groceryList []string
	fmt.Printf("grocery list: %v\n", groceryList)
	fmt.Printf("is nil: %v\n", groceryList == nil)
	fmt.Printf("length: %v", len(groceryList))
}

slice-uninit.go

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A slice can created with default values dependent on the zero value of the datatype used. Creating such a slice is done using the make function:

package main

import "fmt"

func main() {
	shoppingList := make([]string, 5)
	ageSlice := make([]int, 3)
	fmt.Println(shoppingList)
	fmt.Println(ageSlice)
}

make-slice.go

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Arrays

Tue, 24 Jun 2025 21:33:47 -0400

Arrays provide a way for us to store many values of the same type under the same name. These individual values are found within the array via their index.

The format for declaring an array is:


var arrayName [elementCount] dataType

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We can set access the individual elements using the index:

For Loops

Sat, 21 Jun 2025 11:11:37 -0400

We can repeat lines of code by using a for loop in Golang. It is Go’s only looping construct. Other languages have while, do-while constructs, go-to statements, etc. for looping but Go avoids the confusion by giving us a versatile iterative construct to work with.

Single condition

We can use a for loop like a while loop where we have a single condition and change the sentinel value (i) within the loop:

package main

import "fmt"

func main() {
	i := 0
	for i < 5 {
		fmt.Println("i:", i)
		i++
	}
}

for-while.go

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Switch-Case Statements

Sat, 21 Jun 2025 11:11:36 -0400

Switch statements are used as an alternative to if-else statements with many branches in which each branch checks to see if a value or expression matches a target:

package main

import "fmt"

func main() {
	var choice int

	fmt.Println("Please enter a number: ")
	fmt.Scanln(&choice)
	switch choice {
	case 1:
		fmt.Println("You chose option 1")
	case 2, 3:
		fmt.Println("You chose either 2 or 3")
	case 4:
		fmt.Println("You chose option 4")
	default:
		fmt.Println("That is not a valid option")
	}
}

switch.go

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Notice how we can have many values as is listed in case 2, 3. If the value of choice does not match any of the cases, the default will run. In this case, the user is told that the choice is not a valid option.

If-Else Statements

Sat, 21 Jun 2025 10:00:05 -0400

We can have sections run only if a certain condition or conditions is/are satisfied. This can be achieved using if-else statements. Consider the following code:

package main

import "fmt"

func main() {
	age := 19
	if age >= 18 {
		fmt.Printf("You are an adult\n")
	} else {
		fmt.Printf("You are not old enough\n")
	}
}

if-adult.go

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The condition we use here is a check to see if the age is greater than or equal to (coded as >=) the value of $18$. If the age is at least $18$, the program will print “You are an adult” onto the console. If not, it will print “You are not old enough”. Try changing the age to $14$ and re-running the code.

Values and Variables

Fri, 20 Jun 2025 16:48:54 -0400

We have seen how to print a basic set of characters (referred to as a string) to the console. We can work with a host of other values: integers, floats, booleans, etc. We can store these in “containers” in memory, variables. The name of the variable is how we can use the value stored in that container. We use var to declare one or more variables:

package main

import "fmt"

func main() {
	// initialize string variable
	var myName = "Joash"

	// initialize integer variable
	var myAge = 13

	// print variables
	fmt.Println(myName)
	fmt.Println(myAge)
}

using-variables.go

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myName is a variable that will store a string because its initial value to set to “Joash”. myAge is an integer because its initial value is set to a number.

Your First Go Program

Fri, 20 Jun 2025 16:17:20 -0400

We must do the obligatory “Hello World” program. Copy and paste, or preferably type from scratch, the following the program in your favourite text editor:

package main

import "fmt"

func main() {
	fmt.Printf("Hello world!!\n")
}

hello-world.go

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The fmt package contains the Printf() function. This function accepts a set of characters and pushes them into the console.

X-Rays

Tue, 06 May 2025 20:43:16 -0400

X-rays are the result of bombarding a metal surface with high speed electrons. This speed is achieved by subjecting the electrons to a large potential difference. This p.d. causes the electrons to accelerate to a higher speed than usual.

Electromagnetic radiation (Bremsstrahlung radiation) is created, with the wavelength of the rays varying inversely with the acceleration of the particles.

The X-ray tube

This is a device used to produce X-rays. The cathode is heated and electrons are ejected as a result (thermionic emission). By applying a very large potential difference (in the range of $20-100kV$), we cause the electrons to accelerate towards the anode. As these electrons strike the anode, a large deceleration occurs.

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Image Credits: Radiology Cafe

Stopping Potential

Tue, 06 May 2025 19:38:11 -0400

Imagine that we have two parallel plates at the two ends of a vacuum tube. We can shine a light with sufficient energy ($hf\geq\phi$) and cause photoelectrons to travel from one plate onto the next.

This will result in a photoelectric current. We can then apply a potential difference across the two plates such that we oppose the photoelectric current produced.

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Image Credits: Cyberphysics

Theories of Light and the Photoelectric Effect

Tue, 06 May 2025 18:54:48 -0400

Wave theory sufficiently explains the reflection, refraction, diffraction and interference of light. It, however, fails to explain the photoelectric effect.

Intensity of the light

This is the power transmitted to unit cross sectional area of the material containing the electrons. Classical Physics would posit that light with a sufficient intensity (brightness) will be able to dislodge the electrons.

However, it does not matter how intense the light is, if it does not possess the correct frequency, the electrons will never be ejected from the metal. Intensity increases the number of electrons that are ejected (provided that the threshold frequency is exceeded). A greater photoelectric current results from a higher intensity.

Kilometers per Hour to Meters per Second Calculator

Tue, 06 May 2025 08:23:40 -0400

$km/h$ to $m/s$ calculator

Conversion factor: 0.27777777777

A kilometer per hour is the simply a kilometer divided by an hour: $$ \begin{equation}\begin{aligned} 1km/h=\frac{1km}{1h}\\ \end{aligned}\end{equation} $$

We can express $1km$ in meters and $1h$ in seconds: $$ \begin{equation}\begin{aligned} 1km&=1000m\\ 1h&=3600s\\ \end{aligned}\end{equation} $$

Thus we can substitute these values into the original ratio: $$ \begin{equation}\begin{aligned} 1km/h&=\frac{1km}{1h}=\frac{1000m}{3600s}\\ \therefore 1km/h&=0.2\overline{7} m/s\\ \end{aligned}\end{equation} $$

The Photoelectric Effect

Fri, 02 May 2025 18:57:27 +0000

There is evidence that light behaves like a wave - it can undergo reflection, refraction, diffraction and interference. Light, however, is not limited to this wave behaviour. At smaller scales, light behaves like a particle. The photoelectric effect is one phenomenon that helps us to explain this particulate theory. When a photon strikes a metallic surface, it can dislodge an electron:

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Image Credits: Science Info

The Best Things in Life Are Opinionated

Mon, 17 Mar 2025 17:42:17 +0000

With the rapid development of new frameworks and other web technologies, design constraints are more necessary now than ever. There are a host of voices online, posing as authorities in the web space, who are advising new developers to learn the latest tech stacks and tools.

While this may be from a position of good intention, it can lead junior devs to an endless goose chase to test out new tech more than they create useful software.

Electromagnetic Induction

Wed, 05 Mar 2025 17:40:05 +0000

Given that the magnetic flux density $B$ is a measure of the amount of magnetic field that passes through unit area of a surface, the magnetic flux $\phi$ through an area $A$ is: $$ \begin{equation}\begin{aligned} \phi=BA\\ \end{aligned}\end{equation} $$

The angle that the field makes with the surface matters. If an angle of $\theta$ is formed between the normal to the surface and the field then the flux is given by $$ \begin{equation}\begin{aligned} \phi=BA\cos{\theta}\\ \end{aligned}\end{equation} $$

The Hall Effect

Wed, 05 Mar 2025 17:39:26 +0000

Recall that when a conductor is exposed to an electric field, the free electrons in the metal move at drift velocity. If we expose this conductor to a perpendicular external magnetic field, each electron will experience a force: $$ \begin{equation}\begin{aligned} F&=BQv\sin{\theta}\\ F&=Be\nu\\ \end{aligned}\end{equation} $$ since $e$ is the charge on an electron and $\nu$ is the drift velocity of an electron. The angle $\theta=90\degree$ due to the magnetic field being perpendicular.

Electromagnets

Wed, 05 Mar 2025 17:38:48 +0000

Electromagnets make use of the fact that when a current flows through a conductor, a magnetic field is created. The magnetic field is especially strong when we use a solenoid - the shape of this long coil concentrates the magnetic field in the space around the coil.

Effect of using a soft iron core

The soft iron core is used to strengthen the magnetic field created in the solenoid. The soft iron is:

Magnetic Forces

Wed, 05 Mar 2025 17:37:27 +0000

Different magnetic fields can be produced from passing current through a conductor. By changing the shape of the conductor, we can vary the strength of the magnetic field formed.

Force around a long straight wire

When a current is flowing through a straight wire, a magnetic field is formed around the wire:

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Image Credits: HyperPhysics

Magnetic Fields

Wed, 05 Mar 2025 17:36:55 +0000

A lodestone is a naturally occuring piece of magnetic material. It exhibits ferromagnetism. There are actually three (3) types of magnetism:

Ferromagnetism e.g. iron
Paramagnetism e.g. aluminum
Diamagnetism e.g. water

Click/tap here to load video

Credits: Reactions Youtube Channel

Bar magnets, which are typically made of an alloy of iron, show two types of magnetic poles (magnetic north and south). These poles repel or attract each other based on their polarity.

Charging and Discharging Capacitors

Wed, 05 Mar 2025 17:35:07 +0000

A capacitor will behave differently depending on if there is a power source in the same loop. If a power source is present, the capacitor will charge. Otherwise it will discharge and behave like a power source itself.

Charging a capacitor

We usually charge a capacitor through a resistor:

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Capacitors in Series and Parallel

Wed, 05 Mar 2025 17:34:43 +0000

Capacitors can be placed in series and in parallel in order to effectively produce new capacitances. We know how resistance behaves in series and parallel: $$ \begin{equation}\begin{aligned} R_T&=R_1+R_2+R_3\\ \frac{1}{R_T}&=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}\\ \end{aligned}\end{equation} $$ Then the opposite counts for capacitors in series and parallel. For series: $$ \begin{equation}\begin{aligned} \frac{1}{C_T}&=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}\\ \end{aligned}\end{equation} $$

In parallel: $$ \begin{equation}\begin{aligned} C_T&=C_1+C_2+C_3\\ \end{aligned}\end{equation} $$

Deriving the effective capacitance for multiple capacitors placed in series

In series, the same amount of charge is built up across each capacitor, as well as the single capacitor that can be used to replace them: $$ \begin{equation}\begin{aligned} Q_T=Q_1=Q_2=Q_3\\ \end{aligned}\end{equation} $$

Capacitance

Wed, 05 Mar 2025 17:33:08 +0000

The capacitance, $C$ of a capacitor is the charge stored per unit potential difference. It is simply the ratio of the charge stored to the voltage applied the ends of the capacitor: $$ \begin{equation}\begin{aligned} C=\frac{Q}{V}\\ \end{aligned}\end{equation} $$

It is measured in Farads ($F$): $$ \begin{equation}\begin{aligned} \frac{Q}{V}\rightarrow \frac{\text{Coulombs}(C)}{\text{Volts}(V)}=CV^{-1}=F\\ \end{aligned}\end{equation} $$

Because a farad of capacitance is very large for most everyday applications, it is common to see capacitance being stated in microfarads ($\mu F$): $$1\mu F=1\times 10^{-6}F$$

Electric Fields

Wed, 05 Mar 2025 17:31:47 +0000

An electric field is the region around a charged object within which another charged object experiences an attractive or repulsive force.

The direction of an electric field

We define the direction of an electric field at a point as the direction in which a small positive charge will move when placed at that point in the field.

This is why we draw the electric field lines of positively charged objects with arrows leaving (the positive point charge is pushed outwards):

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Positive people give

Electric Potential

Wed, 05 Mar 2025 17:22:45 +0000

The eletric potential at a point is defined as the work done in moving unit charge from infinity to that point: $$ \begin{equation}\begin{aligned} \text{work}&=\text{force}\times \text{distance}\\ W&=F\times r\\ \end{aligned}\end{equation} $$ Electric potential is the work done per unit charge so we divide throughout by $Q$: $$ \begin{equation}\begin{aligned} \color{red}\frac{W}{Q}\color{normal}&=\color{royalblue}\frac{F}{Q}\color{normal}\times r\\ \color{red}V\color{normal}&=\color{royalblue}E\color{normal}\times r\\ V&=\frac{Q}{4\pi\epsilon_0r^2}\times r\\ V&=\frac{Q}{4\pi\epsilon_0r}\\ \end{aligned}\end{equation} $$

Notice that the potential, $V$ does not follow an inverse square law like electric field strength, $E$ does.

Coulomb's Law

Wed, 05 Mar 2025 17:19:57 +0000

Recall Newton’s Law of Gravitation - the force of attraction between two objects is directly proportional to the product of their masses and inversely proportional to the separation distance: $$ \begin{equation}\begin{aligned} F_{gravity}=\frac{Gm_1m_2}{r^2}\\ \end{aligned}\end{equation} $$

Gravity happens by virtue of objects having mass. Electric repulsion happens by virtue of objects having charge, not mass: $$ \begin{equation}\begin{aligned} F_{electric}=\frac{kQ_1Q_2}{r^2}\\ \end{aligned}\end{equation} $$

This inverse square law is known as Coulomb’s Law, with the proportionality constant $k=\frac{1}{4\pi\epsilon_0}$: $$ \begin{equation}\begin{aligned} F=\frac{Q_1Q_2}{4\pi\epsilon_0r^2}\\ \end{aligned}\end{equation} $$ where $\epsilon_0$ is the permittivity of free space, $8.85\times 10^{-12}Fm^{-1}$.

Conductors and Insulators

Wed, 05 Mar 2025 17:19:38 +0000

Recall that there are two ($2$) types of electricity:

Static electricity is associated with the excess/lack of charged particles
Current electricity is associated with the movement of charge

Conductors are materials which allow for the easy flow of electric current. Insulators do not allow this. This does not mean that insulators are undesirable when studying electricity - they are used to produce static electricity.

Electrification (a.k.a. charging) by friction is done by rubbing two unlike materials together. By the triboelectric effect, one material will lose electrons and the other gains them, becoming negatively charged in the process.

Effective Resistance

Wed, 05 Mar 2025 17:18:10 +0000

The effective resistance begs the question: “What single resistor can be used to replace all of these other resistors in my circuit?”. We already know how voltage and current behave in series and parallel circuits so we can easily deduce how the resistance, by Ohm’s Law, will behave.

Effective/equivalent resistance of resistors in series

According to Kirchhoff’s Voltage Law, voltage is additive along a loop (yes, for resistors in series): $$ \begin{equation}\begin{aligned} V_T=V_1+V_2+V_3\\ \end{aligned}\end{equation} $$ Current is also constant due to the Principle of Conservation of Charge: $$ \begin{equation}\begin{aligned} I_T=I_1=I_2=I_3\\ \end{aligned}\end{equation} $$ Dividing each voltage by its corresponding currents (this is allowed because current is the same): $$ \begin{equation}\begin{aligned} \frac{V_T}{I_T}&=\frac{V_1}{I_1}+\frac{V_2}{I_2}+\frac{V_3}{I_3}\\ \end{aligned}\end{equation} $$ Because $\frac{V}{I}=R$: $$ \begin{equation}\begin{aligned} \therefore R_T&=R_1+R_2+R_3\\ \end{aligned}\end{equation} $$

Thermistors

Wed, 05 Mar 2025 17:16:03 +0000

A thermometric property is a property of an object, substance or system that varies with temperature. It can thus be used to measure temperature. A thermistor is a semiconductor whose resistance varies with/is dependent on temperature. The symbol used to represent a thermistor is:

View Original

IEC symbol used to represent a thermistor in circuit diagrams

Ohmic and Non-Ohmic Devices

Wed, 05 Mar 2025 17:08:10 +0000

Not all electrical devices follow Ohm’s Law. These exceptions are referred to as non-ohmic devices. Recall that Ohm’s Law states that current flowing through a device is directly proportional to the voltage across its end, provided that temperature remains constant: $$ \begin{equation}\begin{aligned} V&\propto I\\ V&=IR\\ \end{aligned}\end{equation} $$

This means that if we observe the I-V characteristics (from the graph of current plotted against voltage), we will see for ohmic devices that the gradient will be constant. This constant gradient indicates that resistance remains the same. Gradient will change for non-ohmic devices - the resistance varies with the voltage applied to the device.

The Wheatstone Bridge

Fri, 28 Feb 2025 17:18:34 +0000

This is a device that can be used to find the resistance of a 4th resistor, given the resistance of 3 other resistors. It works by the same principle as the potential divider.

It can be thought of as two potential dividers with the same $\frac{V_1}{V}$ ratio. This ratio is only the same when the galvanometer shows a zero deflection. Consider the diagram:

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Diagram of a Wheatstone bridge

Potential Divider

Fri, 28 Feb 2025 17:18:21 +0000

This device can split a larger potential, $V$ e.g. $9V$ into smaller, more useful potentials e.g. $1.5V$. Consider the two resistors, $R_1$ and $R_2$ in series with $V$ applied across them:

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We know that due to conservation of charge, the same current flows through each of the resistors thus: $$ \begin{equation}\begin{aligned} I=\frac{V_1}{R_1}\\ I=\frac{V_2}{R_2}\\ \end{aligned}\end{equation} $$

Internal Resistance

Fri, 28 Feb 2025 17:17:19 +0000

When we represent a simple circuit, we usually assume that the resistance of the battery is zero or negligible. In real life, of course, this is not the case. A reliable way of thinking about this is that we can represent the battery as a cell (the e.m.f. with no resistance) and a resistor encased in an outer shell:

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The resistance of this imaginary resistor is referred to as internal resistance ($r$).

Ohm's Law Lab

Wed, 26 Feb 2025 19:53:44 -0500

Theory

Ohm’s Law states that the current flowing through a conductor is directly proportional to the voltage across its ends, given that temperature remains constant. It is represented by the equation:

$$ \begin{equation}\begin{aligned} V=IR\\ \end{aligned}\end{equation} $$

This means that resistance is simply the ratio of the voltage applied to the current flowing through the resistor/conductor:

$$R=\frac{V}{I}$$

Thus we can determine the resistance of a device in a circuit by varying the voltage applied to it and measuring the corresponding current.

How to Make Fast Websites

Thu, 13 Feb 2025 07:17:05 -0500

In today’s climate, we have the internet being dominated by WordPress and other CMS’s. It’s high time we addressed some of the bad habits web devs get into when making websites.

Although we do have the infrastructure to handle large websites with high traffic volumes, it is a waste of energy, and thus bad for the environment, to continue increasing the load demand by spinning up more bloated websites.

Here is how we can help the internet become a better place for everyone.

Radioactivity Coin Toss Lab

Sat, 01 Feb 2025 18:35:40 -0500

The following lab can be replicated in person using 100 coins.

Theory

Radioactive decay is a spontaneous process which occurs in certain substances due to their nuclear instability. These substances produce radioactive emissions in the form of alpha particles, beta particles and gamma rays.

The half-life ($t_{\frac12}$) of a radioactive substance is the time taken for its mass, and by extension its activity, to drop to half of its initial value. Provided an initial mass, $m_i$ the mass remaining, $m_f$ after $n$ half-lives would have elapsed is given by: $$ \begin{equation}\begin{aligned} m_f=\frac{m_i}{2^n}\\ \end{aligned}\end{equation} $$

Resistance

Fri, 31 Jan 2025 09:12:32 -0500

Electrical resistance is the tendency of a material to oppose the flow of an electric current. We use the symbol, $R$ to represent resistance. The SI unit is the Ohm ($\Omega$).

Ohm’s Law

This states that the current flowing through a conductor is directly proportional to the voltage across its ends, given that the temperature remains constant. This proportionality can be represented as:

$$V\propto I$$

By introducing the constant of proportionality, $R$, we get: $$V=IR$$ This is the equation commonly used when referring to Ohm’s Law - resistance is simply the ratio of the voltage applied to the current flowing through a material.

Circuits and Components

Fri, 31 Jan 2025 08:54:38 -0500

A circuit consists of four basic types of components:

source to add energy to the circuit e.g. battery
load to use this energy e.g. lamp, heating coil, motor, resistor
conductor to connect the source to the load e.g. wires
control to restrict the connection when desired e.g. switch

A circuit diagram is a simplified graphical representation of an electrical circuit. These diagrams show how components in a circuit are connected relative to each other but not necessarily how the components are positioned in real life. For example, a DC voltage source can be drawn next to a bulb but in real life these components could be in different rooms of a building with confusing bends in the wires connecting the two. We use circuit symbols when constructing circuit diagrams. Below are the circuit symbols listed in the CSEC Physics syllabus.

Electrical Quantities

Wed, 29 Jan 2025 09:16:40 -0500

These are the physical quantities associated with electricity:

Charge, $Q$
Current, $I$
Voltage, $V$
Power, $P$
Energy, $E$

The cause of current flow

In order for a current to be present, electrons or other charge carriers must be moving. This movement is achieved by what is called an electromotive force (emf). An electromotive force is the difference in electric potential which causes charge to move. It is the energy ($E$) supplied per unit charge ($Q$) flowing from the source and is represented by $V$: $$ \begin{equation}\begin{aligned} V=\frac{E}{Q}\\ \end{aligned}\end{equation} $$ This gives rise to the formula: $$ \begin{equation}\begin{aligned} E=QV\\ \end{aligned}\end{equation} $$

Direct and Alternating Current

Wed, 29 Jan 2025 07:55:09 -0500

For direct current, the charge flows in a single direction (the polarity of the power source remains the same). For alternating current, the direction is reversed at regular intervals (the polarity of the power source switches periodically).

Current Electricity

Wed, 29 Jan 2025 07:51:43 -0500

This is the continuous flow of charge around a circuit. Current can be defined as the amount of charge which passes through a point over a given time.

Recall that current is one of the seven(7) fundamental quantities and is measured in amperes(A).

Current is thus given by the formula: $$ \begin{equation}\begin{aligned} current(I)=\frac{charge(Q)}{time(t)}\\ \end{aligned}\end{equation} $$ The ampere is therefore equivalent to 1 coulomb of charge passing a certain point in a circuit in 1 second: $$ \begin{equation}\begin{aligned} 1\ A=\frac{1\ C}{1\ s}=1\ Cs^{-1}\\ \end{aligned}\end{equation} $$ The formula is often rewritten to make charge the subject of the formula. This is particularly useful in electrochemistry to determine the amount of charge required to preferentially discharge a certain mass: $$ \begin{equation}\begin{aligned} Q=It\\ \end{aligned}\end{equation} $$

Kirchhoff's Current and Voltage Laws

Fri, 17 Jan 2025 16:03:34 -0500

Because series circuits involve only one path through current can flow, the same current flows through each component: $$ \begin{equation}\begin{aligned} I_T=I_1=I_2=I_3\\ \end{aligned}\end{equation} $$

Kirchhoff’s Voltage Law states that the sum of voltages (potential differences and electromotive forces) in any loop in a circuit is zero. $$ \begin{equation}\begin{aligned} V_T=V_1+V_2+V_3\\ \end{aligned}\end{equation} $$

In a parallel circuit, the voltage across each branch is the same: $$ \begin{equation}\begin{aligned} V_T=V_1=V_2=V_3\\ \end{aligned}\end{equation} $$

Kirchhoff’s Current Law states that the algebraic sum of currents flowing into a node (any point in a circuit) is equal to the algebraic sum of currents leaving that node. $$ \begin{equation}\begin{aligned} I_T=I_1+I_2+I_3\\ \end{aligned}\end{equation} $$

Newton's Law of Universal Gravitation

Thu, 16 Jan 2025 10:28:22 -0500

This law states that the attractive force between two bodies is directly proportional to the product of the their two masses ($m_1\times m_2$) and inversely proportional to the square of their distance apart ($r^2$).

This law can be written as a proportionality: $$ \begin{equation}\begin{aligned} F\propto \frac{m_1m_2}{r^2}\\ \end{aligned}\end{equation} $$ Introducing a constant of proportionality, $G$, known as the gravitational constant, we get: $$ \begin{equation}\begin{aligned} F_g= \frac{Gm_1m_2}{r^2}\\ \end{aligned}\end{equation} $$

The value of $G$ is $6.67\times 10^{-11} Nm^2kg^{-2}$

Classifying Propositions

Mon, 13 Jan 2025 07:35:12 -0500

We can classify propositions in terms of their truth values:

Tautology
Contradiction
Contingency

Tautology

These are propositions whose truth value is always true. For example, the compound proposition, $(p\land q)\implies q$ is a tautology:

$p$	$q$	$p\land q$	$(p\land q)\implies q$
T	T	T	T
T	F	F	T
F	T	F	T
F	F	F	T

Contradiction

These are propositions whose truth value is always false. An example is $(p\lor q) \land (\neg p\land \neg q)$:

$p$	$q$	$\neg p$	$\neg q$	$p\lor q$	$\neg p\land \neg q$	$(p\lor q) \land (\neg p\land \neg q)$
T	T	F	F	T	F	F
T	F	F	T	T	F	F
F	T	T	F	T	F	F
F	F	T	T	F	T	F

Propositions

Mon, 13 Jan 2025 04:26:40 -0500

A statement is a declaration or a question whose truth value may or may not be evaluated. Some examples are:

Tuesday is the day after Monday
$x+2=5$
What is your name?

Out of these statements, only the first is a proposition. A proposition is a statement whose truth value can be evaluated.

The second statement is not a proposition as we do not know the value of $x$ and thus cannot say whether the statement is true or false. The third is not a proposition because it is a question and thus does not even declare anything we can evaluate the truth value for.

Creating CLI Tools

Sun, 12 Jan 2025 14:02:05 -0500

We can use C in order to create command line interface (CLI) tools. These are tools whose main mode of interaction is characterized by the user inputting commands (usually in the format verb adverb1 adverb2 …).

Passing CLI arguments

The main function can be used without passing any arguments into it but it can also be used in a certain way in order to access the arguments passed into the program via the command line:

Math Functions

Fri, 29 Nov 2024 05:30:56 -0500

There are many math functions available to us via C header files:

sin(angle) for finding the sine of an angle in radians
cos(angle) for finding the cosine of an angle in radians
tan(angle) for finding the tangent of an angle in radians
abs(number) to get the absolute value (modulus) of a number
floor(number) for rounding a number downwards
ceil(number) for rounding a number upwards
pow(base,exponent) for raising a base to the power of exponent

Most of these are available via math.h header file whereas abs() is in the stdlib.h header file.

Applications of Circular Motion

Wed, 27 Nov 2024 15:32:16 +0000

It is important to remember that the centripetal force is always the net force directed towards the center of the circle: $$F_{net}=\frac{mv^2}{r}$$

Horizontal circles

When an object revolves in a circular path around a point because of a force directed towards that point (the center of that circular path) and the circle is horizontal, the tension in the string keeps the object from flying off in any direction.

View Original

Circular Motion

Wed, 27 Nov 2024 10:07:35 +0000

For CSEC Physics and this section of CAPE Physics Unit 1 so far, we have been studying linear motion. You will find that most concepts in linear motion have an equivalent in circular motion - the study of motion along curves.

Angular velocity ($\omega$)

This is known as angular frequency. It is the rate of change of angular displacement($\theta$): $$\omega = \frac{\theta}{t}$$

Recall that the arc length($s$) of a circle when the angle is given in radians is: $$s=\theta r$$

Variadic Functions

Wed, 20 Nov 2024 14:30:11 +0000

These are functions which accept a variable number of arguments. printf and scanf are variadic functions. These functions are most useful if we do not know how many values will be passed to the function at compile time.

We use the stdarg.h header file to access the macros and functions needed to meaningfully interact with variadic functions.

Here is an example of a function used to find the sum of its arguments:

The Ternary Operator

Sat, 16 Nov 2024 16:25:16 -0500

Sometimes we will want to set the value of a variable based on if a condition is fulfilled. In the example below, the value of the variable is_adult is set to 1 if the person is at least 18 otherwise it must be set to 0:

#include <stdio.h>

int main(void) {
 int age;
 printf("Please enter your age: ");
 scanf("%d", &age);
 int is_adult;
 if (age >= 18) {
 is_adult = 1;
 } else {
 is_adult = 0;
 }
 printf("Is adult: %d\n", is_adult);
 return 0;
}

without-ternary.c

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This can be condensed using the ternary operator. The basic format is:

Binary Operations

Thu, 07 Nov 2024 09:44:06 -0500

These are operations involving two operands. Addition, subtraction, multiplication and division are all binary operations. You’re practically an expert at them!

Closure

A number set is closed under an operation if the result of any two elements of the set ALWAYS produces another element in the same number set.

Example: Real numbers under multiplication

Any real number multiplied by another real number will always produce another real number thus we say that the set of real numbers is closed under multiplication.

Multiples

Thu, 07 Nov 2024 07:18:23 -0500

A multiple is a number that can be divided by another number exactly.

Lowest common multiple (LCM)

This is the smallest number that can be divided by a list of numbers. For example, the LCM of 5 and 8 is 40 because it is the smallest number that can be divided by 5 and 8.

How to find the LCM of two or more numbers

Factors

Thu, 07 Nov 2024 07:18:08 -0500

A factor is number that can divide another number without leaving a remainder. For example, the factors of $8$ are $1$,$2$,$4$ and $8$ itself.

Hold a focus!

Q1: Which of the following is a factor of 12?

Newton's Laws of Motion and Linear Momentum

Fri, 01 Nov 2024 20:06:21 -0400

Newton’s three(3) laws of motion are as follows:

1st law (the law of inertia)

A body in motion, or at rest, remains in its state of motion or rest, unless acted upon by an external unbalanced force. Bodies with more mass are more resistant to changes in motion thus mass is a direct measure of a body’s inertia (its ability to resist changes in motion).

The same force that causes a small change in motion for a heavy object (e.g. a boulder) will cause a large change in motion for a lighter object(e.g. a ping pong ball).

Using Structs With File Operations

Mon, 21 Oct 2024 17:05:00 -0400

Structs are great when organizing information in your program. The only issue is that when your program ends, the data you store in those sweet sweet structs also disappears. Because we use files in order to achieve data persistence, we can use file operations to save structs for later use. Pretty neat!

Fwrite

This function accepts $4$ arguments:

A pointer to the data to be written e.g. &total, post_data
The size of the data to be written e.g. sizeof(int), sizeof(Post)
The number of values of the data to be written e.g. 1 integer, 5 posts
The pointer to the file to be written to e.g. file

It returns the number of values that were successfully written to the file

Structs in C

Mon, 21 Oct 2024 16:48:43 -0400

Structs are a way for us to group related data together in C. They can be used to make our code much more readable and relate entities in the code to more familiar objects.

Defining a struct

To define a struct, we give it a name (Person) and member variables (name, age and height):


struct Person {
 char name[100];
 int age;
 float height;
};

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This is now a new custom datatype we can use. In the same way that in declaring a variable we would specify the datatype followed by the name of the variable, we write:

Vim Motions for Writers

Sun, 20 Oct 2024 19:52:46 -0400

I do wonder why more writers are not using Vim as their daily editor. As a piece of software that has existed since the 1990s, Vim has created an arms race for human beings who have deemed that the only correct way of writing text is by doing it at break-neck speeds.

The ability to manipulate text with insane levels of efficiency might have been one of those triumphs of our species that has flown over most heads in the past few decades. Story-telling is central to humanity and thus how we compose those stories and convey them to others is important. Vim is thus important.

File Operations

Fri, 18 Oct 2024 20:44:52 -0400

Hold a focus!

Q1: Why do you think we need to be able to access files in C?

Generating Truth Tables

Fri, 18 Oct 2024 20:35:37 -0400

We can use C’s built-in logical operators for NOT, OR and AND in order to generate truth tables for compound logical statements. An implication is logically equivalent to taking the negation of the first proposition (the hypothesis/antecedent) OR the second (the consequent/conclusion/result):

$$p\implies q\equiv \neg p\lor q$$

Two propositions are logically equivalent when their respective truth values are always the same.

We can thus write functions to return the result of each logical operation:

#include <stdio.h>

// not p
int not(int p) { return !p; }

// p or q
int or (int p, int q) { return p || q; }

// p and q
int and (int p, int q) { return p && q; }

// p implies q
int implies(int p, int q) { return !p || q; }

int main() {
 printf("p\tq\tnot p\tnot q\tp or q\tp and q\tp->q\tp->~q");
 printf(
 "\n----------------------------------------------------------------\n");
 for (int n = 0; n < 4; n++) {
 int p = (n >> 1) & 1;
 int q = n & 1;
 printf("%d\t%d\t", p, q);
 printf("%d\t", not(p));
 printf("%d\t", not(q));
 printf("%d\t", or (p, q));
 printf("%d\t", and(p, q));
 printf("%d\t", implies(p, q));
 printf("%d", implies(p, not(q)));
 printf("\n");
 }
 return 0;
}

truth-tables.c

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Bitwise Operators

Fri, 18 Oct 2024 20:33:42 -0400

There are six (6) bitwise operators in C:

Bitwise NOT/complement (~)
Bitwise AND (&)
Bitwise OR (|)
Bitwise XOR (^)
Left shift («)
Right shift (»)

Bit shifting

We can use the « and » operators to bit shift a number. Left shifting a number by 1 digit is the same as multiplying that number by 2. Right shifting the number by 1 digit is the same as an integer division by 2 (dividing by 2 and rounding the result downwards).

Equation of a Straight Line

Fri, 18 Oct 2024 20:29:07 -0400

Any straight line can be written in the standard form: $$y=mx+c$$

The gradient, $m$ is given by the formula: $$m=\frac{y_2-y_1}{x_2-x_1}$$

The y-intercept, $c$ can be found by substituting the gradient and any of the points (in this case we use $(x_1,y_1)$) into the standard form of the line equation:

$$ \begin{equation}\begin{aligned} y_1&=mx_1+c\\ \therefore c&=y_1-mx_1\\ \end{aligned}\end{equation} $$

The following code snippet shows how we can replicate this in C:

#include <stdio.h>

int main() {
 // storing the points
 double x1 = -2.5, x2 = 0, y1 = 0, y2 = 5;
 printf("Using the points (%g,%g) and (%g,%g)\n", x1, y1, x2, y2);

 // calculating gradient
 double gradient = (y2 - y1) / (x2 - x1);
 printf("The gradient of the line is %g\n", gradient);

 // calculating the y-intercept
 double y_intercept = y1 - gradient * x1;
 printf("The y intercept is %g\n", y_intercept);

 // displaying the final equation of the straight line
 printf("Therefore the equation of the line is:\ny=%gx+%g", gradient,
 y_intercept);

 return 0;
}

finding-the-equation-of-a-line-given-two-points.c

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Converting Between Degrees and Radians

Fri, 18 Oct 2024 20:26:01 -0400

In order to convert degrees to radians, multiply the angle in degrees by $\pi$ and divide by $180\degree$:

$$45\degree = 45\degree \times \frac{\pi}{180\degree} \ =\frac{\pi}{4} $$

Take for example the code:

#include <math.h>
#include <stdio.h>
#define PI acos(-1.0)

void clear_input_buffer() {
 int ch;
 while ((ch = getchar()) != '\n' && ch != EOF)
 ;
}

int main() {

 float angle_in_degrees;
 int correct_inputs = 0;

 do {
 printf("Please enter an angle in degrees to convert to radians:\n");
 correct_inputs = scanf("%f", &angle_in_degrees);
 if (correct_inputs == 0) {
 printf("Invalid input\n");
 }
 clear_input_buffer();
 } while (correct_inputs == 0);

 printf("The angle in radians is %f\n", PI * angle_in_degrees / 180.0);
 return 0;
}

degrees-to-radians.c

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Conversely, we can convert from radians back to degrees by multiplying by $180\degree$ and dividing by $\pi$: $$\frac{\pi}{3}=\frac{\pi}{3}\times \frac{180\degree}{\pi}=60\degree$$

Functions as Modules

Fri, 18 Oct 2024 18:46:14 -0400

In C, we use functions as the basic unit of modular design. Modular design is the practice of designing a system in modules. A module is any entity with an interface and an implementation. The interface provides an abstraction (a simplified view of an entity which omits unimportant details) of the module.

An interface is a contract/intersection between the system and the environment. Credits: Robert Elder

Functions act as modules in C. The definition of the function determines the interface. Take for example the following:

Functions Part 2

Fri, 18 Oct 2024 18:44:38 -0400

We continue by learning about functions with return values and those with both return values and arguments.

Functions with return values but no arguments

Here is a function that is used to get the current time:

#include <stdio.h>
#include <time.h>

char *get_current_time() {
 time_t t;
 time(&t);
 return ctime(&t);
}

int main() {
 printf("The current time is %s\n", get_current_time());
 return 0;
}

current-time.c

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Functions

Fri, 18 Oct 2024 18:38:25 -0400

These are reusable sections of code. They can be built-in or user-defined. Functions allow us to write code that can be modified in one place and change the effect in multiple sections. Functions are also sometimes referred to as routines because of how we use them to group a set of related steps under a single name. A function in C follows the format:


return_type function_name(argument_1,argument_2,...){
 do_something;
 do_something_else;
 return return_value;
}

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Here is an example of a function being used to draw a line:

String Functions

Fri, 18 Oct 2024 18:22:10 -0400

Strings are a very useful data type. The entire internet thrives on the exchange of information as text data in the form of HTML, CSS and JavaScript files. The browser parses this text in order to know what to display on your computer or phone screen or which files to ask the server for. The very code we write is in text. Our code editor needs to be able to manipulate this text in order to display it in the proper syntax highlighting.

Arrays

Fri, 18 Oct 2024 18:13:05 -0400

Arrays are a way for us to store many values of a certain datatype under the same name. Other languages have sets, lists and dictionaries which serve a similar purpose. This saves us the time and energy of having to create unique names for each value we want to store.

The format for defining an array is:


type array_name[number_of_values];

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Indexing of arrays begin at 0. This means that the following gives us 10 numbers (accessed using numbers[0] to numbers[9]):

Break, Continue and Go-To

Wed, 16 Oct 2024 12:28:39 -0400

Sometimes we will want to exit a loop or prematurely end the current iteration of the loop. We use break to break out of the loop and continue to tell the computer to continue the loop from the start of the next iteration.

The break statement

John wants to tell the computer to exit counting in a sequence when the square of the current counter becomes 9. He writes the following code:

#include <stdio.h>

int main(void) {
 int i = 10;
 while (i > 0) {
 printf("i = %d\n", i);
 i--;

 if (i * i == 9) {
 printf("Breaking out of the loop...(i=%d -> i^2=%d)\n", i, i * i);
 break;
 }
 }
 return 0;
}

break-out-of-loop.c

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Logical and Relational Operators

Mon, 14 Oct 2024 09:05:06 -0400

We can use these operators to define the conditions under which conditional and iterative constructs are executed. Logical operators are not(!), and(&&) and or(||) and relational operators are greater than(>), less than(<), greater than or equal to(>=), less than or equal to(<=), equal to(==) and not equal to(!=).

Logical AND example

Martha wants a program to check if her students are between a certain height - students who are too short or too tall cannot be placed on the carnival ride. She comes up with the following code:

Iterative Constructs

Fri, 11 Oct 2024 07:53:08 -0400

It is very useful for us to have the ability to tell the computer to run code for a specific number of times or until a condition is violated.

For loops

This is called a bounded loop. This is because we can predict the number of times the loop will run. There is a sentinel value, usually $i$ or $n$ that is iterated and checked at the beginning of each iteration. If the condition is not fulfilled then the loop no longer runs.

Conditional Constructs

Fri, 11 Oct 2024 07:52:59 -0400

Sometimes we want to run code only if specific conditions are satisfied. Conditional statements allow us to do this.

If statements

With this we can run code if a condition is satisfied. If it is not satisfied then nothing happens. Mr. Jones, a restaurant owner only allows adults into his restaurant. He wants a piece of code that tells the user if they can enter the restaurant based on their age. He comes up with this:

Demonstrating That Projectile Motion Is Parabolic

Thu, 10 Oct 2024 15:40:36 -0400

Recall that the following do not change for projectile motion, given that the angle of projection($\theta$) is relative to the horizontal:

$u_x=u\cos{\theta}$
$u_y=u\sin{\theta}$
$a_x=0$
$a_y=-g$

View Original

Projectile motion can be represented by a parabola of the form: $$y=ax^2+bx+c$$

Projectile Motion

Wed, 09 Oct 2024 11:29:20 -0400

Projectile motion is essentially the motion of an object under the effect of gravity. Consider a projectile thrown at an angle of $\theta$ with an initial velocity of $u$:

View Original

Changing the Flow of the Program

Mon, 07 Oct 2024 07:22:26 -0400

As we have seen so far, the default execution flow (the order in which the code is executed) is sequential. This means that the code runs from top to bottom.

We can change the execution flow of the program by using constructs (control structures). There are two types of constructs:

Conditional constructs
Iterative constructs

Conditional constructs

These are used to execute sections of code when certain conditions are fulfilled. There are 3 conditional constructs in C:

Setting Up Termux for C Development (Android)

Thu, 03 Oct 2024 09:54:55 -0400

This article is for students who do not have access to a laptop. You can still learn C using an android device (android 1, iphone 0).

Installing F-Droid

This is a third party app repository and houses the most recent version of Termux. Download the latest version of the F-Droid apk using this link.

Installing Termux

Open F-Droid and search “Termux”. Download the Termux and Termux Styling apps from the list. You will have to allow F-Droid to install from unknown sources.

Accepting User Input

Tue, 01 Oct 2024 12:35:26 -0400

Notice how we have only been hard-coding values into our program. Often times we will want to have the user input these values. In C, we can use the function scanf() to accept values from the user. There are other functions, some of which we will address later on.

The basic format for using scanf() is:


scanf(format_string,address_1,address_2,...);

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Take for example asking the user for their age:

#include <stdio.h>

int main() {
 int age;
 printf("Please enter your age: ");
 scanf("%d", &age);
 printf("Wow so you are %d years old huh?!\nDas crazyyy!!", age);
 return 0;
}

asking-for-age.c

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Doing Calculations in C

Sat, 28 Sep 2024 17:18:27 -0400

Now that we know how to ask the computer for space to store values, we can do some math! Consider the following code:

#include <stdio.h>

int main(void) {
 // step 1
 float mass = 105.7;
 // step 2
 float height = 2.1;
 // step 3
 float bmi = mass / (height * height);
 // step 4
 printf("The body mass index of someone with a mass of %.2f kilograms and "
 "height of %.2f meters is %.2f\n",
 mass, height, bmi);
 // step 5
 return 0;
}

bmi.c

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Describe what is being done in each step. C is a language hence it is important that we learn to read it.

Variables and Data Types

Wed, 18 Sep 2024 22:15:00 -0400

A variable is an entity whose value can be changed. In C, each variable has a data type. We choose the data type based on what we want the variable to store.

Some common primitive data types in C are:

integer
floating point numbers
character
double floating point numbers

Integer

These are positive and negative whole numbers. An integer can be used to store the age of a person:

Plotting Linear Graphs From Non-Linear Equations

Tue, 10 Sep 2024 08:03:55 -0400

We can take a non-linear equation and plot in the form of the equation of straight line,

$$\color{limegreen}y\color{black}=\color{slateblue}m\color{red}x\color{black}+c$$

We will have to compromise in some situations by not plotting the variables $x$ and $y$.

Quadratic equations

Consider the following equation: $$\color{limegreen}y\color{black}=\color{slateblue}a\color{red}x^2\color{black}+b$$ We will have to plot $y$ on the y-axis and $x^2$ on the x-axis: $$\color{limegreen}y\color{black}=\color{slateblue}a\color{red}x^2\color{black}+b$$ $$\color{limegreen}y\color{black}=\color{slateblue}m\color{red}x\color{black}+c$$

Exponential equations

When we have to make these linear, we take the log of both sides: $$ \begin{equation}\begin{aligned} y&=Ae^{2x}\\ \ln{y}&=\ln{Ae^{2x}}\\ \ln{y}&=\ln{A}+\ln{e^{2x}}\\ \ln{y}&=\ln{A}+2x\ln{e}\\ \color{limegreen}\ln{y}\color{black}&=\color{slateblue}2\color{red}x\color{black}+\ln{A}\\ \end{aligned}\end{equation} $$

Setting Up Visual Studio Code for C Development (Windows)

Mon, 09 Sep 2024 17:23:17 -0400

Here are the steps for getting started with basic C development:

VS Code

Visual Studio Code is the go-to editor for beginner level software engineers. It has a large ecosystem of plugins and themes. Download VS Code by visiting the official website.

Run the installer.

MinGW

This is a Windows distribution containing the GCC compiler. VS Code does not come with built-in support for C compilation so we use MinGW to get access to the compiler. Download the latest MSVCRT runtime zip file from the website.

Physical Quantities

Mon, 09 Sep 2024 09:52:02 -0400

Physical quantities are the properties of a solid, liquid or gas which can be measured. The length of a rod and the temperature of the ocean are examples of physical quantities.

We can classify physical quantities in the following ways:

Fundamental vs. derived quantity
Scalar vs. vector quantity

Fundamental vs. derived quantities

There are seven (7) fundamental quantities:

Quantity	Symbol	SI Unit	Abbreviation for unit
Mass	$m$	kilogram	$kg$
Length	$l$	metre	$m$
Time	$t$	second	$s$
Temperature	$T$	Kelvin	$K$
Amount of substance	$n$	mole	$mol$
Current	$I$	ampere	$A$
Luminous intensity	$I_v$	candela	$cd$

Drift Velocity

Thu, 05 Sep 2024 11:37:08 -0400

Drift velocity is the average velocity of charged particles (e.g. electrons) in a conductor, caused by an external electric field.

The formula associated with this concept is: $$I=ne\nu A$$

Where $I$ is current, $n$ is charge density, $e$ is the elementary charge, $\nu$ is drift velocity and $A$ is the cross-sectional area of the conductor.

Notice that the greater the cross-sectional area of the conductor is, the greater the current allowed to flow.

EMFs and PDs

Thu, 05 Sep 2024 08:08:27 -0400

Electromotive force and potential difference are mentioned when speaking about voltages in a circuit.

Hold a focus!

Q1: Electromotive force is associated with devices that add power to the circuit (a.k.a. active devices).

Resistivity

Wed, 04 Sep 2024 21:36:54 -0400

Resistance ($R$) is the tendency of a material to oppose the flow of an electric current. It is an extensive property meaning that its value is dependent on the amount of substance present.

For example, the longer a piece of copper wire is, the more resistance it will have. If we get a shorter or thinner piece of copper wire then we will have to measure its resistance as well.

Electrical Quantities

Wed, 04 Sep 2024 10:34:43 -0400

Electrical quantities are the physical quantities (the measurable properties of a system or object) related to the study of electricity. Some important electrical quantities are:

current ($I$)
voltage ($V$)
resistance ($R$)
power ($P$)

Charge can be quantized

Elementary charge (a.k.a. quanta) refers to the charge of an electron ($1.6\times 10^{-19}C$). We can thus express the charge on an object in terms of the elementary charge:

$$Q=\pm Ne$$ where $N$ is the number of electrons present.

Forces

Thu, 15 Aug 2024 16:41:41 -0400

A force can be defined as a push or a pull. It is an action which causes a change in shape, size or motion of an object or system. Force is measured in Newtons (N).

Types of forces

Forces are divided into two groups:

Contact forces - these require the objects involved in the interaction to be in physical contact with each other. Examples include:
- friction
- tension
- air resistance
Non-contact forces - these can be applied at a distance, requiring no contact between the object exerting the force and the object experiencing the force. Examples include:
- gravitational force (between any two bodies with mass)
- magnetic force (between magnetic materials)
- electric force (between charged bodies)

Weight

Weight is the force exerted by the Earth (or another planetary body) on the objects within its gravitational field. It can also be thought of as the force exerted by a body on another body which is supporting it – assuming that the bodies are within a gravitational field. Weight can be calculated as the product of the object’s mass and the Earth’s gravitational acceleration ($g$): $$ \begin{equation}\begin{aligned} Weight=&mass\times acceleration\ due\\\ &to\ gravity\\ W=&mg\\ \end{aligned}\end{equation} $$

Combining Vectors

Thu, 15 Aug 2024 16:33:45 -0400

Now that we can split oblique vectors into horizontal and vertical components it is essential that we understand that horizontal vectors are independent of vertical vectors. This statement implies that, for example, an object’s displacement along the x axis cannot give us meaningful information on its displacement along the y axis.

The displacement’s horizontal component is independent of (does not affect/is not affected by) its vertical displacement. Thus if the object is pushed along the x axis its horizontal displacement changes but its vertical displacement does not.

Scalars and Vectors

Thu, 15 Aug 2024 16:16:09 -0400

Physical quantities can be divided into:

Fundamental quantities vs. derived quantities OR
Scalar quantities vs. vector quantities

We have looked at the former pair of categories. Now we shall study the latter.

Scalar quantities

Scalar quantities (or simply scalars) are physical quantities which have magnitude but NO direction. Examples include mass, length, time, distance and speed. When representing a scalar on a diagram, we simply write the measurement next to the corresponding object:

Charging by Conduction

Wed, 14 Aug 2024 13:16:18 -0400

This is when electrons are transferred from one object to another when they come into direct contact with each other. Rubbing one’s feet on a carpet can cause charge to accumulate in the hands if the feet are insulated from the ground

Simulation featuring John Travoltage: John Travoltage

Charging by induction

If electrons are exposed to the external electric field of a charged object then the electric force can attract or repel these electrons
Metals are known for having a ‘sea’ of electrons which can freely move from one atom to the next
When an external electric field is brought close to the surface of the metal, if the field belongs to a negatively charged object then the electrons migrate away from the side of the metal exposed to the electric field (because like charges repel)
The far end thus becomes negatively charged and the close end will be net positive in charge
The electrons on the far end can be conducted away and thus the object will have a net positive charge

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Credits: the Physics Classroom

Charging by polarization

For the atoms which do not have the sea of electrons, the electrons react to the electric field and the individual atoms become polarized (the charge is shifted to one side of the atom)
Similar to induction, the net charge of the object does not change but the charge does buildup on one side of the object
The loss of static electricity (the transfer of charge) from one object to another is called static discharge

What are Electric Fields?

An electric field is the region around a charged particle or body within which any other charged particle or body will experience a force (attractive or repulsive depending on the signs). Field lines are used to visualize the direction of the field. We draw field lines with arrows coming out of positive charges and going into negative charges.

Electrostatics

Wed, 14 Aug 2024 13:11:46 -0400

Electricity is the presence or flow of charged particles. There are two types of electricity:

Static electricity (presence)
Current electricity (flow)

What is electric charge?

Atoms are made up of charged subatomic particles such as electrons (negatively charged) and protons (positively charged). Neutrons have no charge (they are neutral)
Electric charge is the property of a body that causes it to experience an attractive or repulsive force toward another body
Because protons are stuck in the nuclei of the atoms, the net charge of a body is usually dependent on the excess of or lack of electrons (these can be removed from the surface of a material)

Static electricity

This is the buildup of charge on an insulator
An excess of electrons on a surface results in a net negative charge on the object
A lack of electrons on a surface results in a net positive charge on the object
Like charges ($+$ and $+$ OR $-$ and $-$) repel and unlike charges ($+$ and $-$) attract each other

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Credits: ScienceFacts

Image Formation

Fri, 02 Aug 2024 20:30:03 -0400

We define the following terms:

Object distance ($u$) distance between the object and the center of the lens
Image distance ($v$) distance between the focused image and the center of the lens
Focal length ($f$) distance between the focal point and the center of the lens

When images are formed by a lens, they can be:

Real or virtual
Magnified or diminished
Upright or inverted

Descriptions for images

Real image formed by the actual intersection of rays of light. It can be projected onto a screen

Lenses

Fri, 02 Aug 2024 20:20:47 -0400

A lens is a section of transparent material which is used to refract light. There are two types of lenses:

Converging/convex lens - bends light entering it parallel to the principal axis towards the focal point
Diverging/concave lens - bends light entering it parallel to the principal axis away from the focal point

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Credits: Toppr

Total Internal Reflection

Thu, 01 Aug 2024 23:47:49 -0400

Does refraction work for every possible angle of incidence? When light moves from a more optically dense material to a less optically dense material, for angles greater than a certain value, there will be no refracted ray but rather the light will reflect within the first medium.

Total internal reflection is the phenomenon in which light bounces off of the boundary between a more optically dense material and a less optically dense material. The light reflects within the more optically dense material. The angle of incidence at which the refracted ray travels along the boundary separating the two media is called the critical angle. If the angle of incidence is greater than the critical angle then total internal reflection occurs.

Refraction

Thu, 01 Aug 2024 23:37:56 -0400

This is the process whereby a wave changes direction as it moves from one medium to another. The incident ray bends as it crosses the boundary between the two media. Note again that the angles are measured relative to the normal line.

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Credits: KeyStageWiki

Reflection

Thu, 01 Aug 2024 23:31:37 -0400

Light travels in a straight line and all wavelengths of light travel through a vacuum at the same speed ($3\times 10 ^8\ ms^{-1}$). Because light travels in a straight line we have phenomena such as shadows and eclipses and devices such as pinhole cameras

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Credits: TeachEngineering

Wave-Particle Duality

Thu, 01 Aug 2024 19:49:28 -0400

There are many theories on the nature of light. These conflict in some places and bring forth the idea of wave-particle duality. Wave-particle duality is the notion that light behaves like a wave as well as like a particle.

Video:

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Electromagnetic Waves

Mon, 29 Jul 2024 20:08:41 -0400

Light, also known as electromagnetic radiation, is the set of transverse waves which consist of electric and magnetic fields oscillating at right angles to the direction in which the wave is travelling.

Video:

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Wave Phenomena

Mon, 29 Jul 2024 19:49:17 -0400

Waves can participate in four ($4$) phenomena:

Reflection
Refraction
Diffraction
Interference

Reflection

Reflection is the bouncing of waves off of a boundary. Sounds waves produce echoes when they bounce off of certain surfaces. There are two ($2$) types of reflection in the case of light:

Diffuse reflection is when light rays are scattered at different angles from an uneven surface
Specular reflection is when light rays reflect off of the boundary in a uniform manner from a smooth surface

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Image Credits: Shutterstock

Sound

Mon, 29 Jul 2024 19:36:14 -0400

A sound wave is a series of alternating compressions and rarefactions. Sound waves are longitudinal waves. Sound is a vibration propagated as an acoustic wave through a transmission medium such as a gas, liquid or solid.

How are sounds produced?

Vibrating objects make sound by first pressing air molecules together and then letting them thin out. When objects vibrate, they push on the air molecules nearest them, setting them in motion. These molecules in turn push on the others around them. Since the medium is elastic, a series of compressions (air molecules close together/high pressure) and rarefactions (air molecules spread out/low pressure) is produced.

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Credits: Let’s Talk Science

Wave Parameters

Mon, 29 Jul 2024 19:25:36 -0400

A wave can have many properties that may interest us. For example, the frequency of a sound determines how high its pitch is. We can relate certain aspects (such as frequency, wavelength and velocity) of a wave by the following formulae: $$f=\frac{1}{T}$$ $$v=f\lambda$$ $$v=\frac{\lambda}{T}$$

where $$ \begin{equation}\begin{aligned} f&\rightarrow frequency\\ T&\rightarrow period\\ v&\rightarrow velocity\\ \lambda&\rightarrow wavelength\\ \end{aligned}\end{equation} $$

Mission details

Find the frequency of a sound wave which has a period of $0.02\ s$. $$ \begin{equation}\begin{aligned} f=\frac{1}{T}=\frac{1}{0.02\ s}=50\ Hz\\ \end{aligned}\end{equation} $$
Find the velocity of the same wave if its wavelength is $2\ m$. $$ \begin{equation}\begin{aligned} v&=f\times \lambda\\ &=50\color{orange}\ Hz\color{black}\times 2\ m\\ &=100\ m\color{orange}s^{-1}\\ \end{aligned}\end{equation} $$ Alternatively: $$ \begin{equation}\begin{aligned} v=\frac{\lambda}{T}=\frac{2\ m}{0.02\ s}=100\ ms^{-1}\\ \end{aligned}\end{equation} $$
Determine the speed of a wave with wavelength $20\ m$, given that it completes $2$ oscillations in $4\ s$. The period is the time taken to complete $1$ oscillation and we are told it takes $4\ s$ to complete $2$ oscillations thus the period is: $$ \begin{equation}\begin{aligned} T=\frac{4\ s}{2\ oscillations}=2\ s\\ \end{aligned}\end{equation} $$

We do not write ‘oscillations’ as oscillation is dimensionless (e.g. the wheel made 2 oscillations)

Parts of a Wave

Mon, 29 Jul 2024 19:23:04 -0400

Below is a diagram of the various parts of a wave.

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Credits: SECOORA

Wave Motion

Mon, 29 Jul 2024 19:17:52 -0400

A wave is a disturbance which transfers energy from one point to another without the net displacement of matter. If we throw a pebble into the center of a lake it creates a disturbance which travels outwards from the center. The kinetic energy of the stone becomes kinetic energy of the water particles which is carried by the neighboring particles to the corners of the lake (transfer of energy). When the ripple reaches the corners, the particles come back to their rest position (no net displacement).

Radiation

Thu, 25 Jul 2024 23:17:32 -0400

This is the transfer of heat energy via electromagnetic radiation produced by heated surfaces
Heat transfer via the process of radiation does not require a medium (solid, liquid or gas) for transfer - it can happen through a vacuum

Emitters and reflectors of radiation

When electromagnetic radiation strikes a surface, that energy is either absorbed or reflected. Good absorbers of radiation are good emitters of radiation.

The radiation that is not absorbed, is reflected so good absorbers are generally bad reflectors of radiation.

Convection

Thu, 25 Jul 2024 23:16:23 -0400

This form of heat transfer occurs due to differences in temperature causing differences in density
Commonly occurs in fluids (liquids and gases)
By Archimedes Principle, if a material is less dense than the fluid it is suspended in (the material’s relative density less than 1), that material will float in the fluid due to the upthrust on the material being greater than its weight
In convection, one fluid (the hotter portion) floats in another fluid (the cooler portion)

How it works

When water is heated in a beaker, the water closest to the heat source (the water at the bottom of the beaker) is subjected to an increase in temperature
This increase in temperature causes its volume to increase (heating causes expansion) and thus its density is lowered
This heated fluid is thus lighter (less dense) than the rest of the water in the beaker and rises in it
As it cools, its density increases and thus it will sink in the rest of the water

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Convection in a liquid

Convection in gases

Hot air rises due to convection – the hotter air has a lower density compared to the surrounding air
A sea breeze is when the wind blows from the ocean or surrounding body of water to the land due to the sun heating the land faster during the day (the land has a lower SHC than the water)
A land breeze is the breeze which occurs due to the body of water being hotter than the land which is cooler at night

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Land breeze vs. Sea breeze

Credits: Difference Between

Transfer of Thermal Energy

Thu, 25 Jul 2024 23:07:29 -0400

Recall the following:

Archimedes’ Principle: When a body is submerged/immersed in a fluid, that body experiences an upthrust equal to the weight of the displaced fluid.
Heat energy/thermal energy is the energy possessed by objects, substances and systems due to their differences in temperature.
In accordance with the kinetic theory of heat, temperature is a description of the average kinetic energies of the particles within an object, substance or system

Crash Course Video:

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Evaporation vs. Boiling

Wed, 24 Jul 2024 10:29:57 -0400

Methods for Determining Specific Latent Heat

Wed, 24 Jul 2024 10:27:15 -0400

The specific latent heat can be determined in a similar manner to that of the electrical method used to find the specific heat capacity.

For example, in melting a piece of ice to get the SLH of fusion ($l_f$):

Measure the mass $m_i$ of the ice
Measure the initial temperature $T_i$ of the ice
Turn on the heater for certain amount of time $t$, enough for all the ice to melt
Turn off the heater
Measure the final temperature of the melted ice (water)
The heat energy changes are: $$ \begin{equation}\begin{aligned} Q_{heater}=&Q_{heating\ ice\ from\ T_i\ to\ 0\degree C}+Q_{melting\ ice\ at\ 0\degree C\ to\ water\ at\ 0\degree C}&+Q_{heating\ melted\ ice\ at\ 0\degree C\ to\ T_f}\\ \end{aligned}\end{equation} $$
Thus: $$ \begin{equation}\begin{aligned} VIt=m_ic_i(0\degree C-T_i)+m_i\color{green}l_{f(ice)}\color{black}+m_ic_w(T_f-0\degree C)\\ \end{aligned}\end{equation} $$

Video for method of mixtures alternative:

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Methods for Determining Specific Heat Capacity

Wed, 24 Jul 2024 10:24:00 -0400

Because specific heat capacity and specific latent heat are intensive properties, it is important that we have reliable means of measuring their values.

Determining the specific heat capacity

There are two common ways of finding the SHC of a substance:

Electrical method
Method of mixtures

Electrical method

Suitable for liquids
Measure the mass $m$ of the substance
Measure the initial temperature $T_i$ of the substance
Immerse a power heater (immersion heater) with voltage rating $V$ and current rating $I$ into the substance
Heat the substance for an amount of time $t$
Measure the final temperature $T_f$ of the substance
The heat energy supplied to the substance will be $$ \begin{equation}\begin{aligned} E_{heat}=VIt\\ \end{aligned}\end{equation} $$
Use the formula $E_{heat}=mc(T_f-T_i)$ to find the specific heat capacity $c$ of the substance

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Credits: A Level Physics Tutor

Specific Latent Heat

Wed, 24 Jul 2024 08:37:12 -0400

Specific latent heat (symbol $l$) is the amount of heat energy required to convert unit mass ($1\ kg$) of a substance from one phase to another. It is an intensive property. The associated formula is: $$ \begin{equation}\begin{aligned} Q=ml\\ \end{aligned}\end{equation} $$ Thus: $$ \begin{equation}\begin{aligned} l=\frac{Q}{m}\\ \end{aligned}\end{equation} $$

Example

It requires $4,600,000\ J$ of energy to convert $2\ kg$ of water to that same mass of steam. Find the specific latent heat of vaporization of water.

Specific Heat Capacity

Wed, 24 Jul 2024 08:34:38 -0400

These measurements are important when studying the phenomenon of heat in various materials.

Heat capacity

Heat capacity is the heat energy required to raise a substance by unit temperature ($1\ K$). The symbol is $C$. The associated formula is: $$ \begin{equation}\begin{aligned} Heat\ energy\ (Q)=C\Delta T\\ \end{aligned}\end{equation} $$ From this we get: $$ \begin{equation}\begin{aligned} C=\frac{Q}{\Delta T}\\ \end{aligned}\end{equation} $$

The SI Unit is thus Joules per Kelvin ($JK^{-1}$).

Example

Find the heat capacity of a block of copper if it takes $4000\ J$ to produce a temperature change from $300\ K$ to $308\ K$.

Explanation of the Gas Laws Using the Kinetic Theory

Wed, 24 Jul 2024 08:27:22 -0400

The following describes how the various gas laws can be explained by the Kinetic Theory.

Pressure law

Pressure is described as the frequency and strength of collisions by the gas particles with the walls of the container
For a single gas particle trapped in a box which cannot expand (constant volume), the greater the temperature of the gas, the more kinetic energy the particle has
The greater the kinetic energy, the greater the speed the particle has
Greater speed implies a greater strength of collision (greater pressure)
Greater speed also means the particle will bump into the walls of the container more often (greater pressure)

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Charles’ law

Volume is the space that a gas takes up
When the temperature of the gas is increased, the particles increase in their kinetic energy
Their speeds increase and they will hit the walls of the container more often
Thus in order for there to be a constant pressure (rate at which the particles hit the walls), the walls of the container must be further apart (volume increases)

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Boyle’s law

Reducing the size of the container of the gas (volume decreases), the rate at which the particles collide with the sides of the container increases (pressure increases) at constant temperature (constant particle speed)
Increasing the size of the container would reduce the number of collisions per unit time

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Determining the Value of Absolute Zero

Wed, 24 Jul 2024 08:16:47 -0400

We can find a value for absolute zero by doing:

Vary the temperature of a gas under conditions of fixed pressure and take the respective volumes for each temperature
Plot a graph of volume versus temperature and construct a best fit line
Using the best fit line, extrapolate backwards to get the $x$ intercept (the value in degrees Celsius where the volume is zero)

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Extrapolating backwards to get a value for absolute zero

Credits: Socratic

General Gas Law

Fri, 19 Jul 2024 17:52:50 -0400

From Boyle’s Law: $$ \begin{equation}\begin{aligned} PV=k_1\\ \end{aligned}\end{equation} $$

From the Pressure Law: $$ \begin{equation}\begin{aligned} P=k_2T\\ \end{aligned}\end{equation} $$

From Charles’ Law: $$ \begin{equation}\begin{aligned} V=k_3T\\ \end{aligned}\end{equation} $$

Multiplying these equations: $$ \begin{equation}\begin{aligned} PV\times P\times V&=k_1\times k_2T\times k_3T\\ P^2V^2&=k_1k_2k_3T^2\\ \frac{P^2V^2}{T^2}&=k_1k_2k_3\\ \end{aligned}\end{equation} $$

Square-rooting both sides: $$ \begin{equation}\begin{aligned} \sqrt{\frac{P^2V^2}{T^2}}&=\sqrt{k_1k_2k_3}\\ \frac{PV}{T}&=\sqrt{k_1k_2k_3}\\ \end{aligned}\end{equation} $$

The square-root of the product of three constants is itself a constant: $$ \begin{equation}\begin{aligned} \frac{PV}{T}=k\\ \end{aligned}\end{equation} $$

Generally: $$ \begin{equation}\begin{aligned} \frac{P_1V_1}{T_1}&=\frac{P_2V_2}{T_2}\\ \end{aligned}\end{equation} $$

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Pressure Law

Fri, 19 Jul 2024 17:48:59 -0400

Found by Joseph Louis Gay-Lussac in 1808
The pressure of a fixed mass of gas is directly proportional to its absolute temperature given that volume remains constant:

$$ \begin{equation}\begin{aligned} P&\propto T\\ P&=kT\ OR\\ \frac{P}{T}&=k\\ \end{aligned}\end{equation} $$

Thus we can have $\frac{P_1}{T_1}=k$ and $\frac{P_2}{T_2}=k$. Combining these two we get: $$ \begin{equation}\begin{aligned} \frac{P_1}{T_1}=\frac{P_2}{T_2}\\ \end{aligned}\end{equation} $$ Where $P_1$ is the pressure associated with the temperature $T_1$ and $P_2$ is associated with $T_2$.

Example

If the pressure in a car tire is $180\ kPa$ at $27\degree C$, what will be the pressure if the temperature rises to $37\degree C$?

Charles' Law

Fri, 19 Jul 2024 17:28:13 -0400

Named after pioneer balloonist Jacques Charles
The volume of a fixed mass of gas is directly proportional to its absolute temperature given that its pressure is constant:

$$ \begin{equation}\begin{aligned} V&\propto T\\ V&=kT\ OR\\ \frac{V}{T}&=k\\ \end{aligned}\end{equation} $$

Thus we can have $\frac{V_1}{T_1}=k$ and $\frac{V_2}{T_2}=k$. Combining these two we get: $$ \begin{equation}\begin{aligned} \frac{V_1}{T_1}=\frac{V_2}{T_2}\\ \end{aligned}\end{equation} $$ Where $V_1$ and $T_1$ are associated as are $V_2$ and $T_2$.

Example

A balloon of volume $0.006\ m^3$ is kept at a temperature of $0\degree C$. What would be the new volume if the temperature were to be raised to $91\degree C$?

The Gas Laws

Fri, 19 Jul 2024 17:19:29 -0400

These laws describe the relationships between the physical quantities pressure, volume and temperature as they relate to gases.

Why Learn the Gas Laws?

The gas laws tell us how gases behave when subjected to various pressures ($P$), made to fit into certain volumes ($V$) or kept at specific absolute temperatures ($T$)
Very important when combinations of these situations are considered
Each law usually keeps one physical quantity constant while varying the others so as to have us see the relationship between those varied quantities

Boyle’s Law

Named after physicist and chemist Robert Boyle
The pressure of a fixed mass of gas is inversely proportional to its volume at a constant temperature:

$$ \begin{equation}\begin{aligned} P&\propto \frac{1}{V}\\ P&=\frac{k}{V}\ OR\\\ PV&=k\\ \end{aligned}\end{equation} $$

Thus we can have $P_1V_1=k$ and $P_2V_2=k$. Combining these two we get: $$ \begin{equation}\begin{aligned} P_1V_1=P_2V_2\\ \end{aligned}\end{equation} $$ Where $P_1$ is the pressure associated with the gas of volume $V_1$ and $P_2$ is associated with $V_2$.

Absolute Temperature Scale

Fri, 19 Jul 2024 17:09:51 -0400

This is also known as the thermodynamic temperature scale
The Kelvin is the unit for the absolute temperature scale
$0\degree C$ is equivalent to $273\ K$
The distance between two consecutive units on the Kelvin scale is the same for two consecutive units on the Celsius scale e.g. the jump from $1\degree C$ to $3\degree C$ is the same as that from $274\ K$ to $276\ K$

Converting between Kelvin and degree Celsius

To convert degrees Celsius to Kelvin simply add $273$ to the number and change the unit to Kelvin

e.g. $5\degree C\equiv (5+273)K=278\ K$

Types of Thermometers

Fri, 19 Jul 2024 17:02:05 -0400

A thermometer is a device which used to measure temperature. There are many different kinds of thermometers, some more suitable than others to be used in certain situations.

Laboratory Thermometer

Can contain mercury or alcohol
The temperature range depends on which liquid is used
For mercury lab thermometers, the range is $-39\degree C$ to $357\degree C$
For alcohol lab thermometers, the range is $-115\degree C$ to $78\degree C$
We thus wouldn’t use an alcohol thermometer to measure the temperature of water which we are taking up to boiling point ($100\degree C$). In colder climates, alcohol thermometers are preferable
Mercury thermometers are more sensitive to and also respond more quickly to temperature changes when compared to alcohol thermometers
The glass surrounding the capillary tube is thick and acts as a magnifying glass

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Credits: Ministry of Education Guyana

Macroscopic Properties and Phenomena

Fri, 19 Jul 2024 16:53:17 -0400

The adjective macroscopic implies that we can observe these properties and phenomena without the need for a microscope.

Temperature

This refers to the average kinetic energies (translational, rotational and vibrational) of the particles within an object or system. It is how hot or cold something is. Absolute temperature is measured in $Kelvin\ (K)$. Other units used for temperature are:

Degree Celsius ($\degree C$) aka degree centigrade
Degree Farenheit ($\degree F$)

Direction of heat flow

Heat energy moves from hot to cold (from regions of higher temperature to regions of lower temperature). In other words, heat flows along the temperature gradient not against it.

The Nature of Heat

Fri, 19 Jul 2024 16:48:07 -0400

This section focuses on the nature of heat, measuring temperature, the consequences of changes in temperature and the methods of transfer of heat energy.

What is heat energy?

Heat energy is energy which is transferred because of temperature differences between objects. As with any other form of energy, the SI unit is the Joule(J).

Click/tap here to load video

Credits: Crash Course

Work

Wed, 17 Jul 2024 11:21:03 -0400

This is the product of the force applied to an object and the distance the object moves in the direction of the force: $$ \begin{equation}\begin{aligned} work&=force\times distance\\ &=Fd\\ \end{aligned}\end{equation} $$ The unit for work is the Joule(J): $$ \begin{equation}\begin{aligned} work=Fd\rightarrow\ N\times m\rightarrow Nm\ OR\ J\\ \end{aligned}\end{equation} $$ It has the same unit as energy since energy is the ability to do work. Note that the Newton-metre ($Nm$) is comprised of the fundamental units: $$ \begin{equation}\begin{aligned} Nm\rightarrow kgms^{-2}\times m\rightarrow kgm^2s^{-2}\equiv J\\ \end{aligned}\end{equation} $$

Energy

Wed, 17 Jul 2024 11:08:39 -0400

Energy is the ability to do work. It has the same SI unit as work - Joules(J). Some forms of energy are:

gravitational potential
kinetic
elastic
chemical
electrical
magnetic
electromagnetic (light)
thermal
nuclear
sound

Law of conservation of energy

Energy is neither created nor destroyed but it changes in form.

Examples of energy conversion

In an electric motor, electrical energy from the battery is transformed into kinetic energy of the rudder
In a hydroelectric dam, the gravitational potential energy of the water at the top of the dam is converted to kinetic energy as the water falls to the bottom and that is used to turn turbines which convert this kinetic energy to electrical energy
In a battery, chemical energy is converted to electrical energy
In an incandescent light bulb, electrical energy is converted to both light energy and thermal energy
Speakers convert electrical signals into sound energy
When a vehicle comes to a stop, its kinetic energy is converted to thermal energy
When food is cooked in a microwave oven, electrical energy is converted to electromagnetic energy and this in turn is converted into thermal energy
Solar panels convert electromagnetic energy from the sun into electrical energy
Kinetic energy of wind is converted to electrical energy by wind turbines

Types of mechanical energy

Mechanical energy is divided into two (2) types:

Deep Modules and Management of Complexity

Wed, 17 Jul 2024 00:29:47 -0400

In procedural languages like C, we use functions as the basic unit of modular design. Modular design is the practice of designing a system in modules. A module is any entity with an interface and an implementation. The interface provides an abstraction (a simplified view of an entity which omits unimportant details) of the module.

An interface is a contract/intersection between the system and the environment. Credits: Robert Elder

Functions act as modules in C. The definition of the function determines the interface. Take for example the following:

Linear Momentum Lab

Tue, 16 Jul 2024 12:36:02 -0400

Theory

Momentum ($p$) is a vector quantity which is expressed as the product of the mass and the velocity of an object. $$ \begin{equation}\begin{aligned} momentum&=mass\times velocity\\ p&=m\times v\\ \end{aligned}\end{equation} $$

Impulse can be defined as a change in momentum of the object. It is essentially the time-effect of a force. Think about how a cricketer catches and slows down a ball by relaxing the arms rather than keeping them rigid. The effect of applying this retarding force over a time interval changes the momentum of the ball from its maximum value to zero. $$ \begin{equation}\begin{aligned} impulse&=force\times time\\ \Delta p &= Ft\\ \end{aligned}\end{equation} $$

Linear Momentum

Tue, 16 Jul 2024 12:30:01 -0400

Linear momentum is the product of a body’s mass and its linear velocity: $$ \begin{equation}\begin{aligned} momentum&=mass\times velocity\\ p&=mv\\ \end{aligned}\end{equation} $$

The more mass the body has, the greater its momentum
The faster the body is moving, the greater its momentum
The SI unit is kilogram-metres per second ($kgms^{-1}$): $$ \begin{equation}\begin{aligned} p&=mv\\ &\rightarrow kg\times ms^{-1}\\ &\rightarrow kgms^{-1}\\ \end{aligned}\end{equation} $$
Velocity is a vector hence momentum is also a vector
Because momentum is a vector, when we work momentum problems, we must use a sign convention

Law of conservation of linear momentum

For an isolated system, the total momentum of the system before collision is equal to the total momentum of the system after collision.

Equilibrium

Tue, 16 Jul 2024 10:48:50 -0400

Stability is a measure of how easily an object will topple over when a force is applied to it. It refers to the tendency of a body to return to its original position after it experiences a turning effect.

For example, a pencil on its tip will easily fall over when pushed (it has low stability) whereas a living room sofa will easily fall back into place as it is lifted at one end (high stability).

Levers

Tue, 16 Jul 2024 10:40:00 -0400

A lever is a simple machine consisting of a rigid bar (meaning it does not bend) which pivots at a certain point (pivot/fulcrum) along its length and by the effect of a force (called the effort), it can serve to move an object or overcome another force (referred to as the load).

Types of levers

There are three(3) types of levers:

First class levers have the fulcrum in between the load and effort. These can be force multipliers or distance multipliers
Second class levers have the load in between the fulcrum and effort. These are force multipliers
Third class levers have the effort in between the fulcrum and load. These are distance multipliers

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Credits: Pathwayz

Conversions

Mon, 15 Jul 2024 23:26:24 -0400

Recall that when doing standard form, we can shift the decimal point to the left and increase the power of 10. We can also shift the decimal point to the right and decrease the power of 10. Doing these in the opposite order is also valid:

If we increase the power of 10 by 1 then we MUST shift the decimal point to the left by 1 digit If we decrease the power of 10 by 1 then we MUST shift the decimal point to the right by 1 digit

Multiples, Sub-multiples and Standard Form

Mon, 15 Jul 2024 22:48:12 -0400

Sometimes we want to represent very large or very small numbers efficiently. We use multiples and sub-multiples in order to avoid having to write too many digits.

Multiples

These are used to represent large numbers. Below are some commonly used multiples.

Multiple prefix	Symbol	Value	Value expressed as a power of 10
Kilo-	k	1,000	$10^3$
Mega-	M	1,000,000	$10^6$
Giga-	G	1,000,000,000	$10^9$
Tera-	T	1,000,000,000,000	$10^{12}$

Notice that the prefixes are simply placeholders for positive (+ve) powers of 10.

Measurements

Mon, 15 Jul 2024 22:35:34 -0400

Measurements are essential to our understanding of the physical world. Measuring the value of a variable as the values of other variables change is a central aspect of science.

Standardized measurements

What if a meter meant different distances for different regions of the world? Would the world record for longest or highest jump or javelin throw be fairly determined?

Why we need standardized measurements

Without standardized measurements, describing physical quantities to someone else would be difficult - try telling your friend how many hand-spans your seat is and have them draw a line that is the same number of hand-spans but using their hand. You will not have the same measurement unless your hands are identical in length.

Physical Quantities

Mon, 15 Jul 2024 22:29:11 -0400

A physical quantity is a property of a material, substance or system which can be measured/quantified. Examples include the mass of a ball and the volume of a gas.

Fundamental quantities/Base quantities

These are the physical quantities from which all other physical quantities are derived. According to the International System of Units (SI), there are seven (7) fundamental quantities:

Quantity	Symbol	Unit	Abbreviation for unit
Mass	$m$	kilogram	$kg$
Length	$l$	metre	$m$
Time	$t$	second	$s$
Temperature	$T$	Kelvin	$K$
Amount of substance	$n$	mole	$mol$
Current	$I$	ampere	$A$
Luminous intensity	$I_v$	candela	$cd$

Derived quantities

Variables and Relationships

Mon, 15 Jul 2024 19:20:28 -0400

Now that we have studied the various types of variables, we can learn to describe the relationships between variables. There are three(3) types of relationships:

Direct relationship: If we increase one variable then the other variable increases. If we decrease one, the other decreases.
Inverse relationship: Increasing one variable decreases the other
No relationship: Increasing/decreasing one variable shows no noticeable change in the other variable

What do they look like?

If we plot graphs of one variable versus the other then we can tell the relationship by looking at the best fit line/regression line/trend line.

The Scientific Method

Mon, 15 Jul 2024 19:15:28 -0400

Galileo Galilei is attributed as the father of modern science. The video in the link below details his life and contributions.

Click/tap here to load video

Credits: The Biographics Youtube channel

Principle of Moments Lab

Mon, 15 Jul 2024 18:56:01 -0400

The following lab can be replicated in person by using a metre rule, masses with mass holders and a glass prism to act as the base.

Theory

The principle of moments states that for a body in equilibrium, the sum of anti-clockwise moments equals the sum of clockwise moments: $$ \begin{equation}\begin{aligned} \sum ACW\ moments=\sum CW\ moments\\ \end{aligned}\end{equation} $$ A system can thus be made to be in equilibrium by ensuring that these sums are balanced.

Moments

Mon, 15 Jul 2024 18:05:47 -0400

The moment of a force is the turning effect of that force. It is dependent on:

The magnitude and direction of the force
The position of the force’s line of action relative to the pivot

The moment of a force is given by $$ \begin{equation}\begin{aligned} moment=&\text{force}\times\text{perpendicular}\\ &\text{distance between line}\\ &\text{of action of force and pivot}\\ \end{aligned}\end{equation} $$

Example

James pushes a door at the door knob which is located $0.8\ m$ away from the door’s hinge. If he pushes the door with a force of $10\ N$, find the moment of the force.

View Original

$$ \begin{equation}\begin{aligned} moment&=force\times perp.\ distance\\ &=10\ N\times 0.8\ m\\ &=8\ Nm\\ \end{aligned}\end{equation} $$

Hooke's Law Lab

Mon, 15 Jul 2024 14:19:09 -0400

The following lab can be replicated in person by using a metre rule, masses with mass holders and a spring.

Theory

Hooke’s law states that the deformation of an object is directly proportional to the force applied, and is given by the formula $$F=kx$$ where the extension ($x$) is $$x=current\ length-original\ length$$

We can make $x$ the subject of the formula and write it in the form of a straight line equation: $$ \begin{equation}\begin{aligned} x&=\frac{F}{k}\\ \color{limegreen}x&=\color{royalblue}\frac1k\color{red}F\color{normal}+0\\ \color{limegreen}y&=\color{royalblue}m\color{red}x\color{normal}+c\\ \end{aligned}\end{equation} $$

Hooke's Law

Mon, 15 Jul 2024 13:53:22 -0400

Deformation can be defined as any change in shape caused by the application of a force. There are 2 types of deformation:

Elastic/temporary deformation - in which the object returns to its original shape after the force is removed
Plastic/permanent deformation - the object does not revert to its original shape. It may remain in the shape it was in when the force was present (as seen in modelling clay) or may revert only partially to the original shape (like an overstretched elastic band which has not been stretched enough to burst)

Hooke’s Law

Hooke’s Law states that the deformation of an object is directly proportional to the force applied. In other words, as we increase/decrease the force on the object, the deformation seen in the object will increase/decrease respectively. In the case of a spring, the deformation is the spring’s extension($x$), the change in the spring’s length ($x=current\ length-original\ length$):

Never Nesting

Wed, 10 Jul 2024 23:16:06 -0400

This is the practice of preventing code from becoming too long horizontally. When too much code is nested, the text we need to navigate horizontally grows to be unmanageable.

Two techniques we use to reduce nesting are:

Extraction
Inversion

Extraction

In extraction, we extract a block of code and place it within a function. We then call that function from where the code block used to be.

#include <stdio.h>

// checking feature extracted out as function
void even_or_odd(int x) {
 if (x % 2 == 0) {
 printf("%d is even\n", x);
 } else {
 printf("%d is even\n", x);
 }
}

int main() {

 // without extraction
 for (int x = 0; x < 10; x++) {
 if (x % 2 == 0) {
 printf("%d is even\n", x);
 } else {
 printf("%d is even\n", x);
 }
 }

 // with extraction
 for (int x = 0; x < 10; x++) {
 even_or_odd(x);
 }
 return 0;
}

extraction.c

Copy

Simple Pendulum Lab

Mon, 08 Jul 2024 19:30:43 -0400

The following lab can be replicated in person by using an eraser as the pendulum bob, string, a ruler and a stopwatch.

Theory

The period of a simple pendulum is given by the formula: $$T=2\pi\sqrt{\frac{l}{g}}$$

If we square both sides of this equation, we get the following: $$\color{limegreen}T^2\color{black}=\color{slateblue}\frac{4\pi^2}{g}\color{red}l\color{black}+0$$

If we compare this to the standard form of the equation of a straight line: $$\color{limegreen}y\color{black}=\color{slateblue}m\color{red}x\color{black}+c$$

We see that by plotting the period squared ($T^2$) versus the length ($l$), the y-intercept of the best-fit line will be zero(0) and the gradient will be: $$m=\frac{4\pi^2}{g}$$

Vim Motions for Web Developers

Fri, 05 Jul 2024 20:10:25 -0400

There is no doubt that navigating and manipulating text in order to build web pages is much more tedious than typing an essay. Lucky for us, your favourite text editor Vim ships with the right tools for the job - VS Code is fine too once you install the Vim plugin.

Let’s learn some motions to successfully run circles around HTML, CSS and JS. I’ll update this article as more tips come to mind.

Project NibbleSprouts

Thu, 04 Jul 2024 08:25:13 -0400

This website theme is meant to be used to create a scalable and reliable educational content website. Fast web pages help students find what they need without much execution overhead. Special thanks to Luke Smith, Eric Murphy, Robert Elder and Primeagen for the inspiration.

This website theme is:

fast
eco-friendly
reliable
agile
Lean
user-centric
the other corporate buzzwords

Below are some of the features supported by this theme.

System font stack

Why wait for fonts to download when you can use the ones that are already there? The coolest system font stacks can be found at Modern Font Stacks.

Simple Pendulum

Tue, 02 Jul 2024 19:32:47 -0400

A simple pendulum is a heavy mass attached to a light inextensible string. The heavy mass is referred to as the bob and we refer to it as heavy because it should contribute the vast majority, if not all, of the mass of the system (consisting of bob and string).

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Image Credits: Unacademy

Functional and Non-Functional Requirements

Mon, 01 Jul 2024 22:33:35 -0400

There is a difference between working software and good software. What determines the quality of a software product is the set of requirements.

Requirements are the features that a software application or system delivers on. There are two kinds of requirements:

functional requirements - these are what the program does.
non-functional requirements - these dictate the manner in which the program delivers on the functional requirements.

Functional requirements

Our primary goal in making software is to ensure that it does what we promised that it would do. Functional requirements are the features that, when absent, will definitely be noticed by the user. If we fail to fulfill these requirements then our software fails to meet even the bare minimum of what is expected.

Symptoms and Causes of Complexity

Mon, 01 Jul 2024 22:30:56 -0400

This article is based on John Ousterhout’s lessons on software design, specifically his book “A Philosophy of Software Design”. He speaks on what can cause a system to be complex and what ways complexity can manifest itself. A software system doesn’t have to be large in order to be complex. It is very much possible to write a very confusing 100 lines of code. It is also possible to have a code base with 1000’s of lines that are easy to pick up and manage.

Styles of API's

Mon, 01 Jul 2024 22:28:30 -0400

APIs (Application Programming Interfaces) are the interface across which two applications can communicate with each other. An API determines the behaviour of the two applications and the means by which they exchange information. Erik Wilde has a video:

Click/tap here to load video

Credits: Erik Wilde

The Basics of Vim

Mon, 01 Jul 2024 22:13:02 -0400

Vim can be intimidating to learn at first. I recommend you try out the various commands and see which ones peak your interest. Here is a list of some basic commands in Vim. Vim has four (4) modes:

Normal mode
Insert mode
Visual mode
Command mode

Normal mode

The following commands are used in normal mode.

v - Enter visual mode
. - Replay last command
J - Join the next line to the end of the current line
Ctrl+w followed by j,k,h,l,w - Switch between windows
ZZ - Save and exit
ZQ - Exit without saving

Folding

zo - Open a fold
zc - Close a fold
za - Toggle a fold
zO - Open all folds
zM - Close all folds
zR - Open all folds recursively

Basic movement

h - Move cursor left
j - Move cursor down
k - Move cursor up
l - Move cursor right
w - Move cursor to the beginning of the next word, defined by non-white space character
W - Move cursor to the beginning of the next word, defined by white space character
b - Move cursor to the beginning of the previous word, defined by non-white space character
B - Move cursor to the beginning of the previous word, defined by white space character
e - Move cursor to the next end of word, defined by non-white space character
E - Move cursor to the next end of word, defined by white space character
_ - Move to the first non-white space character in current line
0 - Move to the zeroth character in current line
$ - Move to the end of current line

Deleting, replacing and fixing changes

x - Delete character under cursor
rchar - Replace character under cursor with char
dd - Delete current line
D - Delete to the end of the current line
cc - Change current line
C - Delete to the end of the current line and enter Insert mode
u - Undo last change
Ctrl+r - Redo last change
U - Fix entire line

Copying and pasting

yy - Yank current line
p - Paste last yanked or deleted text after cursor
P - Paste last yanked or deleted text before cursor
Shift+v - Enter Visual line mode and highlight the current line; This text can then be deleted (d or x) or yanked (y)
Ctrl+v - Enter visual block mode
I - Insert at the beginning of selected each line in the visual block

Horizontal movement and actions

_ - Jump to first non-white space character in current line
0 - Jump to beginning of current line
$ - Jump to end of current line
i - Enter Insert mode and start inserting before current cursor position
I - Enter Insert mode and start inserting at the first non-white space character in current line
a - Enter Insert mode and start inserting after current cursor position
A - Enter Insert mode and start inserting after the last character in current line
s - Delete the character under the cursor and Enter Insert mode
S - Change the current line and indent to where Vim infers that the cursor should be in the current line
fchar - Jump to position of first instance of char in current line
Fchar - Jump to position of previous instance of char in current line
tchar - Jump to position just before next instance of char in current line
Tchar - Jump to position just before previous instance of char in current line
; and , - Cycle between char selected using f,F,t or T
dichar - Delete in between char
cichar - Delete all text between instances of char in the current line and place the cursor in between and enter Insert mode; The text must be enclosed by two instances of the char
yichar - Yank everything in between char

Vertical movement and actions

gg - Go to first line of file
G - Go to last line of file
gv - Go to text previously selected in Visual Mode
gi - Go to previous insert position in and enter Insert Mode
:line_number - Jump to line number line_number
ochar - Insert line below current line and enter Insert Mode
Ochar - Insert line above current line and enter Insert Mode
[[ and ]] - jump between sections of text
{ and } - jump between paragraphs

Other movements

% - jump between opening and closing {, ( and [

Search and replace

:%s/old_string/next_string/g - replace old_string with new_string globally
:%s/old_string/next_string/gc - replace old_string with new_string globally, asking in each case for confirmation

Finding stuff

/string+enter - Jump to next instance of string in the current file
?string+enter - Jump to previous instance of string in the current file
//+enter - Repeat the last search
* - Search forwards for word (bounded) under cursor
g* - Search forwards for word (unbounded) under cursor
# - Search backwards for word (bounded) under cursor
g# - Search backwards for word (unbounded) under cursor
n - cycle forwards through search results; reversed for ?
N - cycle backwards through search results; reversed for ?
]s - Jump to next misspelled word
[s - Jump to previous misspelled word
zg - Add current word to Vim’s dictionary
zw - Remove current word from Vim’s dictionary
z= - Open a list of word suggestions for the current word
1z= - Replace the current word with the 1st suggestion in the list of word suggestions

Placing the cursor relative to the window

We can place the cursor relative to the window for a better view of the document.

Getting Started With C

Mon, 01 Jul 2024 17:58:04 -0400

This is the start of the lessons on the C programming language. C is an imperative, compiled, statically-typed, portable language.

Imperative: we tell the computer how to accomplish a goal; we give it orders
Compiled: the computer translates the entire code into an executable/binary code which the machine can then understand
Statically-typed: we tell the computer exactly what type of data we want it to use instead of having it guess based on how we use the data; this makes our code run faster because time is not wasted on guessing
Portable: we write our code and use the compiler for whichever platform/device we want to run the code on; the compiler then translates it into the machine code for that device thus saving us from having to rewrite different versions of C for different machines; we simply use different compilers

Boilerplate

Boilerplate is used to refer to the repetitive sections of code that developers have to type with little to no variation.