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 | $cd$ |

It should be noted that some fundamental quantities are disguised under special names in certain circumstances e.g. the perimeter of a playing field is just a

length measurementand the period of a simple pendulum is atime measurement.

The derived quantities are combinations of these fundamental quantities. For example, the speed of an object is the ratio of the distance traveled to the time taken for it to cover that distance:

$$ speed=\frac{distance}{time} $$

### Finding the unit for derived quantities

If we know the formula for a derived quantity and the units of the other quantities in the formula, we can find the equivalent unit: $$ \begin{equation}\begin{aligned} speed&=\frac{distance}{time}\\ &=\frac{m}{s}\\ &=ms^{-1}\\ \end{aligned}\end{equation} $$

## Scalar vs. vector quantities

Scalar quantities have only a magnitude e.g. mass and length. Vector quantities have both magnitude and direction e.g. displacement and force.

### Resolving vectors

Read the lesson on resolving vectors.

### Combining vectors

Read the lesson on combining vectors.

## Reporting measurements of physical quantities

We write measurements as the **product of** a magnitude (**how many**) and a unit (**of what**):
$$
\begin{equation}\begin{aligned}
measurement&\rightarrow magnitude\times unit\\
e.g.\ 3\ kg&\rightarrow 3\times kg\\
\end{aligned}\end{equation}
$$

#### Dimensionless quantities

Some quantities **do not have units**. These are exceptions to the rule above. These include:

- Relative density
- Refractive index
- Mechanical advantage
- Velocity ratio

For example, we can study mechanical advantage (MA): $$ \begin{equation}\begin{aligned} &MA=\frac{load}{effort}\rightarrow \frac{N}{N}\rightarrow no\ units (dimensionless)\\ &relative\ density=\frac{density\ of\ substance}{density\ of\ water}\rightarrow \frac{kgm^{-3}}{kgm^{-3}}\rightarrow no\ units\\ &refractive\ index=\frac{sin(\hat i)}{sin(\hat r)}\rightarrow \frac{no\ units}{no\ units}\rightarrow no\ units\\ \end{aligned}\end{equation} $$

## Variables

These entities whose value can vary/change. There are three (3) types of variables:

**Independent/Manipulated variables**are variables whose values we choose to*change/manipulate***Dependent/Responding variables**are variables whose values change*as a result of/in response to*us changing the value of the manipulated variable**Controlled variables**are variables whose values we choose to keep fixed. These are**NOT**constants. They are still variables because their value*can be changed*but we*choose not to change them*. This is because they may affect the value of the other variables (manipulated and responding)

### Example 1: Using different liquids to water a plant

Plan and design an experiment to see which of three liquids (water, orange juice and soda) will make a plant grow fastest.

- Manipulated variable: The type of liquid used to water the plants (water vs. orange juice vs. soda)
- Responding variable: The growth rate of the plant OR the surface area of the leaves OR the the length of the stem
- Controlled variable(s): amount of each liquid used on the plants (e.g. 100 ml), observation period of each plant (e.g. for 1 week), starting age of the plants (e.g. 1 week-old seedlings), type of soil (e.g. clayey), the type of plant (e.g. black-eye pea)

Notice that any of the controlled variables could have been used as a manipulated variable in another experiment

### Example 2: The effect of the presence of light on fruit ripening

Plan and design an experiment to determine if it is better to store fruits in a dark area or a lit area to speed up ripening.

- Manipulated variable: the amount of light the fruits are exposed to (0 hours of sunlight vs. 3 hours of sunlight daily) OR the location of storage (lit area vs. dark area)
- Responding variable: the rate of ripening OR the time taken to become a certain colour
- Controlled variable(s): temperature at which the fruits are stored, humidity of the environment, shelf-life of the fruit, interval at which the ripening is checked

### Example 3: The effect of the frequency of drinking water on the happiness level of children

Plan and design an experiment to determine if a higher frequency of drinking water makes children happier.

- Manipulated variable: how often we give water to the children (the frequency of drinking)
- Responding variable: the happiness level of the children
- Controlled variable(s): amount of water given each time (e.g. 1 cup), the type of water given (e.g. spring water), temperature of water (e.g. room temperature), the age range of the children (e.g. 9-10 year olds), the colour of the container used (e.g. clear)

Lightning round

1) Which of the following is a scalar quantity?

- Force
- Speed
- Acceleration
- Velocity