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.
Standardized measurements provide a system in which all measurements are consistent and objective:
- Consistent - a kilogram will always be a kilogram because its value is based on the property (mass) of a substance under a set of fixed conditions
- Objective - the value is not affected by opinion
Areas which benefit from standardized measurements
Think about how the following areas would be affected if we did not have standardized measurements:
- Science
- Business
- Sports
- Any other field where information exchange and integrity are crucial
The International System of Units/Systeme international d’unites (SI)
- The international system of units was established in 1960 and adapted by the General Conference on Weights and Measures (CGPM) and has been accepted by most countries worldwide
- It describes seven (7) fundamental quantities with their units
How measurements are reported
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): $$ \begin{equation}\begin{aligned} &MA=\frac{load}{effort}\rightarrow \frac{N}{N}\rightarrow no\ units (dimensionless)\\ &relative\ density=\frac{density\ of\ substance}{density\ of\ water}\rightarrow \frac{kgm^{-3}}{kgm^{-3}}\rightarrow no\ units\\ &refractive\ index=\frac{sin(\hat i)}{sin(\hat r)}\rightarrow \frac{no\ units}{no\ units}\rightarrow no\ units\\ \end{aligned}\end{equation} $$