A physical quantity is what you are trying to measure, for example, length, time, speed are all physical quantities. Instead time is measured in seconds which are the units. With the development of the scientific community, an international standard had to be reached so the SI unit system (Système international (d’unités)) was developed.

There are of course different units associated with length, like meters, feet, miles etc. In order to avoid confusion, the SI decided that the common unit was going to be the meter. The symbols of the quantity can vary depending on the situation but the ones of the unit are always the same.

The SI unit system is one that is valid to everyone around the world and that has evolved from seven ‘base units’, these units work cohesively together and fundamentally underpin all of the SI units used today. Not all countries have chosen to adopt this system, so conversions are frequently needed to be used. For example, in America a unit for distance is feet, whereas in the UK meters is used so the conversion of $1 foot = 0.3048 m$ is used.

Here is an example of some quantities, with their relative symbol, SI unit and SI unit symbol:The seven base quantities and their respective base units are as follows; it is worth becoming familiar with all of these and remembering them:

There are many quantities that you will be aware of that are not listed as base quantities, such as speed for example. All of these other quantities that you can think of may have their own unit but fundamentally, this unit can be written in base units. A simple example of this is speed:
Speed is the rate of change of distance,  $speed = \frac{distance}{time}$ and has the units $ms^{-1}$

A slightly more complex example (of which will become all the more  familiar over time) is kinetic energy.
Kinetic energy is, as it states in the name, a type of energy and therefore is measured in  $Joules, J$  however this is not a base unit. To determine what the joule is in base unity, the equation for kinetic energy is needed:

$E_{k} = \frac{1}{2}mv^{2}$

Since mass and velocity are base quantities, we can substitute their units in to this equation (we can ignore the $\frac{1}{2}$ as their are no units for this):

$E_{k} \rightarrow kg \times (ms^{-1})^{2}$

$E_{k} \rightarrow kgm^{2}s^{-2}$

This is the unit for kinetic energy, in its base units. This tells us that $1 \ J = 1 \ kgm^{2}s^{-2}$.

You may be wondering why the Joule is used at all? Well this unit (in base form) appears long and perhaps complex, which is why the joule is used – it is cleaner and more user friendly.

The power of units

In any exam if you feel you have made a mistake somewhere, perhaps because you are unsure on an equation you have used, you can always substitute in the units to both sides of an equation to check that they balance – a valid equation has to have units balanced on both sides!

Page co-written with Luca Quinci – Thank you!