Cambridge International A-Level Physics

## Physical quantities A physical quantity is a property that can be measured, and it always has two parts: a numerical magnitude and a unit. A length of $2.4\,\mathrm{m}$ is not described by the $2.4$ alone, since the same number of centimetres or miles would be a different length. Every equation in physics relates quantities, so a calculation that loses its units has lost half of its meaning. Some quantities also have a direction. Those are vectors, and they are treated in the note on vectors and describing motion. ## SI base quantities The SI system is built on a small set of base quantities, from which every other quantity is derived. The five used at this level are these. | Base quantity | Base unit | Symbol | |---|---|---| | mass | kilogram | kg | | length | metre | m | | time | second | s | | electric current | ampere | A | | thermodynamic temperature | kelvin | K | A sixth base quantity, amount of substance, has the unit mole (mol) and is used with gases and the Avogadro constant. ## Derived units A derived unit is a product or quotient of base units. Every other unit is one of these, even when it has a name of its own. The work is to reduce a named unit to base units by going back to an equation that defines the quantity. Velocity is displacement divided by time, so its unit is $\mathrm{m\,s^{-1}}$. Acceleration is velocity divided by time, giving $\mathrm{m\,s^{-2}}$. Force is mass times acceleration, so the newton is $$ \mathrm{N} = \mathrm{kg\,m\,s^{-2}} $$…