2.1 Quntities Units

Physical quantities and units

  • A physical quntitiy is what is being measured (e.g length, time, speed)
  • A unit is how each quantity is measured (e.g meters, seconds)

The scientific community developed an international standard to make data easily accessible to other countries, the SI unit system (Systéme International).

Quantities and units

Physical Quantity Quantity Symbol SI Unit Unit Symbol
length l,d,x,s meter m
time t second s
mass m kilograms kg
electrical current I Ampere's A
Temperature T,$\theta$ Kelvin K
Amount of substance n moles mol
Luminous intensity Iv candela cd

All other quantities can be expressed in these SI units.

Examples:

Speed is the rate of change of distance: $$ \text{speed}=\frac{\text{distance}}{\text{time}} $$ Therefore it has the units $ms^{-1}$.

Kinetic energy $$ E_k=\frac{1}{2}mv^2 $$ Or in terms of units $$ \text{J} \to \text{kg}\times(\text{ms}^{-1})^2 $$ $$ \text{J} \to \text{kgm}^2\text{s}^{-2} $$ This is the unit for kinetic energy in it's base units, $1,\text{J}$ of energy is $1,\text{kgm}^2\text{s}^{-2}$

Units can be helpful in an exam to double check your working - if the units on each side match then it is most likely correct.