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SI Units

01SI Units

Base units

This section covers the six SI base quantities and units required for AQA A-level Physics.

Fundamental SI quantities

SI units provide a common system for expressing physical quantities. Other units can be built from a small set of fundamental, or base, units.

There are seven SI base units in the complete SI system, but only the following six are required for this course.

Base quantity SI base unit Symbol
Mass kilogram kg\mathrm{kg}
Length metre m\mathrm{m}
Time second s\mathrm{s}
Amount of substance mole mol\mathrm{mol}
Temperature kelvin K\mathrm{K}
Electric current ampere A\mathrm{A}

Derived units such as the newton, joule and pascal can be reduced to combinations of these base units.

Exam Tip: Know the six required base quantities together with the name and symbol of each associated SI unit.

02SI Units

Derived units

This section covers how derived SI units are obtained from base units using physical equations.

Deriving units from equations

Derived units are combinations of SI base units. To find a derived unit in base-unit form, use an equation defining the physical quantity and substitute the units of the quantities in that equation.

1

Force

Using F=maF=ma:

[F]=kg×m s−2=kg m s−2[F]
    =\mathrm{kg}\times\mathrm{m\,s^{-2}}
    =\mathrm{kg\,m\,s^{-2}}
N=kg m s−2\mathrm{N=kg\,m\,s^{-2}}
2

Energy

Using E=12mv2E=\frac12mv^2:

[E]=kg×(m s−1)2=kg m2 s−2[E]
    =\mathrm{kg}\times(\mathrm{m\,s^{-1}})^2
    =\mathrm{kg\,m^2\,s^{-2}}
J=kg m2 s−2\mathrm{J=kg\,m^2\,s^{-2}}
3

Pressure

Using p=FAp=\dfrac{F}{A}:

[p]=kg m s−2m2=kg m−1 s−2[p]
    =
    \frac{\mathrm{kg\,m\,s^{-2}}}{\mathrm{m^2}}
    =
    \mathrm{kg\,m^{-1}\,s^{-2}}
Pa=kg m−1 s−2\mathrm{Pa=kg\,m^{-1}\,s^{-2}}

The equation defining a quantity therefore provides the route from its named derived unit to its equivalent combination of SI base units.

03SI Units

Unit consistency

This section covers using equations and SI base units to determine the units of physical quantities.

Following units through an equation

Units can be followed through the same mathematical steps as the quantities in an equation. Products, quotients and powers therefore affect the units in the same way.

For example, speed has units m s−1\mathrm{m\,s^{-1}}, so squaring a speed gives:

(m s−1)2=m2 s−2(\mathrm{m\,s^{-1}})^2 = \mathrm{m^2\,s^{-2}}

Worked example: Express the volt in SI base units.

Potential difference is given by:

V=EQV=\frac{E}{Q}

Energy has the base units:

[E]=kg m2 s−2[E]=\mathrm{kg\,m^2\,s^{-2}}

Using Q=ItQ=It, charge has units:

[Q]=A s[Q]=\mathrm{A\,s}

Substitute these into the equation for potential difference:

[V]=kg m2 s−2A s=kg m2 s−3 A−1[V] = \frac{\mathrm{kg\,m^2\,s^{-2}}}{\mathrm{A\,s}} = \mathrm{kg\,m^2\,s^{-3}\,A^{-1}}

Therefore:

V=kg m2 s−3 A−1\mathrm{V=kg\,m^2\,s^{-3}\,A^{-1}}

A reliable unit method

  1. Write the equation connecting the required quantity to known quantities.
  2. Replace each quantity with its units.
  3. Apply any multiplication, division or powers shown by the equation.
  4. Simplify to SI base units.