Published by Patrick Mutisya · 14 days ago
Express derived units as products or quotients of the SI base units and use the derived units for the quantities listed in the syllabus as appropriate.
| Quantity | Symbol | SI Base Unit | Definition (brief) |
|---|---|---|---|
| Length | m | metre | Distance travelled by light in vacuum in \$1/299\,792\,458\$ s |
| Mass | kg | kilogram | Mass of the International Prototype of the Kilogram |
| Time | s | second | Duration of \$9\,192\,631\,770\$ periods of radiation of Cs‑133 |
| Electric current | A | ampere | Current that produces a force of \$2\times10^{-7}\$ N per metre of length between two parallel conductors 1 m apart |
| Thermodynamic temperature | K | kelvin | 1/273.16 of the thermodynamic temperature of the triple point of water |
| Amount of substance | mol | mole | Amount of substance containing as many elementary entities as there are atoms in 0.012 kg of carbon‑12 |
| Luminous intensity | cd | candela | Intensity of a source that emits monochromatic radiation of frequency \$540\times10^{12}\$ Hz and has a radiant intensity of \$1/683\$ W·sr⁻¹ |
Derived units are obtained by combining the base units using multiplication, division and powers. The general form is
\$\text{Derived unit} = \text{(base unit)}^{a}\,\text{(base unit)}^{b}\,\dots\$
where the exponents \$a\$, \$b\$, … are integers (positive for multiplication, negative for division).
| Quantity (syllabus) | Symbol | Derived SI Unit (name) | Expression in Base Units |
|---|---|---|---|
| Speed, velocity | \$v\$ | metre per second (m s⁻¹) | \$\text{m·s}^{-1}\$ |
| Acceleration | \$a\$ | metre per second squared (m s⁻²) | \$\text{m·s}^{-2}\$ |
| Force | \$F\$ | newton (N) | \$\text{kg·m·s}^{-2}\$ |
| Pressure, stress | \$p\$ | pascal (Pa) | \$\text{kg·m}^{-1}\text{s}^{-2}\$ |
| Energy, work, heat | \$E\$, \$W\$, \$Q\$ | joule (J) | \$\text{kg·m}^{2}\text{s}^{-2}\$ |
| Power | \$P\$ | watt (W) | \$\text{kg·m}^{2}\text{s}^{-3}\$ |
| Electric charge | \$q\$ | coulomb (C) | \$\text{A·s}\$ |
| Electric potential difference, voltage | \$V\$ | volt (V) | \$\text{kg·m}^{2}\text{s}^{-3}\text{A}^{-1}\$ |
| Capacitance | \$C\$ | farad (F) | \$\text{kg}^{-1}\text{m}^{-2}\text{s}^{4}\text{A}^{2}\$ |
| Resistance | \$R\$ | ohm (Ω) | \$\text{kg·m}^{2}\text{s}^{-3}\text{A}^{-2}\$ |
| Magnetic flux | \$\Phi\$ | weber (Wb) | \$\text{kg·m}^{2}\text{s}^{-2}\text{A}^{-1}\$ |
| Magnetic flux density (magnetic induction) | \$B\$ | tesla (T) | \$\text{kg·s}^{-2}\text{A}^{-1}\$ |
| Inductance | \$L\$ | henry (H) | \$\text{kg·m}^{2}\text{s}^{-2}\text{A}^{-2}\$ |
| Frequency | \$f\$ | hertz (Hz) | \$\text{s}^{-1}\$ |
| Momentum | \$p\$ | kilogram metre per second (kg m s⁻¹) | \$\text{kg·m·s}^{-1}\$ |
| Angular velocity | \$\omega\$ | radian per second (rad s⁻¹) | \$\text{s}^{-1}\$ (dimensionless radian) |
When solving A‑Level problems, always check that the units on both sides of an equation are consistent. A quick method is to replace each quantity by its base‑unit expression, perform the algebra, and then re‑assemble the result into the appropriate named derived unit.
Example: Calculate the kinetic energy of a 2 kg object moving at 5 m s⁻¹.
\$\$E_{\text{k}} = \frac{1}{2}\;( \text{kg} )\;( \text{m·s}^{-1} )^{2}
= \frac{1}{2}\;\text{kg·m}^{2}\text{s}^{-2}.\$\$
All derived units in the A‑Level syllabus can be written as products or quotients of the seven SI base units. Mastery of these expressions enables quick checks of equation consistency, conversion between units, and confident use of the named derived units (N, Pa, J, W, V, Ω, etc.) in exam answers.