SI units and prefixesAQA A-Level Physics: Revision notes

All physical quantities can be built from a small set of base quantities, each with an SI base unit. For AQA you must use six of them:

• mass, kilogram (kg)
• length, metre (m)
• time, second (s)
• amount of substance, mole (mol)
• thermodynamic temperature, kelvin (K)
• electric current, ampere (A)

A temperature change of 1 K is the same size as a change of 1 °C, but a temperature in kelvin is the Celsius value + 273 (K = °C + 273). The candela is not required, and you do not need to recall the definitions of the base quantities.

A derived unit is a combination of base units, obtained by multiplying or dividing them. Many have their own name:

• newton: N = kg m s⁻²
• joule: J = N m = kg m² s⁻²
• watt: W = J s⁻¹ = kg m² s⁻³
• pascal: Pa = N m⁻² = kg m⁻¹ s⁻²
• coulomb: C = A s
• volt: V = J C⁻¹ = kg m² s⁻³ A⁻¹
• ohm: Ω = V A⁻¹ = kg m² s⁻³ A⁻²

Worked example. Show that ½mv² has the unit of energy. m is in kg and v in m s⁻¹, so ½mv² has the unit kg (m s⁻¹)² = kg m² s⁻², which is the joule.

Prefixes multiply a unit by a power of ten:

• tera T = 10¹², giga G = 10⁹, mega M = 10⁶, kilo k = 10³
• centi c = 10⁻², milli m = 10⁻³, micro µ = 10⁻⁶
• nano n = 10⁻⁹, pico p = 10⁻¹², femto f = 10⁻¹⁵

Standard form writes a number as A × 10ⁿ with 1 ≤ A < 10, for example 532 nm = 5.32×10⁻⁷ m and 6.8 TeV = 6.8×10¹² eV. Use the prefix to convert, then express the result in standard form.

Energy has several units in common use.

• Electronvolt: 1 eV = 1.60×10⁻¹⁹ J (the charge e multiplied by 1 V). To convert eV to J multiply by 1.60×10⁻¹⁹; to convert J to eV divide by it.
• Kilowatt-hour: 1 kW h = 1000 W × 3600 s = 3.6×10⁶ J. To convert kW h to J multiply by 3.6×10⁶.

Worked example. A 2.2 kW kettle runs for 4.5 min. Time = 4.5 ÷ 60 = 0.075 h, so E = 2.2 × 0.075 = 0.165 kW h = 0.165 × 3.6×10⁶ = 5.9×10⁵ J.

The eV suits particle-scale energies, and the kW h suits domestic energy, because each gives numbers of a convenient size.