Units & Calculations
- There are a seemingly endless number of units in Physics
- These can all be reduced to seven base units from which every other unit can be derived
- These seven units are referred to as the SI Base Units; this is the only system of measurement that is officially used in almost every country around the world
SI Base Quantities Table
- The seventh SI base unit is the candela (cd) which is the unit for luminosity
- This is not encountered at GCSE
Derived Units
- The seven SI base units are then used to derive other common units
- The base units of physical quantities such as:
- Newtons, N [kg m / s2]
- Joules, J [N m]
- Pascals, Pa [kg / m s2]
- To deduce the base units, it is necessary to use the definition of the quantity
- The Newton (N), the unit of force, is defined by the equation:
- Force = mass × acceleration
- N = kg × m s–2 = kg m s–2
- Therefore, the Newton (N) in SI base units is kg m s–2
- The Joule (J), the unit of energy, is defined by the equation:
- Energy = ½ × mass × velocity2
- J = kg × (m s–1)2 = kg m2 s–2
- Therefore, the Joule (J) in SI base units is kg m2 s–2
- The Pascal (Pa), the unit of pressure, is defined by the equation:
- Pressure = force ÷ area
- Pa = N ÷ m2 = (kg m s–2) ÷ m2 = kg m–1 s–2
- Therefore, the Pascal (Pa) in SI base units is kg m–1 s–2
Common Units Table
Prefix Notation
- Physical quantities can span a huge range of values
- For example, the diameter of an atom is about 10–10 m (0.0000000001 m), whereas the width of a galaxy may be about 1021 m (1,000,000,000,000,000,000,000 m)
- This is a difference of 31 powers of ten
- Powers of ten are numbers that can be achieved by multiplying 10 times itself
- These come under two categories of units:
- Multiples eg. 102, 103
- Sub-multiples eg. 10−1, 10−2
- Each power of ten is defined by a prefix, these are listed in the table below:
Prefixes Table
- Example conversions:
- 12 GPa = 12 gigapascals = 12 × 109 Pa (12 000 000 000 Pa)
- 5 kN = 5 kilonewtons = 5 × 103 N (5000 N)
- 0.1 μA = 0.1 microamps = 1 × 10–7 A (0.0000001 A)
- 7 nC = 7 nanocoulombs = 7 × 10–9 C (0.000000007 C)
Unit Conversions
- As well as prefix (powers of ten) conversions (eg. km into m) there are also common unit conversions
Time Conversions
- One such unit conversion are those for time
- The main time conversions are shown in the table below:
Time Conversions Table
- A common time unit conversion is between hours and seconds
- 1 hour = 60 minutes
- 1 minute = 60 seconds
- Therefore 1 hour = 60 × 60 = 3600 seconds
- To convert from hours → seconds, multiply by 3600
- To convert from seconds → hours, divide by 3600
Hours × 3600 = Seconds
Temperature Conversions
- Another common temperature unit conversion is between Kelvin and degrees Celsius (ºC)
- The scale is defined as: 0 K = −273.15 ºC
- To convert from Kelvin → Celsius, subtract 273
- To convert from Celsius → Kelvin, add 273
K − 273 = oC
oC + 273 = K
Examiner Tip
Sometimes marks in an exam question are given for the unit, so make sure you remember which is the correct one for the quantity in your answer e.g. If the answer is a force, it must have the units of Newtons (N).
You will often see very large or very small numbers categorised by powers of ten, so it is very important you become familiar with these as getting these prefixes wrong is a very common exam mistake!
