🧠 Learn in groups
Learn them by topic: motion, energy, electricity, waves, pressure. Five or six equations at a time is enough. Say each one in words first, then give the symbols and the units.
The Exam Papers » Equations to Learn and Equations Given
What you'll learn this session
Study time: 30 minutes
Edexcel spec: Physics formulae for relationships (Appendix 7)
- Know which equations you must learn and which are printed on the formulae page
- Know the symbol and unit of every one
- Use a routine to memorise them
- Choose the right equation from the quantities in a question
🔒 Unlock Full Course Content
Sign up to access the complete lesson and track your progress!
Unlock This CourseLearnt or given?
The exam does not treat every equation the same way. Some you must learn. They are not printed in the paper, and they are not given in rearranged form either. In the spec these are the points worded "know and use the relationship". Others are printed on the formulae page of the exam paper. You still have to know how to use them, but you do not have to remember them.
This lesson only organises the equations and helps you recall them. The physics behind each one is taught in its own lesson. Rearranging is covered in the lesson Maths Skills: Algebra and Units.
Key terms:
- Formulae page: the page of equations printed in the exam paper.
Equations you must learn
| Equation in words | Symbols | Units | Paper |
|---|---|---|---|
| average speed = distance moved / time taken | v = s / t | m/s | 1 and 2 |
| force = mass × acceleration | F = m × a | N, kg, m/s2 | 1 and 2 |
| acceleration = change in velocity / time taken | a = (v − u) / t | m/s2 | 1 and 2 |
| momentum = mass × velocity | p = m × v | kg m/s | Paper 2 only |
| density = mass / volume | ρ = m / V | kg/m3 | 1 and 2 |
| work done = force × distance moved | W = F × d | J, N, m | 1 and 2 |
| energy transferred = work done | E = W | J | 1 and 2 |
| kinetic energy = ½ × mass × speed2 | KE = ½ × m × v2 | J, kg, m/s | 1 and 2 |
| gravitational potential energy = mass × g × height | GPE = m × g × h | J, kg, N/kg, m | 1 and 2 |
| weight = mass × gravitational field strength | W = m × g | N, kg, N/kg | 1 and 2 |
| pressure = force / area | p = F / A | Pa, N, m2 | 1 and 2 |
| moment = force × perpendicular distance from the pivot | moment = F × d | N m | Paper 2 only |
| charge = current × time | Q = I × t | C, A, s | 1 and 2 |
| voltage = current × resistance | V = I × R | V, A, Ω | 1 and 2 |
| electrical power = voltage × current | P = I × V | W, A, V | 1 and 2 |
| energy transferred = charge × voltage | E = Q × V | J, C, V | 1 and 2 |
| wave speed = frequency × wavelength | v = f × λ | m/s, Hz, m | 1 and 2 |
| primary voltage / secondary voltage = primary turns / secondary turns | Vp / Vs = Np / Ns | V (turns have no unit) | Paper 2 only |
| refractive index | n = sin i / sin r | no unit | 1 and 2 |
| refractive index and critical angle | sin c = 1 / n | no unit | 1 and 2 |
| efficiency = (useful energy output / total energy output) × 100% | no symbol | % | 1 and 2 |
| pressure difference = height × density × gravitational field strength | p = h × ρ × g | Pa, m, kg/m3, N/kg | 1 and 2 |
| input power = output power (100% efficient transformer) | Vp × Ip = Vs × Is | V, A | Paper 2 only |
Symbol clashes
W means both work done and weight. p means both pressure and momentum. Read the quantities in the question to see which one is meant, and always give the unit.
Equations given on the formulae page
| Equation | Symbols | Paper |
|---|---|---|
| (final speed)2 = (initial speed)2 + 2 × acceleration × distance moved | v2 = u2 + 2as | 1 and 2 |
| force = change in momentum / time taken | F = (mv − mu) / t | Paper 2 only |
| energy transferred = current × voltage × time | E = I × V × t | 1 and 2 |
| frequency = 1 / time period | f = 1 / T | 1 and 2 |
| power = work done / time taken | P = W / t | 1 and 2 |
| change in thermal energy = mass × specific heat capacity × change in temperature | ΔQ = m c ΔT | Paper 2 only |
| pressure of a gas at constant volume | p1 / T1 = p2 / T2 | 1 and 2 |
| pressure and volume of a gas at constant temperature | p1V1 = p2V2 | 1 and 2 |
| orbital speed | v = 2πr / T | 1 and 2 |
| red-shift | Δλ / λ0 = v / c | Paper 2 only |
Paper 2 only
These are examined in Paper 2 only: momentum, moment, the two transformer equations, F = (mv − mu) / t, ΔQ = m c ΔT and the red-shift equation. Paper 1 never asks for them.
A routine for memorising
📝 Cover and recall
Cover the table and write a group from memory. Check it, circle your mistakes, and try only those again tomorrow. Do it again after three days. The flash cards for this lesson help here.
Use units as clues. Newtons go with force and weight. Pascals go with pressure. Joules go with energy. Watts go with power. A unit you remember can lead you back to the equation.
Choosing the right equation
Write down every quantity you are given, and the one you want. Then find the equation that contains exactly those quantities.
| You have | You want | Equation |
|---|---|---|
| mass and speed | energy | KE = ½ × m × v2 |
| current and time | charge | Q = I × t |
| force and area | pressure | p = F / A |
| frequency and wavelength | wave speed | v = f × λ |
| current and resistance | voltage | V = I × R |
| refractive index | critical angle | sin c = 1 / n |
If two equations seem to fit, check the units given in the question. They usually point to the right one.
Worked examples
Worked example 1
A trolley of mass 0.40 kg moves at 6.0 m/s. Calculate its kinetic energy.
Quantities: mass and speed, so use KE = ½ × m × v2.
KE = ½ × 0.40 × 6.02 = ½ × 0.40 × 36 = 7.2 J
Worked example 2
A current of 0.50 A flows for 40 s through a 12 V lamp. Calculate the energy transferred.
Two steps. First the charge, Q = I × t = 0.50 × 40 = 20 C.
Then the energy, E = Q × V = 20 × 12 = 240 J.
Check: E = I × V × t from the formulae page gives 0.50 × 12 × 40 = 240 J as well.
Worked example 3
Glass has a refractive index of 1.5. Calculate the critical angle.
sin c = 1 / n = 1 / 1.5 = 0.667
c = sin-1(0.667) = 42° (to the nearest degree)
Common mistakes
Common mistakes
- Trying to find a learnt equation on the formulae page. Learn it.
- Using g in the wrong place. Weight and GPE both use g, but KE does not.
- Forgetting to square the speed in KE, or squaring the half as well.
- Mixing up W for work done and weight.
- Leaving out the unit, or using g/cm3 when the question needs kg/m3.
Exam-style question
(a) Write down the equation that links voltage, current and resistance. [1 mark]
(b) A lamp has a current of 0.50 A at a voltage of 12 V. Calculate its electrical power. [2 marks]
(c) A block has a mass of 0.60 kg and a volume of 0.00020 m3. Calculate its density. [2 marks]
(d) State whether f = 1 / T must be learnt or is printed on the formulae page. [1 mark]
Model answer
(a) voltage = current × resistance (1)
(b) P = I × V (1) = 0.50 × 12 = 6.0 W (1)
(c) density = mass / volume = 0.60 / 0.00020 (1) = 3000 kg/m3 (1)
(d) It is printed on the formulae page. (1)
Exam tip
Write the equation, the substitution and the answer with its unit on separate lines. If you pick the right equation, you can earn marks even when the arithmetic slips.