This cheat sheet puts every formula tested in O-Level Pure Physics into one reference, grouped as the syllabus topics are examined, from measurement and kinematics through to magnetism and electromagnetism. Each formula comes with its symbols, SI units and when to use it.
Use it when you know the type of question but need the exact symbol or unit. Unless a question states otherwise, take g = 10 N/kg. Some papers use 9.8 N/kg, so always use the value given in the question.
What these notes cover
- •Measurement and uncertainty
- •Kinematics and equations of motion
- •Dynamics: forces and momentum
- •Mass, weight and density
- •Turning effects of forces
- •Pressure
- •Energy, work and power
- •Kinetic particle model of matter
- •Thermal physics
- •Waves and light
- •Electricity
- •Magnetism and electromagnetism
Key definitions
- Zero error
- A systematic, not random, error. Subtract it once from every reading. Repeating and averaging the readings will not remove it.
- Weight
- The force due to gravity on a mass, W = mg, measured in N. Mass (kg) is the same everywhere, but weight changes with g.
- Moment of a force
- The rotational effect of a force about a pivot, equal to F × d. Here d is the perpendicular distance from the pivot to the line of action of the force.
- Principle of moments
- For an object in rotational equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments.
- Critical angle
- The threshold angle for total internal reflection, where sin(c) = 1 ÷ n. Total internal reflection only occurs when light goes from a denser medium into a less dense one, such as glass → air.
Key formulas
Equation of motion (time not given)
v² = u² + 2as
u: initial velocity, v: final velocity (m/s); a: acceleration (m/s²); s: displacement (m). Use this to find velocity or displacement when time is not given.
Conservation of momentum
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Subscripts 1 and 2 identify the objects; u: velocity before, v: velocity after. Applies to collisions and explosions in a closed system. Assign + and − directions before adding momenta.
Pressure in a liquid
p = hρg
p: pressure (Pa); h: height of liquid column (m); ρ: liquid density (kg/m³); g: gravitational field strength (N/kg). h must be in metres and must be the vertical depth.
Heating without a change of state
Q = mcΔθ
Q: heat energy (J); m: mass (kg); c: specific heat capacity J/(kg·°C); Δθ: temperature change (°C). It does not apply during melting or boiling. Use Q = mL for those.
Wave equation
v = fλ
v: wave speed (m/s); f: frequency (Hz); λ: wavelength (m). Applies to any wave, transverse or longitudinal. Multiply f by λ. Do not divide.
Electrical power
P = IV = I²R = V² ÷ R
P: power (W); I: current (A); V: p.d. (V); R: resistance (Ω). Choose the version that matches the quantities given.
Worked example
A 4 Ω resistor is connected in series with a parallel combination of a 6 Ω resistor and a 3 Ω resistor. A battery supplies 12 V across the whole combination. Find the total resistance and the current drawn from the battery.
- 1Work out the parallel section first: 1 ÷ Rₚ = 1 ÷ 6 + 1 ÷ 3 = 1 ÷ 6 + 2 ÷ 6 = 3 ÷ 6, so Rₚ = 2 Ω.
- 2Add the series resistor: R(total) = 4 + 2 = 6 Ω.
- 3Find the current drawn from the battery: I = V ÷ R(total) = 12 ÷ 6 = 2 A.
Watch out: Series and parallel are the two formulas students swap most often in the whole syllabus. In series, add the resistances directly. In parallel, add their reciprocals.
Common mistakes
Depth in the wrong unit or direction
Wrong: Putting h into p = hρg in cm, or using a slant or horizontal distance.
Right: Convert h to metres and use the vertical depth of the liquid column.
Averaging away a zero error
Wrong: Repeating and averaging readings to remove a zero error.
Right: A zero error is systematic. Subtract it once from every reading.
Step-up transformer current
Wrong: Assuming a step-up transformer raises the current as well as the voltage.
Right: In a step-up transformer, Nₛ > Nₚ and Vₛ > Vₚ, but Iₛ < Iₚ. The voltage goes up and the current goes down, since power is roughly conserved.
Questions students ask
What value of g should I use in O-Level Physics?
Unless a question states otherwise, take g = 10 N/kg. Some papers use 9.8 N/kg, so always use the value given in the question.
How do I know which equation of motion to use?
Note which variables the question gives and which one is unknown. Use v = u + at when displacement is not given, s = ut + ½at² when final velocity is not given, and v² = u² + 2as when time is not given.
Is the lens formula tested in O-Level Physics?
No. The lens formula 1 ÷ f = 1 ÷ u + 1 ÷ v belongs to A-Level. Find the image position, size and nature with an accurate scale ray diagram. Draw the ray parallel to the axis, which bends through F, and the ray through the optical centre, which passes through undeviated.
Can efficiency be more than 100%?
No. An efficiency above 100% means an arithmetic or unit slip, not a very efficient machine. The same is true of any ratio-based answer that exceeds its natural limit, such as sin r > 1.
In the full PDF
- •Formulas for all 13 syllabus topics, each with symbols, SI units and when to use it
- •Two further worked examples: a collision using conservation of momentum, and a critical-angle question on total internal reflection
- •The remaining exam tips, including sign conventions for deceleration and momentum, the conditions for Boyle's Law, and heat during a change of state
- •The full electricity and electromagnetism formulas, including the motor effect, transformers and electrical energy
- •A closing summary of five checks: SI units, choosing the right equation, sign conventions, ratio limits and dimensional checks