CAPE Physics Unit 1 cheat sheet

Resolve vectors before applying F = ma or the SUVAT equations

Momentum is a vector: conserve each component only when the corresponding net external impulse is zero

Equilibrium requires both zero resultant force and zero resultant moment

The centripetal component points to the centre; uniform circular motion has constant speed but changing velocity

SHM signature: a = −ω²x, giving T = 2π/ω

State g and sign conventions explicitly at the start of a solution

Phase difference = 2π × path difference/λ

Stationary waves: node spacing λ/2, node–antinode λ/4, no energy transfer

Grating equation d sinθ = nλ with d = 1/N in metres

Young's slits: x = λD/a for small angles

Snell: n₁ sinθ₁ = n₂ sinθ₂; critical angle sinθc = n₂/n₁ requires n₁ > n₂

Keep one lens sign convention throughout and state it

Use kelvin in all gas-law and kinetic-theory calculations

Q = mcΔθ for temperature change; Q = mL for change of state

Mixtures: heat lost by hot bodies = heat gained by cold bodies plus calorimeter

pV = nRT and pV = ⅓Nm⟨c²⟩; mean KE = (3/2)kT

For a fixed amount of an ideal gas, internal energy depends only on temperature

First law: ΔU = Q − W with W defined as work done by the gas

Stress = force/original area; strain = extension/original length.

Young modulus = stress/strain within the specified linear elastic range.

Specimen stiffness depends on length, area and material properties.

One square millimetre equals 10^-6 square metres.

Elastic spring energy is one half kx squared in the linear model.

Elastic recovery, proportional response, yielding and fracture are distinct ideas.

SHM requires a restoring acceleration proportional to minus displacement.

For an ideal mass-spring model, omega = sqrt(k/m) and T = 2pi sqrt(m/k).

Maximum speed is omega A and total energy is kA squared divided by two.

Pendulum period formula requires the small-angle approximation.

Damping removes oscillator energy; a periodic drive can supply energy.

An ideal LC circuit has omega = 1/sqrt(LC).

State resolution and uncertainty convention for each instrument

Random errors → repeats and means; systematic errors → correction

For first-order worst-case bounds, add relative contributions; independent standard uncertainties use quadrature

Gradient from two points on the best-fit line, with units

Average repeated timings and time many oscillations to cut reaction error

Never quote more significant figures than the data justify