FTCE Physics 6-12 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

EMF is per unit charge from the source; terminal p.d. is E − Ir

Kirchhoff's laws follow from conservation of charge and energy

Capacitor energy is ½CV²; discharge is exponential with time constant RC

Magnetic-force magnitude is |q|vB sinθ and its vector is perpendicular to velocity, so magnetic force does no work

Lenz's law: induced effects oppose the change that causes them

RMS values: I₀/√2 and V₀/√2 for sinusoidal quantities

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

hf = φ + KEmax; intensity affects rate, not maximum energy

Threshold frequency f₀ = φ/h in the ordinary single-photon model; below it that model predicts no photoemission

hf = E₂ − E₁ explains line spectra

λ = h/p generally; p = mv for a nonrelativistic massive particle

α: A−4, Z−2; β⁻: Z+1; γ: no change in A or Z

N = N₀e^(−λt) with t½ = ln2/λ; 1 u c² is approximately 931.5 MeV

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

Use homogeneity of units to check any equation

Resolve vectors into components before adding them

Choose axes that give a straight line; state what the gradient means

Gradient units come from the axis units, not the formula

Area under a graph and intercepts often carry physical meaning

Convert all data to SI before calculating gradients

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