North Rhine-Westphalia Zentralabitur Physics 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

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

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

γ = 1/√(1 − v²/c²) ≥ 1.

Dilatación temporal: Δt = γ·Δt₀; contracción: L = L₀/γ.

p = γmv y E = γmc²; E_k = (γ − 1)mc².

E² = p²c² + m²c⁴; para el fotón E = pc.

El tiempo propio se mide en el sistema donde los sucesos ocurren en el mismo lugar.

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).

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

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