NCEA Level 3 Physics cheat sheet

Level 3 Physics is assessed through internally and externally assessed achievement standards; the external standards cover mechanical systems, wave systems, electrical systems, and modern physics, while internally assessed standards cover practical investigation and research-based contexts.

Each standard is graded Not Achieved, Achieved, Merit, or Excellence; Excellence requires demonstrating understanding of the underlying concepts and applying them to complex or unfamiliar situations, not merely correct calculation.

Mechanical systems standard: analyse motion under constant and changing acceleration, use Newton's laws, momentum and energy conservation, circular motion, rotational motion, and simple harmonic motion in translational and rotational contexts.

Wave systems standard: analyse interference, diffraction, and standing waves for mechanical and electromagnetic waves, including the Doppler effect for sound and light, and use the wave equation and superposition principles.

Electrical systems standard: analyse DC circuits with resistors, capacitors, and inductors, including transient behaviour, electromagnetic induction, and AC circuits, applying Kirchhoff's laws and phasor or algebraic methods.

Modern physics standard: analyse photoelectric effect, atomic spectra, nuclear binding energy and radioactive decay, and the wave–particle duality, using Einstein's photoelectric equation and mass–energy equivalence.

Internally assessed standards typically involve carrying out a practical physics investigation, processing and interpreting data with uncertainty analysis, and/or researching a physics-related issue and evaluating the physics involved.

For Excellence in practical investigations, candidates must justify the method, account for sources of uncertainty, and evaluate the validity of conclusions rather than just state results.

Achievement criteria are holistic: a candidate who makes a minor arithmetic slip but shows correct physical reasoning may still achieve at a higher level than one who obtains a correct answer with flawed physics.

Kinematic equations for constant acceleration: v = u + at; s = ut + ½at²; v² = u² + 2as; s = ½(u + v)t. These apply only when acceleration is uniform.

Newton's second law: F_net = ma. Always identify all forces on a body (weight, normal, tension, friction, applied) and resolve into components before applying the equation.

Momentum: p = mv. Conservation of momentum applies when no external net force acts on the system; for collisions and explosions, total momentum before equals total momentum after.

Impulse: J = FΔt = Δp. The area under a force–time graph gives impulse; a longer collision time reduces the average force for the same momentum change.

Work and energy: W = Fd cos θ; kinetic energy KE = ½mv²; gravitational potential energy ΔPE = mgΔh. Mechanical energy is conserved when only conservative forces do work.

Circular motion: centripetal acceleration a = v²/r = ω²r; centripetal force F = mv²/r. The centripetal force is provided by a real force (tension, gravity, friction), not an extra force.

Rotational motion: torque τ = rF sin θ; angular momentum L = Iω; rotational KE = ½Iω²; I depends on mass distribution about the axis.

Simple harmonic motion: a = −ω²x; period T = 2π√(m/k) for a mass–spring system, T = 2π√(l/g) for a simple pendulum. Energy oscillates between kinetic and potential.

Projectile motion: horizontal and vertical motions are independent; horizontal velocity is constant (no air resistance), vertical acceleration is g downward. Time of flight is determined by vertical motion.

Wave equation: v = fλ. Frequency is set by the source and does not change when a wave enters a new medium; speed and wavelength change.

Superposition: displacements of overlapping waves add algebraically. Constructive interference occurs when waves are in phase (path difference = nλ); destructive when out of phase (path difference = (n + ½)λ).

Two-source interference: for coherent sources separated by d, fringe spacing on a distant screen is Δy = λL/d, where L is the source-to-screen distance.

Diffraction grating: d sin θ = nλ, where d is the slit spacing and n is the order. Maxima occur at these angles; the central maximum is at θ = 0.

Single-slit diffraction: minima occur at a sin θ = nλ; the central maximum is twice as wide as the secondary maxima.

Standing waves on a string: fundamental frequency f₁ = v/(2L); harmonics are integer multiples f_n = nf₁. Nodes are points of zero displacement; antinodes have maximum displacement.

Standing waves in pipes: open pipe fundamental f₁ = v/(2L); closed pipe fundamental f₁ = v/(4L). Closed pipes support only odd harmonics.

Doppler effect for sound: observed frequency f' = f(v ± v_o)/(v ∓ v_s), where signs depend on whether observer and source move toward or away from each other.

Refraction: Snell's law n₁ sin θ₁ = n₂ sin θ₂; refractive index n = c/v. Total internal reflection occurs when the angle of incidence exceeds the critical angle sin θ_c = n₂/n₁ (n₁ > n₂).

Ohm's law: V = IR. Resistance of a wire R = ρL/A, so resistance increases with length and decreases with cross-sectional area.

Series circuits: same current through each component; total resistance R_total = R₁ + R₂ + …; voltages add. Parallel circuits: same voltage across each branch; 1/R_total = 1/R₁ + 1/R₂ + …; currents add.

Electrical power: P = VI = I²R = V²/R. Energy dissipated E = Pt.

Kirchhoff's laws: sum of currents at a junction is zero (charge conservation); sum of potential differences around a closed loop is zero (energy conservation).

Capacitors: charge Q = CV; energy stored E = ½CV² = ½QV. In a DC circuit, a capacitor charges with time constant τ = RC; after a long time it acts as an open circuit.

Inductors: oppose changes in current; energy stored E = ½LI². In a DC circuit, an inductor initially opposes current change and eventually acts as a short circuit.

Magnetic force on a current-carrying wire: F = BIL sin θ. Force on a moving charge: F = qvB sin θ; the force is perpendicular to both velocity and magnetic field.

Electromagnetic induction: Faraday's law EMF = −N ΔΦ/Δt; Lenz's law states the induced current opposes the change in magnetic flux that produced it.

AC circuits: RMS values V_rms = V_peak/√2; impedance Z = √(R² + (X_L − X_C)²); resonance occurs when X_L = X_C, giving minimum impedance and maximum current.

Photoelectric effect: photon energy E = hf = hc/λ; maximum kinetic energy of emitted electrons K_max = hf − φ, where φ is the work function. Emission occurs only if f exceeds the threshold frequency f₀ = φ/h.

Photon momentum: p = h/λ. Photons have zero rest mass but carry momentum, which is transferred in collisions such as Compton scattering.

Atomic energy levels: electrons occupy discrete energy levels; photon emission or absorption occurs when an electron transitions between levels, with ΔE = hf.

Atomic spectra: emission spectra show bright lines at wavelengths corresponding to transitions to lower energy levels; absorption spectra show dark lines where photons of matching energy are absorbed.

de Broglie wavelength: λ = h/p = h/(mv). Particles exhibit wave behaviour, demonstrated by electron diffraction.

Nuclear binding energy: mass defect Δm = (mass of nucleons) − (mass of nucleus); binding energy E = Δmc². Binding energy per nucleon peaks near iron-56, indicating maximum stability.

Radioactive decay: activity A = λN; decay constant λ = ln 2 / T_½. Number of undecayed nuclei follows N = N₀e^(−λt).

Half-life: after n half-lives, the fraction remaining is (½)^n. Half-life is independent of temperature, pressure, or chemical state.

Mass–energy equivalence: E = mc². In nuclear reactions, the energy released equals the mass defect multiplied by c²; this accounts for the energy of fission and fusion.