NCEA Level 2 Physics cheat sheet

Average speed = distance ÷ time; average velocity = displacement ÷ time. Acceleration = change in velocity ÷ time. Displacement, velocity and acceleration are vectors, so direction matters.

For constant acceleration: v = u + at; s = ut + ½at²; v² = u² + 2as. Choose a positive direction and apply the same sign convention to every quantity.

Newton's second law: net force F_net = ma. Weight W = mg acts downward; normal force is perpendicular to a surface; friction opposes relative motion.

Work W = Fd cosθ; kinetic energy E_k = ½mv²; change in gravitational potential energy ΔE_p = mgΔh. Mechanical energy is conserved when only conservative forces do work.

Power P = work ÷ time = Fv for a constant force parallel to velocity. Efficiency = useful output energy ÷ total input energy × 100%.

Momentum p = mv. Impulse Δp = FΔt equals the area under a force-time graph. Total momentum is conserved in an isolated system; kinetic energy is conserved only in elastic collisions.

Uniform circular motion: v = 2πr ÷ T; centripetal acceleration a_c = v² ÷ r; centripetal force F_c = mv² ÷ r, directed toward the centre.

Torque τ = Fd, where d is the perpendicular distance from the pivot. A body is in equilibrium when net force is zero and net torque is zero.

Projectile motion without air resistance: horizontal velocity is constant; vertical acceleration is g downward. Time of flight is found from the vertical motion.

Current I = Q ÷ t, where charge Q is in coulombs and time t is in seconds. Conventional current is the direction positive charge would flow.

Ohm's law V = IR applies to ohmic conductors at constant temperature. Resistance R = V ÷ I is measured in ohms (Ω).

Series circuit: the same current flows through each component; voltages add; R_total = R1 + R2 + ... . Parallel circuit: voltage is the same across branches; currents add; 1/R_total = 1/R1 + 1/R2 + ... .

Electrical power P = VI = I²R = V² ÷ R. Energy transferred E = Pt, in joules when power is in watts and time is in seconds.

Resistance of a uniform conductor: R = ρL ÷ A. Resistance increases with length L and resistivity ρ, and decreases as cross-sectional area A increases.

A current-carrying wire in a magnetic field experiences force F = BIL sinθ. The force is maximum when the wire is perpendicular to the field and zero when parallel.

Electromagnetic induction: induced emf is proportional to the rate of change of magnetic flux. Lenz's law states that the induced current opposes the change producing it.

Ideal transformer: V_s ÷ V_p = N_s ÷ N_p. Power is conserved, so V_pI_p = V_sI_s and I_s ÷ I_p = N_p ÷ N_s.

Uniform electric field between parallel plates: E = V ÷ d. Force on charge q is F = Eq, with direction depending on the sign of the charge.

Wave equation v = fλ, where v is wave speed, f is frequency and λ is wavelength. Period T = 1 ÷ f.

Transverse waves oscillate perpendicular to the direction of propagation, such as waves on a string. Longitudinal waves oscillate parallel to propagation, such as sound in air.

Law of reflection: angle of incidence equals angle of reflection, measured from the normal. Reflection does not change wave speed or frequency.

Refraction: Snell's law n1 sinθ1 = n2 sinθ2. Refractive index n = c ÷ v. Frequency stays constant, but speed and wavelength change when a wave enters a new medium.

Total internal reflection occurs only when light travels from a higher to a lower refractive index and the incidence angle exceeds the critical angle, where sinθ_c = n2 ÷ n1.

Diffraction is the spreading of waves after passing an opening or edge. It is more pronounced when the wavelength is comparable to the size of the gap or obstacle.

Two-source interference: constructive interference occurs when path difference = nλ; destructive interference occurs when path difference = (n + ½)λ, for integer n.

Standing waves have nodes of zero displacement and antinodes of maximum displacement. Adjacent nodes are separated by λ ÷ 2, and fixed ends are nodes.

Electromagnetic spectrum from longest to shortest wavelength: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma. All travel at c in a vacuum.

Atomic number Z equals the number of protons; mass number A equals protons plus neutrons. Isotopes have the same Z but different A.

Photon energy E = hf = hc ÷ λ, where h = 6.63 × 10^-34 J s. The electronvolt is useful: 1 eV = 1.60 × 10^-19 J.

Photoelectric effect: emission occurs when photon energy exceeds the work function φ. Maximum kinetic energy is E_k(max) = hf − φ; intensity changes the rate of emission, not the maximum electron energy.

Atomic line spectra arise from electron transitions between energy levels. An emission photon has energy equal to the difference between the higher and lower levels.

Alpha decay emits a helium-4 nucleus, decreasing mass number by 4 and atomic number by 2. Beta-minus decay changes a neutron into a proton and emits an electron and an antineutrino.

Radioactive decay is random and spontaneous. Half-life T½ is the time for half the nuclei in a sample to decay; after n half-lives the fraction remaining is (½)^n.

Activity A = λN, where λ = ln2 ÷ T½. Nuclear equations conserve mass number A and atomic number Z.

Mass defect Δm is the difference between a nucleus's mass and the sum of its separate nucleons' masses. Binding energy is ΔE = Δm c².

Fission splits a heavy nucleus; fusion combines light nuclei. Both release energy when the binding energy per nucleon of the products is greater than that of the reactants.