Cambridge IAL Physics cheat sheet

SI base units: kg, m, s, A, K, mol, cd. Derived units are products/quotients; e.g. N = kg m s^-2, J = kg m^2 s^-2, Pa = kg m^-1 s^-2, W = kg m^2 s^-3, V = kg m^2 s^-3 A^-1, C = A s, Ω = kg m^2 s^-3 A^-2.

Kinematics: v = u + at, s = ut + ½at², v² = u² + 2as, s = ½(u+v)t. These apply only for constant acceleration in a straight line.

Newton's second law in the form F = Δp/Δt = ma holds when mass is constant; momentum p = mv is conserved in any collision or explosion provided no external resultant force acts.

Energy and work: W = Fs cosθ, KE = ½mv², ΔPE = mgΔh, elastic energy = ½Fx for a Hookean spring, power P = W/t = Fv. Efficiency = useful output / total input.

Circular motion: ω = 2π/T = v/r, a = v²/r = ω²r, centripetal force F = mv²/r. The force is always directed toward the centre; the velocity is tangential.

Waves: v = fλ, T = 1/f. For two-source interference, maxima occur where path difference = nλ, minima where path difference = (n + ½)λ.

Superposition and stationary waves: nodes are separated by λ/2; adjacent nodes and antinodes are λ/4 apart. Phase difference = (2π/λ) × path difference.

Electricity: V = W/Q, I = ΔQ/Δt, R = V/I, P = VI = I²R = V²/R. For series, R_total = ΣR; for parallel, 1/R_total = Σ(1/R).

Ideal gases and thermodynamics: pV = nRT = NkT, mean KE per molecule = (3/2)kT, ΔU = q + w where w is work done on the gas.

Particle accelerators (LHC, synchrotrons): charged particles are accelerated by RF cavities and steered by superconducting dipole magnets; radius r = p/(Bq) for a particle in a magnetic field.

PET scanning uses positron-emitting isotopes such as fluorine-18; annihilation of a positron and electron produces two 511 keV photons emitted back-to-back, detected in coincidence.

Medical imaging: X-ray attenuation depends on density and atomic number; ultrasound uses piezoelectric transducers with pulse-echo timing to locate boundaries.

Semiconductors: a p-n junction diode conducts in forward bias above ~0.7 V (silicon); LEDs emit photons with energy ≈ eV of the band gap; photodiodes and solar cells convert light to current.

Superconductors (e.g. NbTi, YBCO) have zero resistance below a critical temperature and expel magnetic flux (Meissner effect), enabling strong electromagnets and MRI scanners.

Nuclear power: fission of U-235 releases ~200 MeV per event; a moderator slows neutrons, control rods absorb them, and E = mc² quantifies mass defect.

Fibre optics: total internal reflection requires the ray to strike the core–cladding boundary above the critical angle, sin C = n_cladding/n_core.

Renewable generation: a wind turbine's power output scales as P ∝ Av³; a solar panel's output depends on irradiance and cell efficiency.

Uncertainty rules: for sums/differences add absolute uncertainties; for products/quotients add percentage uncertainties; for a power multiply the percentage uncertainty by the exponent.

Record readings to the resolution of the instrument; a single reading's uncertainty is typically ± half the smallest division, while a difference of two readings has uncertainty ± one division.

Plot the quantity that linearises the relation (e.g. T² against l for a pendulum) and use gradient = Δy/Δx with the largest triangle that fits the plotted points.

Uncertainty in a gradient from a graph is found from the steepest and shallowest lines consistent with the error bars.

Systematic errors shift all readings by a constant amount (e.g. zero error); random errors scatter readings and are reduced by repeating and averaging.

Precision describes the spread of repeated readings; accuracy describes closeness to the true value. A precise set can still be inaccurate.

Significant figures: the final answer should carry the same number of significant figures as the least precise input, usually 2–3 for experimental data.

When testing a relationship, compare the percentage difference between the experimental and theoretical values with the combined percentage uncertainty before concluding agreement.