ORT Physics cheat sheet

Kinematic equations apply only for constant acceleration: v = u + at, s = ut + ½at², v² = u² + 2as.

Newton's second law in vector form: ΣF = ma; resolve forces into perpendicular components before summing.

Momentum is conserved in all collisions; kinetic energy is conserved only in elastic collisions.

Impulse equals change in momentum: J = FΔt = Δp, where F is the average force over the interval.

Uniform circular motion: a = v²/r directed toward the centre; period T = 2πr/v.

Work-energy theorem: net work done equals change in kinetic energy, W = ΔKE = ½mv² − ½mu².

Hooke's law for an ideal spring: F = −kx, with elastic potential energy U = ½kx².

Projectile motion: horizontal velocity constant, vertical acceleration g; time of flight depends only on vertical component.

For a body in equilibrium, both net force and net torque about any point are zero.

Ideal gas law: pV = nRT, with R = 8.31 J mol⁻¹ K⁻¹; temperature must be in kelvin.

First law of thermodynamics: ΔU = Q − W, where W is work done by the gas.

Mean kinetic energy of a gas molecule: ½m⟨c²⟩ = (3/2)kT, independent of molar mass.

Root-mean-square speed: c_rms = √(3kT/m) = √(3RT/M).

Isothermal process: pV = constant; adiabatic process: pV^γ = constant, with γ = C_p/C_v.

Work done by a gas at constant pressure: W = pΔV; on a p–V diagram, work is the area under the curve.

Specific latent heat: Q = mL for a phase change at constant temperature.

Carnot efficiency limit: η = 1 − T_cold/T_hot, with temperatures in kelvin.

Second law: entropy of an isolated system never decreases; heat flows spontaneously from hot to cold.

Coulomb's law: F = kQ₁Q₂/r², with k = 8.99 × 10⁹ N m² C⁻²; force is along the line joining charges.

Ohm's law for an ohmic conductor at constant temperature: V = IR.

Series: R_total = ΣR, current common; parallel: 1/R_total = Σ(1/R), voltage common.

Electrical power: P = VI = I²R = V²/R.

Magnetic force on a moving charge: F = qvB sin θ; on a current-carrying wire: F = BIL sin θ.

Force per unit length between parallel currents: F/L = μ₀I₁I₂/(2πd); like currents attract.

Faraday's law: induced emf ε = −N dΦ/dt; Lenz's law gives the direction opposing the change in flux.

Capacitance: C = Q/V; energy stored U = ½CV²; for parallel plates C = ε₀A/d.

Uniform field between parallel plates: E = V/d, directed from positive to negative plate.

Snell's law: n₁ sin θ₁ = n₂ sin θ₂; refractive index n = c/v.

Critical angle for total internal reflection: sin θ_c = n₂/n₁, valid only when n₁ > n₂.

Thin lens equation: 1/f = 1/u + 1/v, with magnification m = v/u; use sign conventions consistently.

For a converging lens, f is positive; for a diverging lens, f is negative.

Single-slit diffraction minima occur at a sin θ = nλ; double-slit maxima at d sin θ = nλ.

Young's double slit: fringe spacing Δy = λD/d for small angles.

Diffraction grating: d sin θ = nλ, giving sharper maxima than a double slit.

Photoelectric threshold: maximum kinetic energy K_max = hf − φ, where φ is the work function.

Polarisation by reflection obeys Brewster's law: tan θ_B = n₂/n₁.

Photon energy: E = hf = hc/λ, with h = 6.63 × 10⁻³⁴ J s.

Hydrogen energy levels: E_n = −13.6 eV/n²; spectral lines arise from electron transitions between levels.

de Broglie wavelength: λ = h/p = h/(mv).

Radioactive decay law: N = N₀e^(−λt); activity A = λN; half-life t½ = ln2/λ.

Alpha emission reduces mass number by 4 and atomic number by 2; beta-minus raises atomic number by 1.

Mass defect converts to binding energy via E = Δmc²; 1 u corresponds to about 931 MeV.

Binding energy per nucleon peaks near iron-56, so fusion releases energy for light nuclei and fission for heavy nuclei.

Nuclear radius scales as R = R₀A^(1/3), with R₀ ≈ 1.2 fm.

Photon emission and absorption lines are characteristic of the element; absorption lines appear dark against a continuous spectrum.

Absolute uncertainty of a reading is half the smallest scale division; of repeated readings, use half the range or the standard deviation.

Percentage uncertainty = (absolute uncertainty / measured value) × 100%.

When quantities are added or subtracted, absolute uncertainties add; when multiplied or divided, percentage uncertainties add.

A quantity raised to a power n has percentage uncertainty multiplied by |n|.

For a linearised graph y = mx + c, the gradient gives m and the intercept gives c; error bars show uncertainty.

A systematic error shifts all readings in one direction; a random error scatters readings about the mean.

Significant figures in a result should match the precision of the least precise input, not exceed it.

A micrometer screw gauge reads to 0.01 mm; a vernier caliper typically to 0.1 mm.

Repeat measurements and average to reduce random error; calibrate against a known standard to reduce systematic error.