IB Physics HL cheat sheet

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

Projectile motion: horizontal component has zero acceleration; vertical component has a = −g (9.81 m/s²). Time of flight from vertical motion alone.

Newton's second law in IB form: F_net = ma, and F_net = Δp/Δt is valid when mass changes (e.g. rocket).

Momentum is conserved in all collisions; kinetic energy is conserved only in elastic collisions. Impulse J = FΔt = Δp equals area under an F–t graph.

Work done W = Fs cos θ; work–energy theorem: W_net = ΔE_k. Power P = W/t = Fv.

Circular motion: v = ωr, a = v²/r = ω²r, F_c = mv²/r directed toward the centre. Angular velocity ω = 2π/T.

Gravitation: F = GMm/r²; g = GM/r². Orbital speed v = √(GM/r); Kepler's third law T² = (4π²/GM)r³ for circular orbits.

Gravitational potential energy U = −GMm/r (zero at infinity); gravitational potential V = −GM/r. Total orbital energy E = −GMm/(2r).

Ideal gas law: pV = nRT = NkT, with k = R/N_A = 1.38 × 10⁻²³ J/K. Use T in kelvin.

Kinetic theory: average translational kinetic energy per molecule = (3/2)kT; internal energy of an ideal gas depends only on T.

Root-mean-square speed: v_rms = √(3kT/m) = √(3RT/M). Lighter molecules have higher v_rms at the same T.

First law of thermodynamics: ΔU = Q − W (W is work done by the gas). Q > 0 means heat added to the system.

Specific heat capacity: Q = mcΔT. Specific latent heat: Q = mL, applied at constant temperature during a phase change.

Work done by a gas at constant pressure: W = pΔV (area under a p–V graph). For an isothermal process pV = constant.

Absolute zero is 0 K = −273.15 °C. Pressure and volume extrapolate to zero at 0 K for an ideal gas.

Simple harmonic motion: a = −ω²x; x = x₀ cos(ωt); v_max = ωx₀; a_max = ω²x₀. Period T = 2π/ω.

For a mass–spring system ω = √(k/m); for a simple pendulum ω = √(g/L) (small angles only).

Wave equation: v = fλ. For a wave on a string v = √(T/μ). Intensity ∝ amplitude².

Superposition: constructive when path difference = nλ; destructive when path difference = (n + ½)λ.

Two-source interference: fringe spacing for double slit Δy = λD/d. Diffraction grating maxima at d sin θ = nλ.

Single-slit diffraction: first minimum at sin θ = λ/b (b = slit width). Diffraction is significant when λ ≈ b.

Doppler effect for sound: observed frequency f' = f(v ± v_o)/(v ∓ v_s), signs chosen so approaching source raises f'.

Standing waves: nodes separated by λ/2. Open pipe: fundamental λ = 2L; closed pipe: fundamental λ = 4L.

Field strength is force per unit mass (g = F/m) or per unit charge (E = F/q). Field lines point in the direction of force on a positive test charge or mass.

Uniform field between parallel plates: E = V/d. Point charge field: E = kQ/r² with k = 1/(4πε₀) = 8.99 × 10⁹ N·m²/C².

Electric potential V = kQ/r; potential energy U = qV. Potential is a scalar; field is the negative gradient of potential.

Magnetic force on a moving charge: F = qvB sin θ; on a current-carrying wire: F = BIL sin θ. Direction by Fleming's left-hand rule.

Force between parallel wires: F/L = μ₀I₁I₂/(2πd). Field from a long straight wire: B = μ₀I/(2πr). Field inside a solenoid: B = μ₀nI.

Magnetic flux Φ = BA cos θ; flux linkage = NΦ. Faraday's law: induced emf ε = −N ΔΦ/Δt.

Lenz's law: induced current opposes the change in flux. Motional emf for a rod: ε = BvL.

Transformers: V_s/V_p = N_s/N_p = I_p/I_s (ideal, 100% efficiency assumed).

Radioactive decay: N = N₀e^(−λt); activity A = λN; half-life T½ = ln2/λ ≈ 0.693/λ.

Alpha decay reduces A by 4 and Z by 2; beta-minus increases Z by 1 (A unchanged); gamma emission changes neither A nor Z.

Mass defect and binding energy: E = Δmc². 1 u = 931.5 MeV/c². Binding energy per nucleon peaks near iron-56.

Photoelectric effect: photon energy E = hf = hc/λ; maximum kinetic energy E_k,max = hf − φ, where φ is the work function.

Threshold frequency f₀ = φ/h. Stopping voltage V_s satisfies eV_s = E_k,max. Intensity affects current, not maximum kinetic energy.

Atomic energy levels: photon energy equals the energy difference between levels, hf = E₂ − E₁. Line spectra are characteristic of each element.

de Broglie wavelength: λ = h/p = h/(mv). Electron diffraction confirms wave behaviour of particles.

Quantum tunnelling: a particle can pass through a potential barrier with probability that decreases exponentially with barrier width and height, even when E < barrier height.

The IA report is marked on five criteria (A–E), each out of 6: research design, data collection, data analysis, evaluation, and communication.

Research question must identify the independent and dependent variables and be focused enough to investigate within the available time and equipment.

Methodology must be reproducible: specify apparatus, measurement technique, control of variables, and the range and number of data points.

Uncertainty: for a single reading use the instrument resolution; for repeated readings use half the range. Combine uncertainties for derived quantities.

Analysis should include a graph with error bars, a line of best fit, and a gradient/intercept with its uncertainty compared to the theoretical value.

Evaluation must discuss systematic vs random error, realistic sources of uncertainty, and concrete improvements rather than generic statements.

Personal engagement and safety/ethical considerations are expected in the design and evaluation sections.

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

Projectile motion: horizontal component has zero acceleration; vertical component has a = −g (9.81 m/s²). Time of flight is set by vertical motion alone.

Newton's second law in IB form: F_net = ma, and F_net = Δp/Δt is valid when mass changes (e.g. rocket).

Momentum is conserved in all collisions; kinetic energy is conserved only in elastic collisions. Impulse J = FΔt = Δp equals area under an F–t graph.

Work done W = Fs cos θ; work–energy theorem: W_net = ΔE_k. Power P = W/t = Fv.

Circular motion: v = ωr, a = v²/r = ω²r, F_c = mv²/r directed toward the centre. Angular velocity ω = 2π/T.

Gravitation: F = GMm/r²; g = GM/r². Orbital speed v = √(GM/r); Kepler's third law T² = (4π²/GM)r³ for circular orbits.

Gravitational potential energy U = −GMm/r (zero at infinity); gravitational potential V = −GM/r. Total orbital energy E = −GMm/(2r).