IB Physics SL cheat sheet

Random uncertainty reduces by averaging repeated readings; systematic uncertainty shifts all readings the same way and is not reduced by repetition.

Absolute uncertainty of a single analogue reading: half the smallest scale division; for a digital display, the last digit place value.

For addition/subtraction: absolute uncertainties add, Δz = Δx + Δy.

For multiplication/division: fractional (percentage) uncertainties add, Δz/z = Δx/x + Δy/y.

Powers: if z = x^n then Δz/z = |n|·Δx/x; for z = kx^a y^b, fractional uncertainties combine as |a|Δx/x + |b|Δy/y.

Uncertainty in a mean of n readings: Δ(mean) = Δ(single reading)/√n when random.

Scalar vs vector: displacement, velocity, acceleration, force are vectors; distance, speed, mass, energy are scalars.

SI base units: m, kg, s, A, K, mol, cd; derived unit checks via dimensional analysis (e.g. N = kg·m·s⁻², J = kg·m²·s⁻²).

Graph linearisation: plot y vs x^n to obtain a straight line when the relation is y = kx^n; gradient gives k, intercept gives the constant term.

Equations of uniformly accelerated motion: v = u + at; s = ut + ½at²; v² = u² + 2as; s = (u+v)t/2.

Newton's second law: resultant force F = ma; weight W = mg with g ≈ 9.81 m·s⁻² near Earth's surface.

Friction: limiting static friction f ≤ μsN; kinetic friction f = μkN, acting opposite to relative motion.

Momentum p = mv is conserved in any collision or explosion in the absence of external resultant force.

Impulse J = FΔt = Δp; area under a force–time graph equals impulse.

Work W = Fs cosθ; kinetic energy KE = ½mv²; gravitational potential energy ΔPE = mgΔh near Earth.

Energy conservation: in elastic collisions KE is conserved; in inelastic collisions KE is lost but momentum is still conserved.

Power P = W/t = Fv; efficiency = useful output energy / total input energy.

Hooke's law F = kx; elastic potential energy E = ½kx²; area under a force–extension graph gives stored energy.

Internal energy is the sum of random kinetic and intermolecular potential energies of the particles of a substance.

Temperature in kelvin: T(K) = T(°C) + 273.15; absolute zero is 0 K, where particle kinetic energy is minimum.

Specific heat capacity: Q = mcΔT; specific latent heat: Q = mL for a phase change at constant temperature.

Ideal gas equation: pV = nRT with R = 8.31 J·mol⁻¹·K⁻¹; alternatively pV = NkT with k = 1.38×10⁻²³ J·K⁻¹.

Kinetic theory: average kinetic energy of a molecule = (3/2)kT, independent of gas identity.

Pressure of an ideal gas arises from molecular collisions with container walls; pV = (1/3)Nm⟨c²⟩ gives root-mean-square speed.

First law of thermodynamics: ΔU = Q − W, where W is work done by the gas (sign conventions must be stated).

Molar mass and density link: ρ = pM/(RT) for an ideal gas; n = m/M.

Wave equation: v = fλ; frequency is set by the source, speed by the medium.

Transverse waves oscillate perpendicular to propagation (light, string waves); longitudinal waves oscillate parallel (sound).

Simple harmonic motion: a = −ω²x, with ω = 2π/T = 2πf; period of a mass–spring system T = 2π√(m/k).

Energy in SHM: total energy ∝ amplitude²; KE is maximum at equilibrium, PE maximum at extremes.

Superposition: in-phase waves add constructively (path difference = nλ), antiphase waves cancel (path difference = (n+½)λ).

Standing waves on a string fixed at both ends: λ = 2L/n; for a pipe open at both ends λ = 2L/n; closed at one end λ = 4L/(2n−1).

Doppler effect for a moving source: observed f′ = f·v/(v ± vs), with the sign chosen so approach increases frequency.

Double-slit interference: fringe spacing s = λD/d; single-slit diffraction spreads more when the slit width is comparable to λ.

Snell's law n₁sinθ₁ = n₂sinθ₂; refractive index n = c/v; total internal reflection when θ > critical angle sinθc = n₂/n₁.

Ohm's law V = IR holds for ohmic conductors at constant temperature; resistance R = ρL/A.

Series: R_total = R₁ + R₂ + …; current is the same through each component.

Parallel: 1/R_total = 1/R₁ + 1/R₂ + …; voltage is the same across each branch.

Electrical power: P = VI = I²R = V²/R; energy = power × time.

Kirchhoff's laws: sum of currents at a junction is zero; sum of emf values equals sum of potential drops around a loop.

emf is the work done per unit charge by the source; terminal voltage V = ε − Ir with internal resistance r.

Magnetic force on a current-carrying wire F = BIL sinθ; on a moving charge F = qvB sinθ, direction by Fleming's left-hand rule.

Magnetic flux Φ = BA cosθ; induced emf ε = −NΔΦ/Δt (Faraday); direction opposes change (Lenz).

Charged particle in a uniform magnetic field moves in a circle of radius r = mv/(qB).

Angular velocity ω = 2π/T = v/r; linear speed v = ωr.

Centripetal acceleration a = v²/r = ω²r, directed toward the centre; centripetal force F = mv²/r.

Centripetal force is provided by a real force (tension, gravity, friction, normal force), never a separate outward force.

Newton's law of gravitation: F = Gm₁m₂/r² with G = 6.67×10⁻¹¹ N·m²·kg⁻².

Gravitational field strength g = GM/r²; gravitational potential energy U = −GMm/r (zero at infinity).

Orbital speed for a circular orbit: v = √(GM/r); period T² = (4π²/GM)r³ (Kepler's third law).

Geostationary orbit: period 24 h, equatorial plane, same direction as Earth's rotation.

Gravitational field strength is the gravitational force per unit mass; gravitational potential is potential energy per unit mass.

Photon energy E = hf = hc/λ with h = 6.63×10⁻³⁴ J·s; 1 eV = 1.60×10⁻¹⁹ J.

Photoelectric effect: emission occurs only if hf ≥ work function Φ; maximum KE = hf − Φ; supports photon model.

Atomic energy levels: photon emitted when an electron drops between levels, energy = E_upper − E_lower.

Line spectra arise from discrete energy levels; the hydrogen spectrum follows E = −13.6 eV/n².

Nuclear notation: A = nucleon number, Z = proton number; isotopes have same Z, different A.

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

Alpha decay reduces A by 4 and Z by 2; beta-minus decay converts a neutron to a proton (Z +1, A unchanged); gamma emission changes neither A nor Z.

Mass defect and binding energy: E = Δmc²; binding energy per nucleon peaks near iron-56.

Standard model: quarks (u, d) and leptons (electron, neutrino) are fundamental; hadrons (baryons, mesons) are quark composites; exchange bosons mediate forces.

Energy density of a fuel = energy released per unit mass or volume; specific energy is per unit mass.

Renewable sources: solar, wind, hydroelectric, tidal, wave, geothermal, biomass; fossil fuels and nuclear are non-renewable.

Nuclear fission of uranium-235 releases energy via mass defect; controlled chain reaction in a reactor with moderator and control rods.

Nuclear fusion (e.g. deuterium–tritium) releases more energy per nucleon than fission but requires very high temperature.

Solar constant ≈ 1.36 kW·m⁻² at Earth; incident power on a panel P = I·A·cosθ.

Wind power available P = ½ρAv³; output depends on the cube of wind speed.

Hydroelectric power P = ρgQh, where Q is volume flow rate and h is the head.

Sankey diagrams represent energy transfers; efficiency = useful output / total input, with losses mainly as thermal energy.

Greenhouse effect: certain gases absorb and re-emit infrared radiation, raising the mean surface temperature.