One line each, in the words of the Part glossary it came from. The Roman numeral is the Part: I Mechanics · II Waves · III Thermodynamics · IV Optics · V Electromagnetism · VI Modern Physics.
A15
acceleration I rate of change of velocity (slope of v–t; area under a–t gives Δv). The constant-a equations below hold only when a is constant.
Accommodation IV the lens reshaping to focus both.
achromatic doublet IV An achromatic doublet (converging crown + diverging flint, cemented) cancels it: ω₁/f₁ + ω₂/f₂ = 0.
Adiabatic III no heat exchange (ΔQ = 0): PVᵞ = const, TVᵞ⁻¹ = const; the gas cools on expansion.
Amplitude A II greatest displacement.
Ampère's law V ∮B·dl = μ₀Ienc: the circulation of B counts the threading current. Gives the solenoid (uniform inside, ~0 outside) and toroid instantly.
Angle of deviation (δ) IV the turn between incident and emergent rays. As i increases, δ falls to a minimum δm then rises; at δm the passage is symmetric (i₁ = i₂, r₁ = r₂ = A/2) and the ray inside runs parallel to the base.
Angle of friction λ I resultant of N and f leans at tan λ = μ.
Angle of repose θᵣ I steepest slope a block rests on: tan θᵣ = μₛ; independent of mass.
Angular frequency II ω = 2πf.
Angular momentum I Angular momentum L = Iω conserved with no external torque (the skater's spin).
Anomalous expansion of water III water is densest at 4 °C; between 0 and 4 °C it contracts on heating — why ponds freeze top-down and aquatic life survives.
antinodes II Fixed nodes (always still) and antinodes (largest swing); no net energy transport.
Apparent depth IV an object in a denser medium looks nearer the surface.
Archimedes' principle I upthrust = weight of fluid displaced; float when average density < fluid density.
B10
Banking of a road I tilting the road lets the normal force's horizontal component turn the car with no friction at the design speed.
Bar magnet = dipole V of moment M; cut it and each piece is a full magnet with M/2 — poles never come alone. Its field mirrors the electric dipole (axial twice equatorial).
Beat frequency II equals the difference of the two frequencies (one loud–soft cycle per hertz of difference). Careful: the envelope repeats twice per carrier-beat, so the audible beat rate is Δf, not Δf/2. Wax on a fork adds mass and lowers its frequency — the trick to tell which of two forks is the faster one.
Beats II two tones of nearly equal frequency alternately reinforce and cancel, giving a slow throb in loudness. The result is a fast carrier at the average pitch inside a slow amplitude.
Bernoulli's equation I along a streamline, pressure + kinetic + height energy per volume is constant: fast flow, low pressure.
Binding energy VI Binding energy comes from the mass defect (Δm·c²); the B/A curve peaks near iron, so fusion of light nuclei and fission of heavy ones both release energy.
Biot–Savart V each current element writes a small dB, ⊥ to both the element and the line to the point; integrate for wires, loops, arcs.
blackbody III A blackbody (e = 1) is the perfect emitter/absorber; Kirchhoff: good absorbers are good emitters (e = a).
Bragg reflection VI Bragg reflection lets a crystal diffract X-rays; only λ ≤ 2d can satisfy it.
Brewster angle IV incidence at which the reflected ray is fully plane-polarised.
C22
Capacitance C = Q/V V charge stored per volt; set by geometry alone.
Carnot cycle III two isotherms + two adiabats; the most efficient cycle between two temperatures, η = 1 − Tc/Th. No real engine can beat it (Carnot's theorem).
Centre of curvature (C) / radius (R) IV centre and radius of the sphere the mirror is cut from.
Centre of mass I mass-weighted mean position; external forces move the COM as if all mass sat there.
Centripetal acceleration I velocity turns without changing magnitude; a points at the centre. Something real (tension, gravity, friction, normal) must supply mv² over r — centripetal force is a role, not a new force.
Characteristic lines VI Characteristic lines Kα, Kβ — inner-shell transitions fixed by the target element.
Chromatic aberration IV f is shorter for violet than red, so white light focuses over a stretch of axis. Longitudinal CA = fr − fv = ω f.
Circular motion in a magnetic field V a charge ⊥ B runs in a circle; the period is independent of speed (the cyclotron's trick). v at an angle adds a drift → helix. Crossed E and B pass only v = E/B (.
closed pipe II An open pipe gives all harmonics; a closed pipe only odd ones.
Coefficient of restitution I Coefficient of restitution e — separation speed over approach speed: e = 1 elastic (KE kept), e = 0 perfectly inelastic (bodies merge, max KE loss).
coercivity V Hysteresis — B lags H around a loop; retentivity (B left at H = 0), coercivity (reverse H to kill B); loop area = energy lost per cycle.
Coherent sources IV constant phase difference (needed for a steady interference pattern).
Conduction of heat III energy passed molecule to molecule through a solid (Fourier's law).
Conservative force I work independent of path (gravity, spring); only then does potential energy exist.
Continuity equation I what flows in must flow out: Av constant.
Continuous spectrum VI Bremsstrahlung with a sharp cutoff λ_min set only by the tube voltage (Duane–Hunt).
Convection of heat III heat carried bodily by a moving fluid (natural, from density differences, or forced).
Coulomb's law V the force between two point charges, along the line joining them, inverse-square in the separation.
Critical angle (θc) IV the angle of incidence in the denser medium for which the refracted ray grazes the surface (r = 90°).
critical point III Phase (P–T) diagram — maps solid/liquid/gas regions; the triple point is where all three coexist, the critical point ends the liquid–vapour line.
cross product I Dot product gives a scalar (work); cross product a vector ⊥ to both (torque, L).
Cyclic process III the gas returns to its start, so ΔU = 0 and the net work equals the enclosed loop area (clockwise = work out).
D16
Damped oscillation II amplitude decays as e−bt/2m.
de Broglie wavelength VI every moving particle has a wavelength λ = h/p, so matter diffracts too.
Degrees of freedom (f) III independent ways a molecule stores energy (equipartition: ½kT each). Monatomic f = 3, diatomic 5, so Cv = (f/2)R and γ = 1 + 2/f.
dielectric V A dielectric (constant K) multiplies C by K by polarising and weakening the internal field.
Diffraction IV bending of light into the geometric shadow of an edge or slit.
Dimensional formula I every mechanical quantity written as MᵃLᵇTᶜ. An equation must be.
dimensionally homogeneous I every added term carries the same dimensions.
dip δ V Earth's field — described by declination (compass vs true north), dip δ (tilt below horizontal) and the horizontal component BH.
Dispersion IV a prism spreads white light because n is larger for shorter wavelengths, so violet deviates most, red least.
Dispersive power (ω) IV measures the spread relative to the mean deviation. Cauchy: n = A + B/λ².
Displacement current V a changing electric flux acts like a current, id = ε₀ dΦE/dt; it completes Ampère's law and closes the circuit across a capacitor gap.
Displacement method IV a lab way to get f from the two sharp positions of a lens between a fixed object and screen (needs D > 4f).
Displacement vs pressure wave II the pressure wave leads the displacement wave by π/2: where displacement is zero (a node of s) the pressure swing is greatest. Amplitude p₀ = Bk·s₀ = ρvω·s₀.
Doppler effect II relative motion between source and observer changes the observed frequency. Approach bunches the wavefronts (higher pitch); recession stretches them (lower pitch). Only the component along the line joining them counts.
Dot product I Dot product gives a scalar (work); cross product a vector ⊥ to both (torque, L).
Drift velocity V electrons crawl at vd (~mm/s) though the signal moves near light speed.
E15
Eddy currents V induced swirls in bulk metal: brakes and induction stoves (friend), core losses (foe — laminate!).
Efficiency III Efficiency η = W/Qh.
Einstein's equation VI gives the maximum kinetic energy.
Electric dipole V charges ±q a distance d apart; moment p = qd points − → +. Axial field is twice the equatorial field at the same distance.
Electric flux Φ V field lines threading a surface; counts E across area, weighted by the tilt cosθ.
Electrolysis V Faraday: mass deposited ∝ charge passed, and ∝ chemical equivalent (M/z). F = 96,500 C deposits one gram-equivalent.
Electromagnetic spectrum V (λ falling): radio · micro · IR · visible (400–700 nm) · UV · X · γ — the name records the source.
EM wave travel V along E × B; E, B and v are mutually perpendicular.
EMF ε V work per charge by the source; terminal voltage V = ε − Ir droops under load. Max power transfer at R = r (efficiency then only 50%).
Emission and absorption spectra IV continuous (hot solids), line (atoms), band (molecules), absorption (dark Fraunhofer lines)
End correction II e ≈ 0.6r extends the effective length.
Entropy III Entropy ΔS = Qrev/T measures the one-way spread of energy.
envelope II The result is a fast carrier at the average pitch inside a slow amplitude envelope.
equipotentials V E points down the steepest fall of V and is everywhere ⊥ to equipotentials.
Errors I absolute error Δa; fractional errors add for products and quotients, and powers multiply them. Significant figures survive multiplication as the least count of the inputs.
F6
Faraday's law of induction V a changing flux Φ = BA cosθ induces an EMF equal to its rate of change.
Field E V = force per unit positive test charge.
Field lines V leave + charge, enter −; density ∝ strength; they never cross.
First law (Newton) I no net force, no change of velocity (defines inertial frames).
First law of thermodynamics III ΔQ = ΔU + ΔW (heat in = rise in internal energy + work done by the gas).
Frequency II f = 1/T (Hz).
G1
Gauss's law V the total flux through ANY closed surface equals the enclosed charge over ε₀; charge outside contributes nothing. Choose surfaces that match the symmetry (sphere, cylinder, pillbox).
H5
Heat capacity III Heat capacity = mc.
Heat engine III takes Qh from a hot source, dumps Qc to a cold sink, and delivers work W = Qh − Qc each cycle.
Heat ΔQ III + when supplied TO the system, − when released.
Huygens’ principle IV every point on a wavefront is a source of secondary wavelets; their envelope is the next wavefront.
Hypermetropia (long sight) IV near objects blur; eyeball too short; corrected with a convex lens.
I7
Ideal gas III U depends on temperature alone, U = (f/2)nRT.
Inductance V a coil's flux per ampere: NΦ = LI. It resists changes in current, stores ½LI² in the field, and sets the LR time constant.
Intensity & loudness II intensity falls as 1/r² from a point source.
interference II in phase (δ = 2nπ) build up, out of phase (δ = (2n−1)π) cancel.
Isobaric III Isobaric (const P): W = PΔV.
Isochoric III (const V): W = 0, ΔQ = ΔU.
Isothermal III (const T, ideal gas): ΔU = 0, W = nRT ln(V₂/V₁).
J1
Joule heating V collisions turn electrical work into heat; the basis of fuses, heaters, bulbs.
K5
Kepler's laws I ellipses with the sun at a focus; equal areas in equal times (L conserved); T² ∝ a³.
Kinetic friction I fixed at μₖN (μₖ < μₛ), opposing sliding.
Kinetic pressure III pressure is the drum of molecular impacts on the walls: P = ⅓ρc̄², and the mean translational energy per molecule is ½m c̄² = (3/2)kT — temperature IS molecular kinetic energy.
Kirchhoff's circuit laws V junction (charge) + loop (energy).
Kirchhoff's radiation law III good absorbers are good emitters (e = a). Stefan–Boltzmann: emitted power ∝ T⁴.
L10
Laplace's correction II corrected it to adiabatic (v = √γP/ρ). It rises with temperature (v ∝ √T) and, in air, with humidity.
Latent heat (L) III heat per unit mass absorbed or released at a phase change (fusion, vaporisation) at constant temperature — the plateaus on a heating curve.
lateral shift IV the sideways offset of a ray leaving a parallel slab (it emerges parallel to its original path).
Laws of reflection IV the incident ray, reflected ray and normal lie in one plane; angle of incidence = angle of reflection.
length contraction VI Time dilation (moving clocks run slow) and length contraction (moving rulers shrink along the motion) are reciprocal.
Lenz's law V induced effects oppose the change in flux that made them — energy conservation in disguise.
Lenz's minus sign V sets the direction (oppose the change).
Longitudinal wave II particles move along travel (sound).
Lorentz force V F = qE + qv×B. The magnetic part is ⊥ v, so it does no work — it only bends the path.
Loudness (decibel) II in decibels is β = 10 log(I/I₀).
M14
Magnifying power IV ratio of the angle an image subtends at the eye to the angle the object would subtend unaided (at D = 25 cm). Every instrument is angle inflation.
Maxwell distribution III the spread of speeds, peaking at vmp and skewed to high speeds.
Mayer's relation III Cp − Cv = R.
Mean free path (λ) III average distance a molecule travels between collisions.
Mechanical energy I Mechanical energy E = KE + PE is conserved when only conservative forces act; friction bleeds it into heat.
Melde's experiment II relates loop count to tension (p ∝ 1/√T).
Molar specific heat III Specific heat (c) — heat to raise unit mass by one degree; molar specific heat per mole.
Molecular speeds III rms > average > most-probable, all ∝ √T.
Moment of inertia I rotational mass; grows with distance² from the axis.
Momentum conserved I whenever ΣF_ext = 0 — the working law of every collision.
Moseley's law VI Moseley's law orders elements by nuclear charge Z.
Motional EMF V a rod sweeping flux at speed v generates BLv; on rails it drives a current, feels a retarding force, and the mechanical power in equals the I²R heat out.
moving-coil galvanometer V Currents feel it too — force on a wire, torque on a loop with moment m = NIA; a spring restores the moving-coil galvanometer to make deflection ∝ current.
Myopia (short sight) IV distant objects blur; the eyeball is too long; corrected with a concave lens (f = −far point).
N4
n-type VI (donors, majority electrons)
Near / far point IV closest (25 cm) and farthest (∞) points of clear vision for a normal eye.
Newton's law of cooling III for a small excess over the surroundings, the rate of cooling is proportional to that excess.
nodes II Fixed nodes (always still) and antinodes (largest swing); no net energy transport.
O3
Ohm's law V V ∝ I when ρ is constant; ρ rises with temperature in metals, falls in carbon/semiconductors.
open pipe II An open pipe gives all harmonics; a closed pipe only odd ones.
Orbit energy I negative — a bound satellite must be given energy to escape.
P32
p-type VI n-type (donors, majority electrons) and p-type (acceptors, majority holes) obey the mass-action law, staying neutral.
Parallel currents V attract when parallel, repel when anti-parallel — the old definition of the ampere.
Parallel-axis theorem I I about any axis = I_cm + Md².
Paraxial ray IV rays: close to and nearly parallel with the axis — the clean-image assumption.
Particle velocity II u = ∂y/∂t is the slope of the displacement–time graph.
Particle velocity ∂y/∂t II ≠ wave velocity v. A crest is where the phase = π/2.
Pascal's law I an applied pressure change reaches every point undiminished (the hydraulic press).
Path difference (Δ) IV the extra distance one wave travels — whole λ give brightness, half-λ give darkness.
Period T II time for one full cycle.
Phase (P–T) diagram III maps solid/liquid/gas regions.
Phase constant φ II where in the cycle the motion starts. Velocity leads displacement by π/2; acceleration by π.
Phase difference II from a path gap Δx: Δφ = (2π/λ)·Δx. From a time gap Δt: Δφ = (2π/T)·Δt.
Phase of a wave II of y = A sin(ωt + φ): φ is the head-start. +φ leads, −φ lags.
phasor / reference circle II The projection of uniform circular motion onto a diameter (the phasor / reference circle).
Photon VI light arrives in quanta of energy E = hν = hc/λ and momentum p = h/λ.
Plane mirror IV image is virtual, erect, same size, as far behind as the object is in front, laterally inverted.
Polarisation IV restricting the light’s vibration to one plane — proof light is a transverse wave.
Pole (P) IV centre of the mirror surface.
pole / optical centre IV Measure all distances from the pole / optical centre along the axis.
Potential V V work per unit charge brought from infinity; a scalar. E points down the steepest fall of V and is everywhere ⊥.
Potentiometer V compares EMFs by balancing lengths, drawing no current.
Power I rate of doing work.
Power & intensity II a string carries P = ½μω²A²v; intensity ∝ A².
Power (P) IV P = 1/f in dioptres (f in metres); converging +, diverging −. In contact, powers add.
power factor V Only the in-phase current does work: power factor cosφ; a pure reactance draws wattless current.
Pressure I Pressure in a still fluid depends only on depth.
Principal focus (F) IV where paraxial rays parallel to the axis converge (concave) or appear to diverge from (convex).
Principle of calorimetry III in an insulated mix, heat lost by the hot bodies = heat gained by the cold, until a common equilibrium temperature.
Progressive wave II a disturbance that carries energy and momentum, not matter.
Projectile I independent horizontal (uniform) and vertical (free-fall) motions.
Pseudo-force I in a frame accelerating at a₀, add −ma₀ to every body; only then does ΣF = ma hold inside that frame.
p–n junction VI a one-way diode: forward bias conducts past the knee V_b, reverse bias blocks.
Q2
Quantised orbits VI angular momentum comes in units of h/2π, so only certain radii and energies are allowed. Energy is negative (bound) and rises toward zero as n grows.
Quincke's tube II shows interference by a sliding path difference.
R18
Radiation of heat III emitted as electromagnetic waves, no medium needed.
Radiation pressure V absorbed energy U carries momentum U/c; reflection doubles the push.
Radioactivity VI α, β, γ emissions; the number left decays exponentially, with activity A = λN and half-life t½ = 0.693/λ.
Reactance V frequency-dependent opposition: XL = ωL (V leads I by 90°), XC = 1/ωC (V lags by 90°) — remember CIVIL.
Rectifiers VI Rectifiers make DC (full-wave ripple = 2f); transistor gains α, β amplify.
Reflection of a wave II at a fixed end the pulse flips (π phase change); at a free end it does not.
Refractive index IV n = c/v, a measure of optical density. Frequency is fixed at a boundary; speed and wavelength both fall by n. Relative index n₂₁ = n₂/n₁ = v₁/v₂ = λ₁/λ₂.
Refrigerator / heat pump III the engine run in reverse: work pumps heat from cold to hot. Rated by coefficient of performance (COP).
Regelation III ice melting under pressure and refreezing.
Relative velocity I v_AB = v_A − v_B.
Resolution of a vector I Aₓ = A cos θ, A_y = A sin θ.
Resolving power IV ability to see two close objects as separate (Rayleigh criterion).
Resonance II driving at the natural frequency ω₀ gives the largest response.
Resonance tube II finds the speed of sound.
Retentivity V Hysteresis — B lags H around a loop; retentivity (B left at H = 0), coercivity (reverse H to kill B); loop area = energy lost per cycle.
Right-hand grip V thumb along I, fingers curl along B (wire); fingers curl along I, thumb gives B (loop/solenoid).
RMS value V the steady DC that heats identically; meters read rms, insulation survives the peak (√2 higher). Mean over a cycle is zero.
Rolling motion I the k = I over MR² ratio decides who wins the race downhill; less spin energy, more speed.
S20
Second law (Newton) I ΣF = ma per axis.
Second law of thermodynamics III heat will not flow cold → hot unaided (Clausius) and no engine turns all heat into work (Kelvin–Planck).
Series resonance V at ω₀ the reactances cancel, Z = R, current peaks; sharpness Q, bandwidth Δω = R/L. Only the in-phase current does work.
SHM I restoring acceleration proportional to displacement, a = −ω²x; the shadow of uniform circular motion. Period independent of amplitude. Velocity leads displacement by π/2.
Silvered lens IV a lens with one face mirrored behaves as an equivalent mirror; the lens power counts twice.
Simple harmonic motion II acceleration is proportional to displacement and always directed toward the mean position: a = −ω²x. The projection of uniform circular motion onto a diameter (the.
Sonic boom II vs = v makes the formula diverge.
Specific heat (c) III heat to raise unit mass by one degree.
Spectral series VI a jump from n₂ to n₁ emits a photon set by the Rydberg formula; Lyman (n₁=1, UV), Balmer (n₁=2, visible), Paschen (n₁=3, IR). Hydrogen-like ions scale with Z².
spectrometer IV Spectra: continuous (hot solids), line (atoms), band (molecules), absorption (dark Fraunhofer lines); a spectrometer (collimator · prism table · telescope) reads A and δm to get n(λ).
Speed of sound II Newton assumed isothermal (v = √P/ρ, too low)
Standing wave II two equal waves travelling opposite ways: y = 2A sin(kx) cos(ωt). Fixed.
State function (ΔU) III (end-states only); ΔQ and ΔW are path functions. Per cycle ΔU = 0.
Static friction I self-adjusting, anything from 0 up to μₛN; it equals the applied force until slipping.
stopping potential VI Einstein's equation gives the maximum kinetic energy; the stopping potential V₀ measures it.
strain I fractional deformation; their ratio (the modulus) belongs to the material. Elastic below the elastic limit; permanent set beyond the yield point; fracture past the ultimate strength.
Stress I restoring force per area.
Strings & pipes II boundary conditions pick discrete frequencies (harmonics).
Superposition II where waves overlap, displacements add. Two coherent waves give.
Surface tension I a surface costs energy T per area, so liquids minimise it; a wetting liquid climbs a capillary.
T14
Temperature III the quantity that decides the direction of heat flow; measured on the Celsius, Fahrenheit or absolute (Kelvin) scale. Absolute zero (0 K) is the point of least molecular motion.
Thermal expansion III most solids grow on heating: linear (α), area/superficial (β) and volume/cubical (γ) coefficients, related α: β: γ = 1: 2: 3.
Thermal resistance III Thermal resistance R = x/KA adds like electrical resistance: series R = R₁ + R₂, parallel 1/R = 1/R₁ + 1/R₂.
Thermal stress III a rod clamped so it cannot expand develops a compressive stress YαΔT, independent of length.
Thermoelectricity V a junction pair at different temperatures drives a thermo-emf (Seebeck), parabolic in θ with a neutral temperature (max) and inversion temperature (sign flip). Peltier and Thomson are its reversible cousins.
Thin lens IV two refracting surfaces a negligible distance apart. Beyond 2F: real, inverted, small; between F and 2F: real, inverted, large; inside F: virtual, erect, magnified (the magnifier).
Third law (Newton) I forces come in equal-and-opposite pairs on different bodies.
Time dilation VI Time dilation (moving clocks run slow) and length contraction (moving rulers shrink along the motion) are reciprocal.
Torque I turning effect, force × lever arm.
Total internal reflection IV beyond θc, all light is reflected back — the basis of optical fibres and the sparkle of diamond.
transformer V The transformer trades volts for amps at constant power.
Transistor VI Rectifiers make DC (full-wave ripple = 2f); transistor gains α, β amplify.
Transverse wave II particles move ⊥ to travel (waves on a string, light).
triple point III Phase (P–T) diagram — maps solid/liquid/gas regions; the triple point is where all three coexist, the critical point ends the liquid–vapour line.
U2
Unit vector I Unit vector â = A divided by its magnitude.
Universal law of gravitation I every pair of masses attracts along the line joining them. g falls off as 1 over r² outside the Earth and grows linearly from zero at the centre.
V5
Vector I magnitude + direction + triangle law of addition.
Velocity I rate of change of displacement (slope of x–t)
velocity selector V Crossed E and B pass only v = E/B (velocity selector).
Virtual image IV they only appear to.
Viscosity I fluid friction; a small falling sphere reaches terminal velocity when Stokes' drag balances net weight.
W12
Water equivalent III Water equivalent w = mc/cwater: the mass of water needing the same heat.
Wave number II k = 2π/λ.
Wave speed II v = fλ = ω/k.
wave velocity II Particle velocity u = ∂y/∂t is the slope of the displacement–time graph; the wave velocity v is fixed by the medium.
Wavefront IV a surface of constant phase.
Wavelength λ II one spatial cycle.
Wheatstone bridge V Wheatstone bridge balances at P/Q = R/S — the galvanometer reads zero.
Wien's displacement law III the emission peak shifts to shorter wavelength as a body heats: hotter looks bluer.
Work function φ VI least energy to free an electron; emission needs ν ≥ ν₀ regardless of intensity.
Work in a gas process III W = ∫P dV is the area under the P–V (indicator) curve; positive on expansion.
Work ΔW III + when done BY the gas (expansion), − on compression.
Work–energy theorem I the net work of all forces equals the change in kinetic energy.
Z1
Zeroth law of thermodynamics III bodies in thermal equilibrium share one temperature — what a thermometer reads.