Cameroon GCE A-Level Physics cheat sheet

Equations of motion for constant acceleration: v = u + at, s = ut + ½at², v² = u² + 2as, s = ½(u + v)t.

Newton's second law: resultant force F = ma; weight W = mg with g ≈ 9.8 m/s² (often 10 m/s² in GCE data).

Momentum p = mv is conserved in all collisions; kinetic energy is conserved only in perfectly elastic collisions.

Impulse equals change in momentum: FΔt = m(v − u); the area under a force–time graph gives impulse.

Projectile motion: horizontal velocity constant; vertical motion uses a = −g with initial component u sin θ.

Circular motion: v = ωr, a = v²/r = ω²r, centripetal force F = mv²/r directed toward the centre.

Moment of a force = F × perpendicular distance from pivot; for equilibrium, resultant force and resultant moment are both zero.

Work W = Fs cos θ; power P = W/t = Fv; efficiency = useful output energy ÷ total input energy × 100%.

Hooke's law F = kx up to the limit of proportionality; elastic potential energy stored = ½Fx = ½kx².

Wave equation v = fλ; for a stretched string v = √(T/μ) and for sound in air v ≈ 330–340 m/s at room temperature.

Transverse waves have displacement perpendicular to propagation; longitudinal waves (sound) have displacement parallel to propagation.

Superposition adds displacements; constructive interference needs path difference nλ, destructive needs (n + ½)λ.

Two-source interference condition: coherent sources with constant phase difference; fringe spacing y = λD/d for double slits.

Diffraction grating: d sin θ = nλ, where d is the slit spacing and n the order; maxima are sharp and bright.

Snell's law n₁ sin θ₁ = n₂ sin θ₂; refractive index n = c/v = 1/sin c, where c is the critical angle.

Total internal reflection occurs only when light travels from denser to less dense medium and the angle exceeds the critical angle.

Thin converging lens: 1/f = 1/u + 1/v with real-is-positive convention; magnification m = v/u = image height ÷ object height.

Stationary waves on a string fixed at both ends have nodes at the ends and λ = 2L/n; fundamental n = 1.

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

Resistors in series add; in parallel 1/R = 1/R₁ + 1/R₂ + …; potential divider V_out = V_in × R₂/(R₁ + R₂).

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

Kirchhoff's laws: sum of currents at a junction is zero; sum of e.m.f.s equals sum of p.d.s around a loop.

Capacitance C = Q/V; energy stored = ½QV = ½CV²; discharge decays as Q = Q₀e^(−t/RC) with time constant RC.

Coulomb's law F = kQ₁Q₂/r² with k = 1/(4πε₀) ≈ 8.99 × 10⁹ N m² C⁻¹; field E = F/q and E = V/d for uniform fields.

Magnetic force on a current F = BIL sin θ; on a moving charge F = qvB sin θ; direction given by Fleming's left-hand rule.

Faraday's law: induced e.m.f. equals rate of change of magnetic flux linkage; Lenz's law gives the direction opposing the change.

Transformer relation V_s/V_p = N_s/N_p; for an ideal transformer V_pI_p = V_sI_s.

Temperature in kelvin T = θ(°C) + 273.15; absolute zero is 0 K, where molecular kinetic energy is minimal.

Specific heat capacity: E = mcΔθ; specific latent heat: E = mL for a change of state at constant temperature.

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

Mean kinetic energy of a gas molecule = (3/2)kT; r.m.s. speed v_rms = √(3kT/m) = √(3RT/M).

First law of thermodynamics: ΔU = Q − W, where W is work done by the gas; W = pΔV at constant pressure.

Boyle's law pV = constant at constant T; Charles's law V/T = constant at constant p; pressure law p/T = constant at constant V.

Thermal conduction rate through a slab: dQ/dt = kAΔθ/L, where k is thermal conductivity and L the thickness.

A Carnot engine has maximum efficiency η = 1 − T_cold/T_hot, with temperatures in kelvin.

Internal energy of an ideal gas depends only on temperature, since there are no intermolecular potential energy terms.

Photoelectric effect: photon energy E = hf; maximum kinetic energy of emitted electrons = hf − φ, where φ is the work function.

Threshold frequency f₀ satisfies hf₀ = φ; no emission occurs below f₀ regardless of intensity.

Einstein mass–energy relation E = mc²; mass defect in a nucleus appears as binding energy.

de Broglie wavelength λ = h/p = h/(mv), applicable to electrons and other particles.

Atomic energy levels: photon emitted or absorbed has energy hf = E₂ − E₁; spectral lines are characteristic of the element.

Radioactive decay N = N₀e^(−λt); half-life t½ = ln 2/λ ≈ 0.693/λ; activity A = λN.

Nuclear notation: mass number A = protons + neutrons; isotopes have the same Z but different A.

Alpha decay reduces A by 4 and Z by 2; beta-minus emission increases Z by 1 with A unchanged.

Planck constant h ≈ 6.63 × 10⁻³⁴ J s; electron charge e ≈ 1.60 × 10⁻¹⁹ C; electronvolt 1 eV = 1.60 × 10⁻¹⁹ J.

A vernier caliper typically reads to 0.01 cm or 0.1 mm; a micrometer screw gauge reads to 0.01 mm; always record the zero error.

Repeat readings and average them to reduce random error; systematic errors shift all readings in the same direction.

Percentage uncertainty of a quotient or product equals the sum of the percentage uncertainties of the quantities.

For a quantity raised to a power n, the percentage uncertainty is multiplied by n.

Plot the quantity expected to give a straight line, then use gradient and intercept to extract constants.

A valid conclusion must state the relationship supported by the graph and compare with the accepted value within experimental uncertainty.

Precautions: avoid parallax when reading scales, check for zero error, and keep conditions constant for the variable being controlled.

Oscilloscope: time per division × divisions gives period; signal frequency f = 1/T; voltage peak = divisions × volts per division.

Significant figures in a final result should match the precision of the measuring instrument, usually 2–3 s.f.

Straight-line form y = mx + c: identify which measured quantities give y and x so the gradient yields the required constant.

Logarithmic linearisation: if y = axⁿ then log y = n log x + log a, giving gradient n and intercept log a.

Exponential linearisation: if y = y₀e^(−kx) then ln y = −kx + ln y₀, giving gradient −k.

Inverse-square linearisation: if y = k/x² then y against 1/x² is a straight line through the origin with gradient k.

Gradient = Δy/Δx using two widely separated points on the line of best fit, not raw data points.

Uncertainty in a gradient can be estimated from the steepest and shallowest lines consistent with the error bars.

Scalars add algebraically; vectors add by resolving into perpendicular components and recombining with Pythagoras and tan θ.

Mean of n readings has uncertainty reduced by a factor √n compared with a single reading.

Convert units before substitution; check that final units are consistent with the formula used.

Diode: conducts when forward biased above about 0.6–0.7 V for silicon; blocks current when reverse biased.

Light-emitting diode emits photons when forward biased; energy of emitted photon approximately equals the band-gap energy.

Zener diode in reverse breakdown holds a nearly constant voltage and is used for voltage regulation.

Operational amplifier: ideal properties are infinite open-loop gain, infinite input impedance and zero output impedance.

Inverting amplifier gain = −R_f/R_in; non-inverting amplifier gain = 1 + R_f/R₁.

Op-amp as comparator: output saturates near the supply rails depending on which input is at higher potential.

Transistor as a switch: base current controls collector current; I_C = βI_B in the active region.

Logic gates: AND gives 1 only if all inputs are 1; OR gives 1 if any input is 1; NOT inverts; NAND and NOR are universal gates.

Potential divider with a thermistor or LDR forms a sensor circuit whose output voltage varies with temperature or light.

SI base units: kg, m, s, A, K, mol, cd; derived units such as the newton = kg m s⁻² and joule = kg m² s⁻².

Dimensional analysis can confirm an equation's form but cannot determine a dimensionless constant.

Density ρ = m/V; pressure p = F/A measured in pascals (N m⁻²).

Friction: limiting static friction is usually greater than kinetic friction; frictional force opposes relative motion.

Sound intensity level in decibels: L = 10 log₁₀(I/I₀) with I₀ = 1 × 10⁻¹² W m⁻².

For a source moving toward a stationary observer, observed frequency rises: f' = fv/(v − v_s).

Resonance tube: first resonance at λ/4 above the tube end, second at 3λ/4, giving λ = 2(L₂ − L₁).

Polarisation shows light is transverse; a Polaroid filter halves intensity when rotated 45° from the plane of polarisation.

Electric field lines point from positive to negative charge and are perpendicular to conductor surfaces.

Magnetic flux Φ = BA cos θ; flux linkage = NΦ; induced e.m.f. = −N dΦ/dt.

A capacitor in series with a resistor charges with time constant RC; after one time constant it reaches about 63% of final charge.

Parallel-plate capacitor: C = ε₀ε_r A/d.

Convection requires a fluid; it transfers heat by bulk movement driven by density differences.

Thermal radiation is emitted by all bodies above 0 K; net loss rate rises with the fourth power of absolute temperature.

A good absorber is a good emitter; dull black surfaces absorb and emit better than shiny silver ones.

Evaporation cools a liquid because the most energetic molecules escape, lowering the mean kinetic energy.

Binding energy per nucleon peaks near iron-56, so fusion of light nuclei and fission of heavy nuclei both release energy.

Activity is measured in becquerels (1 Bq = 1 decay per second); absorbed dose is measured in grays.

Half-life is independent of temperature, pressure and chemical state.

Line spectra arise from electron transitions between discrete energy levels; a continuous spectrum comes from a hot dense body.

Random errors scatter readings about a mean; systematic errors shift the whole set away from the true value.

A line of best fit should pass through the centroid of the plotted points and balance points above and below.

The uncertainty in a single reading from an analogue scale is typically half the smallest division.

When a measured quantity is squared in a formula, its percentage uncertainty doubles in the final result.

Resolution: F_x = F cos θ and F_y = F sin θ where θ is measured from the x-axis.

Resultant of two perpendicular vectors: R = √(F_x² + F_y²) and direction tan θ = F_y/F_x.

Small-angle approximation sin θ ≈ tan θ ≈ θ in radians is used for pendulum and Young's slit derivations.

Simple pendulum period T = 2π√(L/g), so a graph of T² against L has gradient 4π²/g.

NTC thermistor resistance falls as temperature rises, so it can be used in a potential divider to give a temperature-dependent voltage.

LDR resistance falls as light intensity rises; it forms the input stage of light-sensing circuits.

A relay uses a small current in a coil to switch a larger current in a separate circuit.

Rectification: a half-wave rectifier uses one diode; a bridge rectifier uses four diodes to give full-wave output.