CSEC Physics cheat sheet

Average speed = total distance / total time; average velocity = total displacement / total time, so velocity can be zero while speed is not (e.g. a closed loop).

Acceleration a = (v − u)/t; for uniform acceleration use v = u + at, s = ut + ½at², v² = u² + 2as, and s = ½(u + v)t.

Newton's second law: resultant force F = ma; weight W = mg with g ≈ 9.8 N/kg (10 N/kg for rough work), acting vertically downward through the centre of gravity.

Newton's third law pairs act on two different bodies, are equal in magnitude, opposite in direction and of the same type - they never cancel on one body.

Momentum p = mv is a vector; in any collision or explosion total momentum is conserved provided no net external force acts. Impulse Ft = Δp = mv − mu.

Friction opposes relative motion; on a horizontal surface limiting friction F = μR where R is the normal reaction, and μ is a dimensionless coefficient.

Moments: for a body in equilibrium about a point, sum of clockwise moments = sum of anticlockwise moments, and the resultant force is zero (principle of moments).

Work W = Fs cos θ (only the component along the displacement does work); power P = W/t = Fv; kinetic energy ½mv², gravitational potential energy mgh.

For a machine, efficiency = useful output energy / total input energy × 100%; for a pulley or lever, mechanical advantage = load / effort.

Temperature measures the average kinetic energy of particles; thermal energy transfer stops only at thermal equilibrium, but total internal energy is not the same as temperature.

Heat capacity C = Q/Δθ (J/K); specific heat capacity c = Q/(mΔθ), the energy to raise 1 kg by 1 K. For water c ≈ 4200 J/(kg·K).

Specific latent heat L = Q/m: latent heat of fusion melts/freezes at constant temperature, latent heat of vaporisation boils/condenses; no temperature change occurs during the change of state.

Thermal energy flows from higher to lower temperature by conduction (solids, mainly free electrons and lattice vibration), convection (fluids, density-driven currents) and radiation (infrared, needs no medium).

Dark, matt surfaces are good absorbers and good emitters of infrared; shiny, light surfaces are poor absorbers and poor emitters.

Ideal gas: pV = nRT with T in kelvin; at constant temperature pV = constant (Boyle), at constant pressure V/T = constant (Charles), at constant volume p/T = constant (pressure law).

Kelvin temperature T = θ + 273; absolute zero (0 K ≈ −273 °C) is where particle kinetic energy is minimum.

A bimetallic strip bends because the two metals expand by different amounts for the same temperature rise; the metal with the greater expansivity is on the outside of the bend when heated.

Thermal expansion: ΔL = L₀αΔθ, where α is the linear expansivity; gaps in rails and bridges allow for expansion.

Wave speed v = fλ; frequency f = 1/T. Frequency is set by the source, wave speed by the medium; when a wave enters a new medium f stays constant and λ changes.

Transverse waves oscillate perpendicular to energy transfer (light, water ripples); longitudinal waves oscillate parallel to it (sound). Sound cannot travel through a vacuum.

Reflection: angle of incidence = angle of reflection, measured from the normal. Refraction occurs because wave speed changes; light bending towards the normal means it entered a denser (slower) medium.

Snell's law: n₁ sin θ₁ = n₂ sin θ₂; refractive index n = c/v = sin i / sin r for light entering from air. Total internal reflection occurs when i exceeds the critical angle C, where sin C = 1/n.

A converging (convex) lens has a real focal point; a diverging (concave) lens has a virtual focal point. Lens power P = 1/f with f in metres, in dioptres.

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

For a converging lens: object beyond 2F gives a real, inverted, diminished image; between F and 2F gives real, inverted, magnified; inside F gives a virtual, upright, magnified image.

Diffraction is the spreading of waves at gaps or edges; it is greatest when the gap width is comparable to the wavelength. Two-source interference requires coherent sources.

For two slits, fringe spacing x = λD/a where D is slit-to-screen distance and a is slit separation; for a diffraction grating d sin θ = nλ.

Current I = Q/t (ampere = coulomb per second); conventional current flows from positive to negative, while electrons drift the opposite way.

Ohm's law V = IR applies to ohmic conductors at constant temperature; a filament lamp's resistance rises as it heats, so its I–V graph curves.

Series: same current everywhere, V divides, R_total = R₁ + R₂ + … Parallel: same voltage across each branch, I divides, 1/R_total = 1/R₁ + 1/R₂ + …

Electrical power P = VI = I²R = V²/R; energy E = Pt = VIt, billed in kilowatt-hours (1 kW·h = 3.6 MJ).

EMF is the energy supplied per coulomb by the source; terminal voltage = EMF − Ir where r is internal resistance.

A magnetic field surrounds a current-carrying conductor (right-hand grip rule) and a solenoid acts like a bar magnet; field strength increases with current and turns per metre.

Force on a current-carrying conductor F = BIL sin θ (maximum when perpendicular to the field), direction by Fleming's left-hand rule; a moving charge experiences F = qvB.

Electromagnetic induction: a changing magnetic flux through a conductor induces an EMF; Fleming's right-hand rule gives the induced current direction, and Lenz's law says it opposes the change.

A transformer obeys V_s/V_p = N_s/N_p and, for an ideal transformer, V_pI_p = V_sI_s; step-up increases voltage and decreases current.

Density ρ = m/V; relative density (specific gravity) = density of substance / density of water, and a body floats when its average density is less than the fluid's.

Pressure p = F/A, measured in pascals; in a liquid p = hρg, and pressure depends only on depth and density, not on the shape of the container.

Archimedes' principle: upthrust = weight of fluid displaced. A floating body displaces its own weight of fluid; an immersed body loses apparent weight equal to the upthrust.

Hooke's law: extension is proportional to the applied force up to the limit of proportionality (F = kx); beyond the elastic limit the material is permanently deformed.

The kinetic model of matter: particles in solids vibrate about fixed positions, in liquids are close but free to move, and in gases are far apart moving randomly at high speed.

Brownian motion of smoke particles in air is evidence for the random motion of invisible molecules; diffusion in gases and liquids is faster at higher temperature.

Atomic structure: a nucleus of protons (positive) and neutrons (neutral) surrounded by electrons (negative); proton number Z defines the element and nucleon number A = Z + N.

Isotopes have the same proton number but different neutron numbers; alpha decay reduces A by 4 and Z by 2, beta-minus decay leaves A unchanged and raises Z by 1, gamma emission changes neither.

Half-life is the time for half the nuclei in a sample to decay; after n half-lives the fraction remaining is (1/2)ⁿ. Alpha, beta and gamma differ in ionising power, penetrating power and deflection in electric and magnetic fields.