HKDSE Physics cheat sheet

Kinematic equations apply only for uniform acceleration: v = u + at, s = ut + ½at², v² = u² + 2as, s = ½(u + v)t.

Newton's second law is a vector relation: net force F = ma, so resolve forces into perpendicular components before applying it.

In a uniform gravitational field, weight W = mg and the centre of gravity coincides with the centre of mass for a uniform body.

Moment of a force about a point = F × perpendicular distance from the point to the line of action; for equilibrium, net moment about any point is zero.

Momentum p = mv is conserved in any collision or explosion with no net external force; kinetic energy is conserved only in elastic collisions.

Projectile motion: horizontal velocity stays constant while vertical motion has acceleration g downward; time of flight depends only on vertical displacement.

Circular motion requires a centripetal force of magnitude mv²/r directed toward the centre; the speed is constant but velocity changes.

Work done W = Fs cos θ and power P = W/t = Fv cos θ; gravitational potential energy change near Earth is mgh.

For a body in equilibrium under three non-parallel forces, the lines of action of the three forces must be concurrent.

Specific heat capacity c: energy = mcΔT; specific latent heat L: energy = mL, applied at constant temperature during a change of state.

Internal energy of an ideal gas depends only on its temperature; for a monatomic ideal gas, average kinetic energy per molecule = (3/2)kT.

Ideal gas law pV = nRT = NkT, with R = 8.31 J mol⁻¹ K⁻¹ and k = 1.38 × 10⁻²³ J K⁻¹; T must be in kelvin.

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

Pressure exerted by a gas arises from molecular collisions with the container walls; p = (1/3)ρ⟨c²⟩ for a gas of density ρ.

Conduction transfers energy by molecular vibration and free electrons without bulk movement of the material; metals conduct better than non-metals.

Convection requires bulk fluid movement driven by density differences; it cannot occur in solids.

Net rate of energy transfer by radiation depends on surface temperature and area; black surfaces are good absorbers and emitters, shiny surfaces poor.

At constant temperature, rate of evaporation depends on surface area, temperature, air movement and humidity, but not on the volume above the liquid once saturated.

Wave equation v = fλ; for a wave crossing a boundary, frequency stays constant while speed and wavelength change.

Transverse waves have displacement perpendicular to energy transfer (light, water surface); longitudinal waves have displacement parallel (sound).

Reflection: angle of incidence equals angle of reflection, measured from the normal; the image in a plane mirror is virtual, same size, laterally inverted.

Refraction obeys Snell's law n₁ sin θ₁ = n₂ sin θ₂; light bends toward the normal when entering a denser medium.

Total internal reflection occurs only when light travels from a denser to a less dense medium and the angle of incidence exceeds the critical angle, sin C = 1/n.

For a thin converging lens, 1/f = 1/u + 1/v with real-is-positive convention; magnification m = v/u.

Diffraction is most noticeable when the slit width is comparable to or smaller than the wavelength.

For two-source interference, constructive interference occurs where path difference = mλ and destructive where it is (m + ½)λ.

In a stationary wave, adjacent nodes are separated by λ/2, and the distance between a node and the next antinode is λ/4.

Ohm's law V = IR holds for ohmic conductors at constant temperature; resistance R = ρL/A depends on material, length and cross-sectional area.

For resistors in series, R = R₁ + R₂ + …; in parallel, 1/R = 1/R₁ + 1/R₂ + …; voltage divides in series and current divides in parallel.

Electrical power P = VI = I²R = V²/R; energy consumed = Pt, billed in kilowatt-hours.

Kirchhoff's laws: at a junction, sum of currents in equals sum out; around any closed loop, sum of potential differences is zero.

Ammeters are connected in series and have low resistance; voltmeters are connected in parallel and have high resistance.

Coulomb's law: force between point charges F = kQ₁Q₂/r², attractive for opposite signs and repulsive for like signs.

Magnetic flux density B is measured in tesla; a straight wire carrying current I in a field B experiences force F = BIL sin θ.

A charged particle moving perpendicular to a magnetic field follows a circular path of radius r = mv/(qB).

Electromagnetic induction: induced e.m.f. equals the rate of change of magnetic flux linkage, ε = −N ΔΦ/Δt (Faraday's law).

Alpha decay emits a helium nucleus (⁴₂He): mass number decreases by 4 and atomic number by 2.

Beta-minus decay converts a neutron into a proton, emitting an electron and an antineutrino: atomic number increases by 1, mass number unchanged.

Gamma emission is a photon released from an excited nucleus; mass number and atomic number are unchanged.

Radioactive decay is random and spontaneous; the number of undecayed nuclei follows N = N₀e^(−λt), and activity A = λN.

Half-life t½ = ln 2/λ ≈ 0.693/λ; after n half-lives the remaining fraction is (1/2)ⁿ.

Alpha particles are the most ionising but least penetrating; gamma radiation is the least ionising but most penetrating.

Mass defect in a nucleus is converted to binding energy by E = mc²; binding energy per nucleon peaks near iron-56.

Nuclear fission splits a heavy nucleus and releases energy; nuclear fusion joins light nuclei and powers stars.

Background radiation comes from cosmic rays, radon gas, rocks and medical sources; it must be subtracted when measuring a source's count rate.