HSC Physics cheat sheet

Projectile motion: horizontal velocity is constant (a_x = 0); vertical acceleration a_y = −g ≈ −9.8 m s⁻². Resolve initial velocity as u_x = u cos θ and u_y = u sin θ; range on level ground R = u² sin 2θ / g.

Circular motion: centripetal acceleration a_c = v²/r = 4π²r/T², directed toward the centre; centripetal force F_c = mv²/r. Speed is constant but velocity changes because direction changes, so the object is accelerating.

Newton's law of universal gravitation: F = Gm₁m₂/r², with G = 6.674 × 10⁻¹¹ N m² kg⁻². Kepler's third law for orbits about a central mass: r³/T² = GM/4π², so r³ ∝ T².

Energy and work: W = Fs cos θ, kinetic energy E_k = ½mv², gravitational potential energy near Earth ΔE_p = mgΔh. Work done equals change in kinetic energy (work–energy theorem).

Momentum and impulse: p = mv is conserved in any collision or explosion when net external impulse is zero. Impulse J = FΔt = Δp; elastic collisions conserve kinetic energy, inelastic collisions do not.

Forces in equilibrium: resolve into perpendicular components, ΣF_x = 0 and ΣF_y = 0. On an inclined plane of angle θ, the weight component along the slope is mg sin θ and the normal force is mg cos θ (frictionless).

Electric fields and circuits: F = qE for a charge in a uniform field E = V/d; parallel plates give constant field strength. Ohm's law V = IR, power P = VI = I²R = V²/R; series resistances add, parallel resistances satisfy 1/R_total = Σ1/R.

Magnetic force and induction: a straight wire in a field experiences F = BIl sin θ; a moving charge experiences F = qvB sin θ. Faraday's law gives emf = −N ΔΦ/Δt, and Lenz's law fixes the induced current direction to oppose the flux change.

Waves and sound: v = fλ; for a stretched string v = √(F/μ) where μ is mass per unit length. The Doppler effect for sound is f' = f(v ± v_o)/(v ∓ v_s), with signs chosen so approach raises the observed frequency.

Special relativity: the speed of light in vacuum c = 3.00 × 10⁸ m s⁻¹ is invariant for all inertial observers. Time dilation t = t₀/√(1 − v²/c²) and length contraction L = L₀√(1 − v²/c²) apply to measurements between frames.

Relativistic mass increase is expressed as m = m₀/√(1 − v²/c²); rest energy E = mc² and total energy E = mc²/√(1 − v²/c²). At everyday speeds the Lorentz factor γ ≈ 1, so Newtonian results are recovered.

The photoelectric effect: photons of energy E = hf (h = 6.626 × 10⁻³⁴ J s) eject electrons only if hf ≥ W, the work function. Maximum kinetic energy K_max = hf − W; increasing intensity raises current, not K_max.

Atomic spectra: each element emits discrete line spectra because electrons transition between quantised energy levels, with photon energy ΔE = hf = hc/λ. Absorption lines occur at the same wavelengths as emission lines.

Blackbody radiation: peak wavelength obeys Wien's law λ_max T = 2.898 × 10⁻³ m K; total emitted power per unit area follows Stefan's law P/A = σT⁴ with σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴.

de Broglie wavelength: λ = h/p = h/(mv), giving measurable wave behaviour for electrons accelerated through a potential difference V, where λ = h/√(2meV).

Nuclear physics: strong nuclear force binds nucleons over ranges of order 10⁻¹⁵ m; mass defect converts to binding energy via E = Δmc². Radioactive decay follows N = N₀e^(−λt) with half-life t₁/₂ = ln 2/λ.

Standard Model: matter consists of quarks (up, down, etc.) and leptons (electron, neutrino); forces are mediated by gauge bosons - photon (electromagnetic), W and Z (weak), gluon (strong).

Semiconductors: doping with pentavalent atoms gives n-type (majority electrons), trivalent atoms give p-type (majority holes). A p–n junction forms a depletion layer whose barrier is lowered by forward bias, allowing current.

SI units and prefixes: force in newtons (N = kg m s⁻²), energy in joules (J = N m), power in watts (W = J s⁻¹), charge in coulombs (C = A s), magnetic flux in webers (Wb = T m²). Prefixes: nano 10⁻⁹, micro 10⁻⁶, milli 10⁻³, kilo 10³, mega 10⁶, giga 10⁹.

Graph interpretation rules: the gradient of a displacement–time graph is velocity; gradient of a velocity–time graph is acceleration; area under a velocity–time graph is displacement; area under a force–displacement graph is work done.

Significant figures and error: the result of multiplication or division carries the smallest number of significant figures among inputs; absolute uncertainty adds for sums and differences, percentage uncertainties add for products and quotients.

Free-body diagrams: draw only forces acting on the chosen object, each as an arrow from the object with length proportional to magnitude. Weight always acts vertically down; normal force is perpendicular to the contact surface.

Projectile decision rule: treat horizontal and vertical motions independently; time of flight is set by vertical motion only, and horizontal range follows from that time multiplied by constant u_x.

Circular motion decision rule: if the net force is insufficient for the required mv²/r, the object leaves the circular path tangentially; if the path is vertical, tension is minimum at the top and maximum at the bottom.

Conservation checks: momentum is a vector, so conserve components separately; energy is a scalar. In explosions momentum is conserved but kinetic energy increases because stored energy is released.

Field line conventions: electric field lines point from positive to negative charge and never cross; magnetic field lines form closed loops, emerging from a north pole and entering a south pole outside the magnet.

Data-analysis rule for radioactive decay: a plot of ln N against t is linear with gradient −λ; a plot of activity against time is exponential, and half-life is read as the time for activity to halve.