SACE Stage 2 Physics cheat sheet

Average velocity v = Δs/Δt is a vector; average speed uses distance, not displacement, and can never be negative.

Uniform acceleration equations: v = u + at; s = ut + ½at²; v² = u² + 2as; s = ½(u + v)t - valid only when a is constant.

Newton's second law ΣF = ma; weight W = mg with g ≈ 9.8 m/s² near Earth's surface, acting toward Earth's centre.

Projectile motion: horizontal and vertical components are independent; a_x = 0, a_y = −g; time of flight from vertical motion only.

Circular motion: v = 2πr/T, a_c = v²/r = 4π²r/T², centripetal force F = mv²/r directed toward the centre.

Momentum p = mv is conserved in any collision or explosion in an isolated system; impulse J = FΔt = Δp.

Relativity postulates: laws of physics are identical in all inertial frames, and light speed in vacuum c is the same for all inertial observers.

Time dilation Δt = γΔt₀ and length contraction L = L₀/γ, with Lorentz factor γ = 1/√(1 − v²/c²) ≥ 1; Δt₀ and L₀ are proper quantities.

Relativistic mass-energy: E = γmc², rest energy E₀ = mc², kinetic energy KE = (γ − 1)mc²; no massive object reaches c.

Coulomb's law F = kq₁q₂/r² with k ≈ 8.99 × 10⁹ N·m²/C²; force is along the line joining charges, repulsive for like signs.

Electric field E = F/q (N/C or V/m); field of a point charge E = kq/r², pointing away from positive charge.

Uniform field between parallel plates: E = V/d; work done moving charge q through potential difference V is W = qV.

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

Series: R_total = ΣR, same current everywhere, voltages add. Parallel: 1/R_total = Σ(1/R), same voltage, currents add.

Electrical power P = VI = I²R = V²/R; energy consumed E = Pt, with the kilowatt-hour equal to 3.6 × 10⁶ J.

Magnetic force on a current-carrying wire F = BIL sin θ, and on a moving charge F = qvB sin θ; direction by right-hand rule.

Magnetic flux Φ = BA cos θ and Faraday's law ε = −N ΔΦ/Δt; the induced emf opposes the change (Lenz's law).

A changing magnetic flux induces an emf; a conductor moving through a field or a changing current in a coil both produce induction.

Wave relation v = fλ; frequency is set by the source and is unchanged on crossing a boundary, while speed and wavelength change.

Transverse waves oscillate perpendicular to propagation; longitudinal waves oscillate parallel, as in sound.

Superposition: overlapping waves add displacements; constructive interference occurs at path difference nλ, destructive at (n + ½)λ.

Young's double slit: fringe spacing Δy = λL/d, where L is slit-to-screen distance and d is slit separation.

Diffraction grating: maxima at d sin θ = nλ; larger slit spacing d gives smaller angular separation of orders.

Refraction obeys Snell's law n₁ sin θ₁ = n₂ sin θ₂, with n = c/v; light bends toward the normal entering a denser medium.

Total internal reflection occurs only going from denser to less dense medium when θ exceeds the critical angle, sin θ_c = n₂/n₁.

Standing waves form when a wave reflects and superposes; nodes are displacement minima, antinodes are maxima, separated by λ/2.

Photoelectric effect: photons of energy E = hf; emission occurs only if hf exceeds the work function W, with maximum KE = hf − W.

Photon energy E = hf = hc/λ, with h ≈ 6.63 × 10⁻³⁴ J·s and c ≈ 3.00 × 10⁸ m/s.

Atomic energy levels are discrete; a photon is emitted when an electron drops to a lower level, with energy equal to the level difference.

Emission spectra are bright lines; absorption spectra are dark lines at the same wavelengths, matching the same transitions.

de Broglie wavelength λ = h/p = h/(mv), showing wave behaviour of matter.

Nuclear notation ᴬZX: Z protons, A − Z neutrons; isotopes share Z but differ in neutron number.

Alpha decay emits a helium nucleus (⁴₂He), reducing A by 4 and Z by 2; beta-minus decay converts a neutron to a proton, increasing Z by 1.

Half-life: after n half-lives the remaining fraction is (½)ⁿ; activity A = λN and N = N₀e^(−λt).

Mass defect converts to binding energy via E = Δmc²; higher binding energy per nucleon means greater nuclear stability.

Fission splits a heavy nucleus into lighter fragments; fusion joins light nuclei, releasing energy in both cases when binding energy per nucleon increases.