JCE Physics cheat sheet

Kinematics: v = u + at, s = ut + ½at², v² = u² + 2as apply only for constant acceleration; each symbol is a vector component along a chosen axis.

Newton's second law: ΣF = ma; weight W = mg, and normal force is not automatically equal to mg on inclines or in accelerating frames.

Friction: static friction satisfies f ≤ μsN and adjusts to the applied force; kinetic friction is f = μkN and opposes relative sliding.

Work–energy theorem: W_net = ΔKE = ½mv² − ½mu²; a force perpendicular to motion (e.g. centripetal force) does zero work.

Conservation of mechanical energy holds only when non-conservative forces do no work; otherwise ΔKE + ΔPE = W_nc.

Momentum: p = mv, impulse J = FΔt = Δp; total momentum is conserved in collisions, kinetic energy only in elastic ones.

Circular motion: centripetal acceleration a = v²/r = ω²r directed toward the centre; tangential acceleration changes speed only.

Universal gravitation: F = Gm₁m₂/r²; orbital speed for a circular orbit is v = √(GM/r), independent of satellite mass.

Ideal gas law: pV = nRT with T in kelvin; combined with kinetic theory, mean translational KE per molecule = (3/2)k_BT.

First law of thermodynamics: ΔU = Q − W, where W is work done by the gas; for an isothermal process ΔU = 0 and Q = W.

Adiabatic process: pV^γ = constant with γ = C_p/C_v; no heat exchange, so work done comes at the expense of internal energy.

Specific heat: Q = mcΔT; latent heat Q = mL applies at constant temperature during a phase change.

Efficiency of a heat engine: η = W/Q_H = 1 − Q_C/Q_H; Carnot limit is η_max = 1 − T_C/T_H with absolute temperatures.

Wave equation: v = fλ; for a stretched string v = √(T/μ) and for sound in a gas v depends on √(T/M).

Snell's law: n₁sinθ₁ = n₂sinθ₂; total internal reflection occurs only when light travels from higher to lower refractive index beyond the critical angle.

Standing waves: nodes are displacement minima; a string fixed at both ends supports λ = 2L/n, and pipes differ by end conditions (open vs closed).

Coulomb's law: F = kq₁q₂/r²; the electric field of a point charge is E = kq/r², pointing away from positive charge.

Uniform field between parallel plates: E = V/d; potential difference is the work per unit charge, and potential decreases along field lines.

Capacitance: C = Q/V; for parallel plates C = ε₀A/d, and stored energy is U = ½CV² = ½QV.

Ohm's law and resistance: V = IR, R = ρL/A; resistivity ρ is a material property, resistance also depends on geometry.

Series circuits share current; parallel circuits share voltage. Equivalent resistance: series adds, parallel adds reciprocals.

Electrical power: P = IV = I²R = V²/R; the power dissipated in a resistor appears as heat.

Kirchhoff's rules: junction rule conserves charge (ΣI = 0), loop rule conserves energy (ΣΔV = 0 around a closed loop).

Magnetic force: F = qvB sinθ on a moving charge and F = BIL sinθ on a current-carrying wire; direction from the right-hand rule.

Electromagnetic induction: induced emf ε = −dΦ/dt with flux Φ = BA cosθ; Lenz's law fixes the direction so as to oppose the change.

A straight wire moving through a field generates motional emf ε = BLv when B, L and v are mutually perpendicular.

Photoelectric effect: maximum kinetic energy K_max = hf − φ, where φ is the work function; no emission below the threshold frequency f₀ = φ/h.

Photon energy: E = hf = hc/λ; intensity controls photon number, frequency controls photon energy.

de Broglie wavelength: λ = h/p = h/(mv), observable for electrons and other low-mass particles.

Atomic energy levels: a photon is emitted when an electron drops to a lower level, with energy equal to the level difference; E = hf.

Half-life: N = N₀(1/2)^(t/T½); activity A = λN and λ = ln2/T½ for radioactive decay.

Mass–energy equivalence: E = mc²; nuclear binding energy is the mass defect times c², and fusion of light nuclei releases energy.