MATSEC AM Physics cheat sheet

Equations of motion (constant a): v = u + at; s = ut + ½at²; v² = u² + 2as; s = ½(u+v)t.

Newton's second law: resultant force F = ma; momentum p = mv and impulse J = FΔt = Δp.

Projectile motion: horizontal component constant (u cosθ); vertical component a = −g; time of flight from vertical equation only.

Circular motion: v = rω, a = v²/r = rω², centripetal F = mv²/r; angular velocity ω = 2π/T.

Moments: for equilibrium, sum of clockwise moments = sum of anticlockwise moments about the same pivot; couple moment = F × perpendicular distance between forces.

Hooke's law: F = kx up to the limit of proportionality; elastic PE = ½Fx = ½kx²; Young modulus E = stress/strain = (F/A)/(Δl/l).

Stress–strain curve features: limit of proportionality, elastic limit, yield point, ultimate tensile strength, breaking point; area under curve = energy per unit volume.

Conservation of momentum applies in all collisions (elastic and inelastic); kinetic energy conserved only in elastic collisions.

Work, energy, power: W = Fs cosθ, KE = ½mv², ΔPE = mgΔh, P = W/t = Fv.

Ohm's law V = IR; resistivity R = ρl/A; conductance and drift velocity I = nAve.

Series: R = R₁ + R₂ + …; parallel: 1/R = 1/R₁ + 1/R₂ + …; potential divider V_out = V_in × R₂/(R₁+R₂).

Electrical power: P = VI = I²R = V²/R; energy = Pt.

EMF and internal resistance: ε = I(R + r); terminal p.d. V = ε − Ir.

Capacitors: Q = CV, energy = ½CV² = ½QV; time constant τ = RC; discharge Q = Q₀e^(−t/RC).

Magnetic force on a current: F = BIl sinθ; on a moving charge: F = Bqv sinθ; radius of circular path r = mv/(Bq).

Magnetic flux Φ = BA cosθ; induced EMF ε = −N dΦ/dt (Faraday); Lenz's law gives the direction opposing the change.

Transformer: V_s/V_p = N_s/N_p; ideal transformer input power = output power.

Coulomb's law F = kQ₁Q₂/r²; uniform field E = V/d; force on charge F = qE.

Wave equation v = fλ; period T = 1/f; for a stretched string v = √(T/μ) where μ is mass per unit length.

Transverse waves oscillate perpendicular to propagation; longitudinal waves oscillate parallel (e.g. sound).

Superposition: displacements add; constructive interference requires path difference = nλ; destructive requires (n + ½)λ.

Two-source interference condition for observable pattern: coherent sources with constant phase difference and comparable amplitude.

Stationary waves on a string fixed at both ends: λ = 2L/n; fundamental f₁ = v/(2L).

Diffraction grating: d sinθ = nλ; double slit fringe spacing x = λD/d.

Doppler effect (sound, source moving): observed f' = f v/(v ± v_s), sign chosen by approach or recession.

Intensity of a wave is proportional to amplitude squared; intensity falls as 1/r² for a point source in 3D.

Electromagnetic spectrum order by increasing frequency: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma.

Refraction: Snell's law n₁ sinθ₁ = n₂ sinθ₂; refractive index n = c/v.

Critical angle: sinθ_c = n₂/n₁; total internal reflection occurs only when travelling from denser to less dense medium.

Thin lens/mirror equation: 1/f = 1/u + 1/v; magnification m = v/u = image height/object height.

Real images are formed by converging lenses when u > f; virtual images are upright and on the same side as the object for a converging lens when u < f.

Specific heat capacity: E = mcΔθ; specific latent heat: E = mL.

Ideal gas law: pV = nRT; kinetic theory gives pV = ⅓Nm⟨c²⟩ and mean KE per molecule = (3/2)kT.

First law of thermodynamics: ΔU = Q − W (W done by the gas); for an isothermal process ΔU = 0.

Efficiency of a heat engine: η = W/Q_in = 1 − Q_out/Q_in; Carnot limit η = 1 − T_c/T_h (absolute temperatures).

Thermal conduction rate: dQ/dt = kAΔT/L; Stefan–Boltzmann law for a black body: P = σAT⁴.

Photoelectric equation: hf = φ + KE_max; threshold frequency f₀ = φ/h; stopping potential eV_s = KE_max.

Photon energy E = hf = hc/λ; de Broglie wavelength λ = h/p = h/(mv).

Einstein mass–energy: E = mc²; mass defect Δm converts to binding energy via ΔE = Δmc².

Radioactive decay: N = N₀e^(−λt); activity A = λN; half-life t½ = ln2/λ.

Nuclear notation: A = nucleon number, Z = proton number; alpha decay reduces A by 4 and Z by 2; beta-minus increases Z by 1.

Uncertainty: for a single reading use the instrument resolution; for repeated readings use half-range or standard deviation of the mean.

Combining uncertainties: add absolute uncertainties for sums/differences; add percentage uncertainties for products/quotients/powers.

Graphical analysis: plot to obtain a straight line, then gradient and intercept give the physical constants; error bars show uncertainty.

Significant figures in a final answer should match the least precise measurement used in the calculation.