MATSEC IM Physics cheat sheet

Newton's second law: resultant force F = ma; momentum form F = dp/dt holds when mass changes.

SUVAT equations apply only for constant acceleration: v = u + at, s = ut + ½at², v² = u² + 2as.

Projectile motion: horizontal velocity constant, vertical acceleration g downward; time of flight from vertical motion alone.

Conservation of linear momentum: total momentum constant in a closed system; elastic collisions also conserve kinetic energy.

Circular motion: centripetal acceleration a = v²/r = ω²r directed toward the centre; force is the resultant, not an extra force.

Hooke's law F = kx up to the limit of proportionality; elastic potential energy stored = ½Fx = ½kx².

Stress = F/A, strain = extension/original length, Young modulus E = stress/strain; units Pa.

Pressure in a fluid at depth h: p = p₀ + ρgh; upthrust equals weight of displaced fluid (Archimedes).

Density ρ = m/V; moments: sum of clockwise moments about a point equals sum of anticlockwise moments in equilibrium.

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

Transverse waves: oscillation perpendicular to energy transfer; longitudinal waves: oscillation parallel (sound).

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

Two-source interference requires coherent sources (constant phase difference) and comparable amplitudes.

Diffraction grating: d sinθ = nλ gives principal maxima; larger λ gives larger spacing between orders.

Snell's law n₁ sinθ₁ = n₂ sinθ₂; refractive index n = c/v; critical angle sinθc = n₂/n₁.

Simple harmonic motion: a = −ω²x, T = 2π/ω; for a pendulum T = 2π√(l/g), for a mass-spring T = 2π√(m/k).

Resonance occurs when driving frequency equals natural frequency; damping reduces amplitude and shifts resonance.

Thin lens/mirror equation 1/f = 1/u + 1/v; magnification m = v/u; real images form where rays actually converge.

Ohm's law V = IR holds for ohmic conductors at constant temperature; resistance R = ρL/A.

Series: same current, voltages add, R_total = R₁ + R₂; parallel: same voltage, currents add, 1/R = 1/R₁ + 1/R₂.

Power dissipated P = VI = I²R = V²/R; energy = power × time.

EMF ε = I(R + r) with internal resistance r; terminal voltage falls as current rises.

Kirchhoff's laws: sum of currents at a junction is zero; sum of EMFs equals sum of p.d.s around a loop.

Capacitor charge Q = CV; energy stored = ½CV²; time constant τ = RC for charge/discharge.

Magnetic force on a current: F = BIL sinθ; on a moving charge F = Bqv sinθ; direction from Fleming's left-hand rule.

Faraday's law: induced EMF equals rate of change of magnetic flux linkage; Lenz's law gives the opposing direction.

Operational amplifier: ideal infinite open-loop gain and input resistance; inverting gain = −R_f/R_in, non-inverting = 1 + R_f/R_in.

Specific heat capacity c: Q = mcΔT; specific latent heat L: Q = mL at constant temperature.

Ideal gas equation pV = nRT; alternative form pV = NkT with k = 1.38 × 10⁻²³ J K⁻¹.

Absolute temperature must be used in gas laws; T(K) = θ(°C) + 273.15.

Kinetic theory: mean kinetic energy of a molecule = (3/2)kT, independent of gas identity.

First law of thermodynamics: ΔU = Q − W, where W is work done by the gas.

Internal energy of an ideal gas depends only on temperature; it is the sum of molecular kinetic energies.

Boyle's law pV constant at fixed T; pressure law p/T constant at fixed V; volume law V/T constant at fixed p.

Thermal conduction rate through a slab: dQ/dt = kAΔT/L; metals conduct via free electrons.

Photoelectric equation hf = φ + K_max; threshold frequency f₀ = φ/h; no emission below f₀ regardless of intensity.

Photon energy E = hf = hc/λ; h = 6.63 × 10⁻³⁴ J s.

de Broglie wavelength λ = h/p = h/(mv); electron diffraction confirms wave behaviour.

Einstein mass-energy E = mc²; mass defect in a nucleus appears as binding energy.

Radioactive decay N = N₀e^(−λt); half-life t½ = ln2/λ ≈ 0.693/λ.

Nuclear notation: A = nucleon number, Z = proton number; alpha decay reduces A by 4 and Z by 2.

Gravitational field strength g = GM/r²; potential V = −GM/r; escape velocity v = √(2GM/r).

Electric field of a point charge E = Q/(4πε₀r²); uniform field between plates E = V/d.

Coulomb's law F = Q₁Q₂/(4πε₀r²); field lines point from positive to negative charge.

Intensity of a wave is proportional to amplitude squared; doubling amplitude quadruples intensity.

Doppler effect for sound: observed frequency rises as source and observer approach.

Stationary waves on a string fixed at both ends: λ = 2L/n; nodes are points of zero displacement.

Polarisation proves a wave is transverse; light can be polarised, sound cannot.

Total internal reflection occurs only when light travels from denser to less dense medium and angle exceeds critical angle.

Progressive wave displacement y = A sin(ωt − kx) with k = 2π/λ.

Energy in SHM: total energy = ½mω²A², constant; kinetic and potential interchange.

Optical fibre cladding has lower refractive index than core to allow total internal reflection.

Potential difference is energy transferred per unit charge: V = W/Q; EMF is energy gained per unit charge.

Charge carriers in metals are electrons; conventional current is opposite to electron drift.

Drift velocity I = nAve, where n is number density and e is elementary charge.

Semiconductor diode conducts above about 0.7 V forward bias (silicon); reverse bias gives negligible current.

A potential divider gives V_out = V_in × R₂/(R₁ + R₂).

Magnetic flux Φ = BA cosθ; flux linkage = NΦ; unit weber.

A transformer with ideal efficiency: V_s/V_p = N_s/N_p; step-up raises voltage and lowers current.

A capacitor blocks direct current but passes alternating current; reactance falls as frequency rises.

Temperature measures average kinetic energy of particles; thermal energy transfers from hot to cold spontaneously.

Avogadro constant N_A = 6.02 × 10²³ mol⁻¹; number of moles n = N/N_A = m/M.

Universal gas constant R = 8.31 J mol⁻¹ K⁻¹; R = N_A k.

Root-mean-square speed of gas molecules: v_rms = √(3kT/m) = √(3RT/M).

Pressure from kinetic theory arises from molecular collisions with container walls; p ∝ (1/3)ρ(v_rms)².

Convection transfers heat by bulk fluid movement; radiation needs no medium and is emitted by all bodies above 0 K.

A black body is a perfect absorber and emitter; peak wavelength decreases as temperature rises (Wien's law).

In an adiabatic change no heat enters or leaves, so ΔU = −W for work done by the gas.

Atomic energy levels are discrete; photon emission occurs when an electron drops to a lower level, with hf = E₁ − E₂.

Line spectra are evidence for quantised energy levels; absorption lines match emission lines of the same element.

Work function φ is the minimum energy needed to remove an electron from a metal surface.

Half-life is the time for half the nuclei of a sample to decay; it is unaffected by temperature or pressure.

Activity A = λN, measured in becquerels (decays per second).

Gravitational potential energy near Earth's surface: ΔE = mgΔh; field strength g = F/m.

Electric potential energy between two charges: E = Q₁Q₂/(4πε₀r).

Field lines never cross; their density indicates field strength.

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