Myanmar Matriculation Physics cheat sheet

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

Newton's second law: F = ma; weight W = mg with g ≈ 9.8 m s⁻². Momentum p = mv and impulse FΔt = Δp.

Conservation of linear momentum applies when net external force is zero; for elastic collisions kinetic energy is also conserved, for perfectly inelastic collisions bodies stick together.

Projectile motion: horizontal component ux = u cosθ (constant); vertical uy = u sinθ with a = −g. Time of flight T = 2u sinθ/g, range R = u² sin2θ/g, max height H = u² sin²θ/(2g).

Circular motion: angular velocity ω = 2π/T = v/r; centripetal acceleration a = v²/r = ω²r; centripetal force F = mv²/r.

Work W = Fs cosθ; kinetic energy ½mv²; gravitational potential energy mgh; power P = W/t = Fv.

Hooke's law F = kx within the elastic limit; elastic potential energy = ½kx²; stress = F/A, strain = e/L, Young modulus E = stress/strain.

Torque τ = Fd (perpendicular distance); principle of moments: sum of clockwise moments = sum of anticlockwise moments about a point in equilibrium.

Universal gravitation F = Gm₁m₂/r²; g = GM/r²; orbital speed v = √(GM/r); Kepler's third law T² ∝ r³.

Temperature conversion: T(K) = θ(°C) + 273.15; absolute zero is 0 K = −273.15 °C.

Linear expansion ΔL = αL₀Δθ; area ΔA = βA₀Δθ with β ≈ 2α; volume ΔV = γV₀Δθ with γ ≈ 3α.

Heat energy Q = mcΔθ (specific heat capacity) and Q = mL (latent heat); at a change of state temperature stays constant while latent heat is absorbed or released.

Boyle's law pV = constant at constant T; Charles's law V/T = constant at constant p; pressure law p/T = constant at constant V; combined ideal gas law pV/T = constant.

Ideal gas equation pV = nRT with R ≈ 8.31 J mol⁻¹ K⁻¹; also pV = NkT with k ≈ 1.38 × 10⁻²³ J K⁻¹.

Kinetic theory: pV = ⅓Nm⟨c²⟩; mean kinetic energy per molecule = (3/2)kT; root-mean-square speed c_rms = √(3RT/M).

First law of thermodynamics: ΔU = Q − W, where W is work done by the gas; W = pΔV at constant pressure.

Isothermal process: T constant, ΔU = 0, so Q = W. Adiabatic process: Q = 0, so ΔU = −W.

Efficiency of a heat engine η = W/Q₁ = (Q₁ − Q₂)/Q₁; Carnot maximum efficiency η = 1 − T₂/T₁ using kelvin temperatures.

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

Transverse waves: particle displacement perpendicular to propagation (light, waves on strings). Longitudinal waves: displacement parallel to propagation (sound).

Superposition: resultant displacement is the vector sum of individual displacements; constructive interference when path difference = nλ, destructive when (n + ½)λ.

Stationary waves on a string fixed at both ends: λ = 2L/n, f = nv/(2L); nodes are points of zero displacement, antinodes of maximum displacement.

Distance between adjacent nodes (or adjacent antinodes) is λ/2; distance between a node and the next antinode is λ/4.

Reflection: at a fixed (denser) boundary the reflected wave is inverted; at a free boundary it is not inverted.

Refraction: v₁/v₂ = λ₁/λ₂ = sin i/sin r; frequency is unchanged when a wave crosses a boundary.

Diffraction is significant when the slit width is comparable to the wavelength; diffraction grating maxima at d sinθ = nλ.

Doppler effect for sound: observed frequency f′ = f(v ± v₀)/(v ∓ vₛ), using upper sign for approach.

Speed of sound in air ≈ 330–340 m s⁻² at room temperature; it increases with temperature and is independent of pressure at constant temperature.

Sound needs a material medium; it cannot travel through a vacuum. Audible range for humans ≈ 20 Hz to 20 kHz; ultrasound is above 20 kHz.

Intensity level in decibels: L = 10 log₁₀(I/I₀) with I₀ = 1 × 10⁻¹² W m⁻².

Closed pipe (one closed end): f = (2n − 1)v/(4L), odd harmonics only. Open pipe (both ends open): f = nv/(2L), all harmonics.

Law of reflection: angle of incidence = angle of reflection, both measured from the normal. Snell's law: n₁ sin i = n₂ sin r; refractive index n = c/v = real depth/apparent depth.

Critical angle: sin C = n₂/n₁ (n₁ > n₂); total internal reflection occurs only when the angle of incidence exceeds C.

Thin lens/mirror formula: 1/f = 1/u + 1/v; magnification m = v/u = image height/object height; power P = 1/f in dioptres (f in metres).

Real images are formed by converging lenses when u > f and are inverted; convex mirrors and concave lenses always give virtual, diminished images.

Two-slit interference: fringe spacing x = λD/d; light wavelength ≈ 5 × 10⁻⁷ m; dispersion occurs because refractive index varies with wavelength.

Ohm's law V = IR at constant temperature; resistance R = ρL/A; resistors in series add, in parallel 1/R = 1/R₁ + 1/R₂.

Electrical power P = VI = I²R = V²/R; energy = Pt; charge Q = It.

Kirchhoff's laws: sum of currents at a junction = 0; sum of emf = sum of p.d. around a closed loop. EMF ε = I(R + r) with internal resistance r.

Capacitance C = Q/V; energy stored = ½QV = ½CV²; capacitors in parallel add, in series 1/C = 1/C₁ + 1/C₂.

Coulomb's law F = kq₁q₂/r² with k = 1/(4πε₀) ≈ 9 × 10⁹ N m² C⁻²; electric field E = F/q and E = V/d for uniform fields.

Magnetic force on a current-carrying wire F = BIL sinθ; on a moving charge F = qvB sinθ; force is maximum when the current is perpendicular to B.

Force per unit length between parallel wires F/L = μ₀I₁I₂/(2πd); currents in the same direction attract.

Electromagnetic induction: induced emf = −N dΦ/dt (Faraday); Φ = BA cosθ; Lenz's law gives the direction opposing the change producing it.

Transformer: Vₛ/Vₚ = Nₛ/Nₚ; ideal transformer input power equals output power; step-up increases voltage and decreases current.

Photoelectric effect: E = hf = W + K_max, with W the work function; threshold frequency f₀ = W/h; stopping potential eVₛ = K_max.

Photon energy in eV: E(eV) = hf/e; h ≈ 6.63 × 10⁻³⁴ J s; use E = hc/λ for a photon of wavelength λ.

de Broglie wavelength λ = h/p = h/(mv); electrons show diffraction, confirming wave–particle duality.

Bohr model: Eₙ = −13.6/n² eV for hydrogen; photon emitted when an electron falls from a higher to a lower level, energy = E₂ − E₁ = hf.

Radioactive decay N = N₀e^(−λt); half-life T½ = ln2/λ ≈ 0.693/λ; activity A = λN.

Nuclear notation ᴬZX: Z protons, A − Z neutrons; isotopes have the same Z but different A. Mass defect converted to energy by E = mc².

Alpha decay reduces Z by 2 and A by 4; beta-minus decay increases Z by 1 and leaves A unchanged; gamma emission changes neither.

Diode: conducts when forward biased above about 0.7 V (silicon); in reverse bias it blocks current. A Zener diode in reverse breakdown regulates voltage.

Transistor (npn) current relation Iₑ = I_b + I_c; current gain β = I_c/I_b; for a silicon transistor forward bias V_BE ≈ 0.7 V.

Logic gates: AND output 1 only if all inputs 1; OR output 1 if any input 1; NOT inverts; NAND and NOR are universal gates.