Érettségi Physics cheat sheet

Uniformly accelerated motion: v = v₀ + at, s = v₀t + at²/2, v² = v₀² + 2as; these hold only for constant acceleration.

Projectile motion separates into independent horizontal (constant v) and vertical (a = g) components; range is maximal at 45° when launch and landing heights are equal.

Newton's second law in vector form: ΣF = ma; on an incline the driving component is mg·sinθ and the normal force is mg·cosθ.

Friction: static friction satisfies F ≤ μs·N; kinetic friction equals μk·N and opposes relative sliding, not the direction of motion itself.

Work–energy theorem: W_net = ΔEk = mv²/2 − mv₀²/2; work by a constant force is W = F·s·cosα.

Conservation of momentum applies to any isolated system (ΣF_ext = 0); in collisions total momentum is conserved, kinetic energy only in elastic ones.

Torque about an axis: τ = F·d⊥; a rigid body is in static equilibrium when both ΣF = 0 and Στ = 0.

For a body in equilibrium, the line of action of its weight must pass above the base of support; the centre of mass height and base width set stability.

Linear expansion: ΔL = α·L₀·ΔT; volume expansion uses β ≈ 3α for isotropic solids.

Heat transfer: Q = c·m·ΔT for temperature change, Q = L·m for phase change at constant temperature (L_f fusion, L_v vaporisation).

Ideal gas law: pV = nRT = (N/N_A)RT; with N particles, pV = NkT and k = R/N_A.

Kinetic theory: average translational kinetic energy per molecule = (3/2)kT, so internal energy of a monatomic ideal gas is U = (3/2)nRT.

First law: ΔU = Q + W where W is work done on the gas; work by the gas at constant pressure is W = pΔV.

Isothermal work by an ideal gas: W = nRT·ln(V₂/V₁); adiabatic processes obey pV^κ = constant with κ = C_p/C_v.

Carnot efficiency of a heat engine: η = 1 − T_cold/T_hot, with temperatures in kelvin; no engine between two reservoirs exceeds this.

Second law: entropy of an isolated system never decreases; heat flows spontaneously from hot to cold, never the reverse without work input.

Coulomb's law: F = k·q₁q₂/r² with k ≈ 9×10⁹ N·m²/C²; field of a point charge E = kQ/r², and E inside a conductor in equilibrium is zero.

Uniform field between parallel plates: E = U/d; potential energy change of a charge moving through voltage U is ΔE = qU.

Ohm's law for a conductor segment: U = IR; series resistances add, parallel conductances add (1/R_total = Σ1/Rᵢ).

Power dissipation: P = UI = I²R = U²/R; a real source delivers maximum power to a load when R_load = r_internal.

Kirchhoff's laws: the sum of currents at a node is zero, and the sum of potential differences around any closed loop is zero.

Magnetic force on a moving charge: F = qvB·sinα (perpendicular to v and B); on a current-carrying wire of length L: F = BIL·sinα.

Long straight wire field: B = μ₀I/(2πr); inside a long solenoid B = μ₀nI with n turns per metre.

Faraday's law: induced emf ε = −N·ΔΦ/Δt, with flux Φ = B·A·cosα; Lenz's law fixes the direction so the induced effect opposes the change.

Wave relation: v = λf; for a stretched string the speed is v = √(F/μ) with μ the linear mass density.

Sound speed in air ≈ 340 m/s at room temperature and rises with temperature; audible range is roughly 20 Hz to 20 kHz.

Snell's law: n₁·sinθ₁ = n₂·sinθ₂; total internal reflection occurs only going from denser to rarer medium beyond the critical angle sinθ_c = n₂/n₁.

Thin lens and mirror equation: 1/f = 1/k + 1/t (object distance t, image distance k); magnification m = −k/t for lenses.

Young's double slit: fringe spacing Δy = λL/d; constructive interference needs path difference mλ, destructive needs (m + ½)λ.

Single-slit and grating: grating maxima at d·sinθ = mλ; the first single-slit minimum at a·sinθ = λ.

Diffraction limit of resolution: θ ≈ 1.22·λ/D for a circular aperture of diameter D.

Doppler effect for sound: f' = f·(v ± v_observer)/(v ∓ v_source); sign choice depends on whether approach or recession occurs.

Photon energy: E = hf = hc/λ; h ≈ 6.63×10⁻³⁴ J·s, and 1 eV ≈ 1.6×10⁻¹⁹ J.

Photoelectric effect: emission occurs only above a threshold frequency f₀; maximum kinetic energy is Ek_max = hf − W, where W is the work function.

Bohr model: E_n = −13.6 eV/n² for hydrogen; spectral lines arise from transitions with ΔE = hf.

de Broglie wavelength: λ = h/p = h/(mv), expressing wave–particle duality for matter.

Radioactive decay law: N = N₀·(1/2)^(t/T½); activity A = λN with λ = ln2/T½, measured in becquerel.

Alpha decay reduces mass number by 4 and atomic number by 2; beta-minus decay raises atomic number by 1 with unchanged mass number.

Mass defect and binding energy: ΔE = Δm·c²; 1 u corresponds to about 931.5 MeV.

Nuclear fission of heavy nuclei and fusion of light nuclei both release energy because the binding energy per nucleon peaks near iron (A ≈ 56).

Newton's law of gravitation: F = G·m₁m₂/r² with G ≈ 6.67×10⁻¹¹ N·m²/kg².

Gravitational field strength of a point mass or sphere: g = GM/r²; potential energy U = −GMm/r with the zero at infinity.

Circular orbital speed: v = √(GM/r); orbital period satisfies Kepler's third law T² = 4π²r³/(GM).

Kepler's laws: elliptical orbits with the central body at one focus, equal areas in equal times, and T² ∝ a³.

Escape velocity from a body of mass M and radius R: v_esc = √(2GM/R), about 11.2 km/s from Earth's surface.

Geostationary orbit lies above the equator with a period of one sidereal day, radius about 42,000 km from Earth's centre.

Hubble's law: v = H₀·d, with H₀ ≈ 70 km/s/Mpc; cosmological redshift indicates an expanding universe.

Light-year ≈ 9.46×10¹² km; 1 parsec ≈ 3.26 light-years ≈ 3.09×10¹⁶ m, the distance at which 1 AU subtends 1 arcsecond.

SI base units: metre, kilogram, second, ampere, kelvin, mole, candela; derived units such as newton, joule, watt, volt, tesla are combinations of these.

Dimensional analysis checks equations: both sides must have identical base-unit exponents; it cannot supply dimensionless numerical factors.

Measurement uncertainty: for repeated readings use the standard deviation; for a single scale reading use half the smallest division.

Relative error of a product or quotient adds the relative errors of the factors; for sums and differences absolute errors add.

Efficiency of a device: η = useful output energy / total input energy, always below 1 because of losses, chiefly heat.

Transformer relation: U₁/U₂ = N₁/N₂; an ideal transformer conserves power, so higher voltage means proportionally lower current.

Household mains in Hungary is about 230 V, 50 Hz; fuses and circuit breakers protect against overload by interrupting excess current.

Historical milestones: Newton's Principia (1687), Faraday's induction (1831), Maxwell's equations (1865), Planck's quantum hypothesis (1900), Einstein's relativity (1905).