Armenia Physics Unified Exam cheat sheet

Uniformly accelerated motion: v = v0 + at, x = v0·t + at²/2, v² − v0² = 2a·x; these hold only for constant acceleration.

Projectile motion separates into independent components: horizontal velocity constant, vertical acceleration g ≈ 9.8 m/s² downward.

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

Friction: static friction satisfies f ≤ μs·N; kinetic friction is f = μk·N and opposes relative sliding.

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

Conservation of mechanical energy applies when only conservative forces do work: Ek + Ep = constant, with Ep = mgh or kx²/2.

Momentum is conserved in collisions and explosions: Σmv before = Σmv after; kinetic energy is conserved only in elastic collisions.

Static equilibrium requires both ΣF = 0 and Στ = 0 about any chosen axis; torque τ = F·d·sinθ with d the lever arm.

Circular motion: centripetal acceleration a = v²/r directed toward the center; centripetal force is a net force, not a new kind of force.

Ideal gas law: pV = nRT = (N/N_A)·kT, with R ≈ 8.31 J/(mol·K) and k ≈ 1.38×10⁻²³ J/K.

Average translational kinetic energy of a gas molecule is (3/2)kT, independent of gas type; rms speed v = √(3kT/m).

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

Internal energy of a monatomic ideal gas is U = (3/2)nRT; temperature is a measure of average molecular kinetic energy.

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

Efficiency of a heat engine is η = W/Q_hot = 1 − Q_cold/Q_hot; Carnot limit is η = 1 − T_cold/T_hot in kelvin.

Absolute humidity is water-vapor density; relative humidity is the ratio of actual vapor pressure to saturation pressure at that temperature.

Heat transfer by conduction follows Q/t = k·A·ΔT/L; evaporation cools a liquid because the fastest molecules escape.

Coulomb's law: F = k·q1·q2/r², k ≈ 9×10⁹ N·m²/C²; force is along the line joining the charges and is repulsive for like signs.

Electric field E = F/q; for a point charge E = kq/r², and field lines point away from positive charge toward negative charge.

Ohm's law for a conductor: I = U/R; resistance R = ρL/A, so longer or thinner wires have greater resistance.

Series: R_total = ΣR, current is the same everywhere; parallel: 1/R_total = Σ(1/R), voltage is the same across branches.

Electric power: P = UI = I²R = U²/R; energy consumed is P·t, measured in joules or kilowatt-hours.

Magnetic force on a moving charge is F = qvB·sinθ, perpendicular to both v and B; on a current-carrying wire F = BIL·sinθ.

Faraday's law: induced emf ε = −N·ΔΦ/Δt; Lenz's law says the induced current opposes the change in magnetic flux.

A straight wire carrying current I produces B = μ0·I/(2πr) at distance r; the field direction follows the right-hand rule.

Simple harmonic motion: restoring force F = −kx, period of a spring oscillator T = 2π√(m/k), of a pendulum T = 2π√(L/g).

In SHM, displacement x = A·sin(ωt), velocity is maximum at equilibrium, and acceleration is maximum at the turning points.

Wave relation: v = λ·f = λ/T; frequency is set by the source and does not change when the wave enters a new medium.

Resonance occurs when the driving frequency equals the natural frequency; amplitude peaks and energy transfer is maximal.

Sound intensity level β = 10·log(I/I0) dB with I0 = 10⁻¹² W/m²; each 10 dB rise means tenfold intensity.

Reflection law: angle of incidence equals angle of reflection; refraction follows Snell's law, n1·sinθ1 = n2·sinθ2.

Thin lens or mirror: 1/f = 1/d_o + 1/d_i; real images form when d_i > 0, virtual images give negative image distance.

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

Light wavelength relates to frequency by c = λ·f; in a medium of refractive index n, the speed becomes v = c/n.

Photoelectric effect: photon energy E = hf = hc/λ; emission occurs only if hf exceeds the work function A.

Einstein's photoelectric equation: Ek_max = hf − A, where Ek_max is independent of light intensity.

Stopping voltage satisfies e·U_stop = Ek_max; the saturation photocurrent is proportional to light intensity.

Bohr model: hf = E_high − E_low for emitted photons; hydrogen levels E_n = −13.6 eV/n².

de Broglie wavelength: λ = h/p = h/(mv), showing wave behavior for moving particles.

Nucleus notation ᴬ_Z X: Z is the proton number, A − Z is the neutron number; isotopes share Z but differ in A.

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

Radioactive decay law: N = N0·e^(−λt), half-life T1/2 = ln2/λ ≈ 0.693/λ.

Mass defect converts to binding energy by E = Δm·c²; 1 u corresponds to about 931.5 MeV.

Report a measurement as x = x_mean ± Δx, where Δx is the absolute uncertainty of the measurement, not the spread of the mean alone.

For repeated readings, uncertainty is often taken as half the instrument division or the standard deviation of the mean.

Relative (percentage) uncertainty is Δx/x_mean × 100%; it adds when multiplying or dividing quantities.

When adding or subtracting values, absolute uncertainties add; when multiplying or dividing, relative uncertainties add.

Plot the quantity on the y-axis against the controlled variable on the x-axis; a straight line indicates direct proportionality.

Slope of a linear graph equals the change in y divided by the change in x, and its units are y-units per x-unit.

Estimate orders of magnitude by rounding inputs to one significant figure, then check the result against physical plausibility.

Significant figures in a result should match the least precise input; do not report more digits than the data justify.

Uniformly accelerated motion: v = v0 + at, x = v0·t + at²/2, v² − v0² = 2a·x; these hold only for constant acceleration.

Projectile motion separates into independent components: horizontal velocity constant, vertical acceleration g ≈ 9.8 m/s² downward.

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

Friction: static friction satisfies f ≤ μs·N; kinetic friction is f = μk·N and opposes relative sliding.

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

Conservation of mechanical energy applies when only conservative forces do work: Ek + Ep = constant, with Ep = mgh or kx²/2.

Momentum is conserved in collisions and explosions: Σmv before = Σmv after; kinetic energy is conserved only in elastic collisions.

Static equilibrium requires both ΣF = 0 and Στ = 0 about any chosen axis; torque τ = F·d·sinθ with d the lever arm.

Circular motion: centripetal acceleration a = v²/r directed toward the center; centripetal force is a net force, not a new kind of force.

Ideal gas law: pV = nRT = (N/N_A)·kT, with R ≈ 8.31 J/(mol·K) and k ≈ 1.38×10⁻²³ J/K.

Average translational kinetic energy of a gas molecule is (3/2)kT, independent of gas type; rms speed v = √(3kT/m).

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

Internal energy of a monatomic ideal gas is U = (3/2)nRT; temperature is a measure of average molecular kinetic energy.

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

Efficiency of a heat engine is η = W/Q_hot = 1 − Q_cold/Q_hot; Carnot limit is η = 1 − T_cold/T_hot in kelvin.

Absolute humidity is water-vapor density; relative humidity is the ratio of actual vapor pressure to saturation pressure at that temperature.

Heat transfer by conduction follows Q/t = k·A·ΔT/L; evaporation cools a liquid because the fastest molecules escape.

Coulomb's law: F = k·q1·q2/r², k ≈ 9×10⁹ N·m²/C²; force is along the line joining the charges and is repulsive for like signs.

Electric field E = F/q; for a point charge E = kq/r², and field lines point away from positive charge toward negative charge.

Ohm's law for a conductor: I = U/R; resistance R = ρL/A, so longer or thinner wires have greater resistance.

Series: R_total = ΣR, current is the same everywhere; parallel: 1/R_total = Σ(1/R), voltage is the same across branches.

Electric power: P = UI = I²R = U²/R; energy consumed is P·t, measured in joules or kilowatt-hours.

Magnetic force on a moving charge is F = qvB·sinθ, perpendicular to both v and B; on a current-carrying wire F = BIL·sinθ.

Faraday's law: induced emf ε = −N·ΔΦ/Δt; Lenz's law says the induced current opposes the change in magnetic flux.

A straight wire carrying current I produces B = μ0·I/(2πr) at distance r; the field direction follows the right-hand rule.

Simple harmonic motion: restoring force F = −kx, period of a spring oscillator T = 2π√(m/k), of a pendulum T = 2π√(L/g).

In SHM, displacement x = A·sin(ωt), velocity is maximum at equilibrium, and acceleration is maximum at the turning points.

Wave relation: v = λ·f = λ/T; frequency is set by the source and does not change when the wave enters a new medium.

Resonance occurs when the driving frequency equals the natural frequency; amplitude peaks and energy transfer is maximal.

Sound intensity level β = 10·log(I/I0) dB with I0 = 10⁻¹² W/m²; each 10 dB rise means tenfold intensity.

Reflection law: angle of incidence equals angle of reflection; refraction follows Snell's law, n1·sinθ1 = n2·sinθ2.

Thin lens or mirror: 1/f = 1/d_o + 1/d_i; real images form when d_i > 0, virtual images give negative image distance.

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

Light wavelength relates to frequency by c = λ·f; in a medium of refractive index n, the speed becomes v = c/n.

Photoelectric effect: photon energy E = hf = hc/λ; emission occurs only if hf exceeds the work function A.

Einstein's photoelectric equation: Ek_max = hf − A, where Ek_max is independent of light intensity.

Stopping voltage satisfies e·U_stop = Ek_max; the saturation photocurrent is proportional to light intensity.

Bohr model: hf = E_high − E_low for emitted photons; hydrogen levels E_n = −13.6 eV/n².

de Broglie wavelength: λ = h/p = h/(mv), showing wave behavior for moving particles.

Nucleus notation ᴬ_Z X: Z is the proton number, A − Z is the neutron number; isotopes share Z but differ in A.

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

Radioactive decay law: N = N0·e^(−λt), half-life T1/2 = ln2/λ ≈ 0.693/λ.

Mass defect converts to binding energy by E = Δm·c²; 1 u corresponds to about 931.5 MeV.

Report a measurement as x = x_mean ± Δx, where Δx is the absolute uncertainty of the measurement, not the spread of the mean alone.

For repeated readings, uncertainty is often taken as half the instrument division or the standard deviation of the mean.

Relative (percentage) uncertainty is Δx/x_mean × 100%; it adds when multiplying or dividing quantities.

When adding or subtracting values, absolute uncertainties add; when multiplying or dividing, relative uncertainties add.

Plot the quantity on the y-axis against the controlled variable on the x-axis; a straight line indicates direct proportionality.

Slope of a linear graph equals the change in y divided by the change in x, and its units are y-units per x-unit.

Estimate orders of magnitude by rounding inputs to one significant figure, then check the result against physical plausibility.

Significant figures in a result should match the least precise input; do not report more digits than the data justify.