Georgia Unified Physics cheat sheet

Kinematics: v = v₀ + at, Δx = v₀t + ½at², v² = v₀² + 2aΔx; these apply only for constant acceleration.

Projectile motion separates axes: horizontal velocity is constant, vertical acceleration is g = 9.8 m/s² downward; time of flight depends only on vertical motion.

Newton's second law: ΣF = ma; weight is W = mg, and normal force equals mg only on a level surface with no other vertical forces.

Friction: static friction satisfies f_s ≤ μ_sN and adjusts to applied force; kinetic friction is f_k = μ_kN and opposes relative sliding.

Uniform circular motion: a_c = v²/r directed toward the center; the net force must point inward, and no outward 'centrifugal force' exists in an inertial frame.

Work-energy: W = Fd cosθ, kinetic energy KE = ½mv², and W_net = ΔKE; gravity and springs are conservative, so they have potential energy.

Momentum: p = mv, impulse J = FΔt = Δp; total momentum is conserved when net external force is zero, including inelastic collisions.

Torque and equilibrium: τ = rF sinθ about a pivot; static equilibrium requires ΣF = 0 and Στ = 0 about any chosen axis.

First law: ΔU = Q − W, with W the work done by the gas; for a monatomic ideal gas U = (3/2)nRT.

Ideal gas law: PV = nRT with R = 8.31 J/(mol·K); at constant T, P₁V₁ = P₂V₂ (Boyle), and at constant P, V₁/T₁ = V₂/T₂ (Charles).

Isothermal work by an ideal gas is W = nRT ln(V₂/V₁); adiabatic processes have Q = 0, so ΔU = −W.

Second law: entropy of an isolated system never decreases; no cyclic engine converts heat entirely to work, so efficiency e = W/Q_H < 1.

Carnot efficiency sets the ceiling: e_Carnot = 1 − T_C/T_H, with both temperatures in kelvin.

Heat transfer: Q = mcΔT for temperature change and Q = mL for phase change at constant temperature; the two are never applied to the same interval.

Kelvin conversion: T(K) = T(°C) + 273; doubling Celsius temperature does not double kelvin temperature, so gas-law ratios require kelvin.

Wave relation: v = fλ; frequency is set by the source and stays fixed when a wave crosses into a new medium, while speed and wavelength change.

For a string fixed at both ends, standing-wave wavelengths are λ = 2L/n and frequencies f = nv/(2L); a pipe open at both ends has the same set.

A pipe closed at one end supports only odd harmonics: f = nv/(4L) with n = 1, 3, 5, ...

Snell's law: n₁sinθ₁ = n₂sinθ₂ with n = c/v; light bending toward the normal means it entered a higher-index medium.

Total internal reflection occurs only when light travels from higher to lower index and the incident angle exceeds θ_c = sin⁻¹(n₂/n₁).

Thin lens and mirror equation: 1/f = 1/d_o + 1/d_i with magnification m = −d_i/d_o; a negative d_i means a virtual image on the same side as the object for lenses.

Double-slit maxima occur at d sinθ = mλ; single-slit minima at a sinθ = mλ with m = 1, 2, 3, ...

Doppler effect: observed frequency rises when source and observer approach and falls when they separate; the shift depends on relative velocity, not distance.

Coulomb's law: F = kq₁q₂/r² with k = 8.99×10⁹ N·m²/C²; force follows the inverse square and acts along the line joining charges.

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

Ohm's law V = IR holds for ohmic resistors at constant temperature; power dissipated is P = IV = I²R = V²/R.

Series: R_eq = R₁ + R₂ + ..., current is the same everywhere, and voltage divides. Parallel: 1/R_eq = 1/R₁ + 1/R₂ + ..., voltage is the same, and current divides.

Kirchhoff's rules: junction rule conserves charge (ΣI_in = ΣI_out); loop rule conserves energy (ΣΔV = 0 around any closed loop).

Magnetic force on a moving charge is F = qvB sinθ, perpendicular to both v and B; it does no work and changes direction, not speed.

Force on a current-carrying wire is F = BIL sinθ; a long straight wire produces B = μ₀I/(2πr).

Faraday's law: induced emf equals the negative rate of change of magnetic flux, ε = −NΔΦ/Δt; Lenz's law says the induced current opposes the flux change.

Photon energy: E = hf = hc/λ with h = 6.63×10⁻³⁴ J·s; shorter wavelength means higher photon energy.

Photoelectric effect: maximum kinetic energy is K_max = hf − φ, where φ is the work function; below threshold frequency no electrons are emitted regardless of intensity.

de Broglie wavelength: λ = h/p = h/(mv); macroscopic objects have unmeasurably small wavelengths.

Mass-energy: E = mc²; mass defect in a nucleus appears as binding energy, and binding energy per nucleon peaks near iron-56.

Radioactive decay: N = N₀(1/2)^(t/T½); after n half-lives the remaining fraction is (1/2)ⁿ, and activity falls at the same rate.

Nuclear equations conserve mass number A and atomic number Z; alpha decay subtracts 4 from A and 2 from Z, beta-minus decay adds 1 to Z.

Hydrogen energy levels: E_n = −13.6 eV/n²; photon energy for a transition equals the difference between levels, and n = 1 is the ground state.

Standard model: protons and neutrons are baryons made of quarks (uud and udd); the strong force binds nucleons, and the weak force drives beta decay.

Significant figures: for multiplication and division, keep the least number of significant figures in the inputs; for addition and subtraction, keep the least decimal places.

Percent error compares to an accepted value: % error = |measured − accepted|/|accepted| × 100; percent difference compares two measurements instead.

Slope of a linearized graph carries the physical constant: a plot of T² versus L for a pendulum has slope 4π²/g, so g = 4π²/slope.

Uncertainty propagation: for sums and differences add absolute uncertainties; for products and quotients add fractional (percent) uncertainties.

In a graph, the independent variable goes on the horizontal axis; a linear fit is justified only when the plotted points follow a straight line within uncertainty.

Random error scatters repeated readings and is reduced by averaging; systematic error shifts all readings the same way and is not reduced by averaging.

A vernier or digital scale's least count sets the reading precision; record one estimated digit beyond the smallest marked division for analog instruments.

Control variables are held constant to isolate the effect of the independent variable; a conclusion requires a comparison to a control or accepted value.