OAE Physics (035) cheat sheet

Scientific method cycle: observation → question → hypothesis → controlled experiment → analysis → peer review → replication; a hypothesis must be falsifiable to count as scientific.

Independent variable is manipulated by the experimenter; dependent variable is measured; controlled variables are held constant to isolate cause and effect.

Accuracy = closeness to the accepted value; precision = repeatability of measurements. Random error scatters both ways and averages out; systematic error shifts all readings in one direction.

Percent error = |measured − accepted| / accepted × 100%. Percent difference compares two measured values using their average in the denominator.

Significant figures: nonzero digits and interior zeros count; leading zeros do not; trailing zeros count only with a decimal point. Multiplication keeps the least number of sig figs; addition keeps the least decimal places.

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

A scientific theory is a well-tested explanatory framework supported by many independent lines of evidence, not a guess; a law describes a relationship, often mathematically.

Scale intuition: 1 nm = 10⁻⁹ m, 1 μm = 10⁻⁶ m, 1 Å = 10⁻¹⁰ m; SI base units include kg, m, s, A, K, mol, cd.

Correlation does not establish causation; a valid conclusion requires a control group, adequate sample size, and elimination of confounding variables.

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

Projectile motion separates into constant-velocity horizontal motion and free-fall vertical motion with a = −g ≈ −9.8 m/s²; time of flight depends only on vertical motion.

Newton's second law: ΣF = ma. On an incline, the down-slope component of weight is mg sin θ and the normal force is mg cos θ (frictionless surface).

Friction: static friction satisfies f_s ≤ μ_sN; kinetic friction is f_k = μ_kN and opposes sliding.

Circular motion requires centripetal acceleration a_c = v²/r directed toward the center; the net inward force is F_c = mv²/r.

Momentum p = mv is conserved in all collisions; kinetic energy is conserved only in elastic collisions. Impulse J = FΔt = Δp.

Work W = Fd cos θ; work–energy theorem: W_net = ΔKE = ½mv² − ½mv₀². Gravitational potential energy near Earth: PE = mgh.

Angular quantities mirror linear ones: τ = Iα, L = Iω, and rotational KE = ½Iω²; a rolling object's total KE is translational plus rotational.

Kepler's third law: T² ∝ r³; Newton's law of gravitation F = Gm₁m₂/r² gives g = GM/r² at distance r from a planet's center.

Coulomb's law: F = kq₁q₂/r², with k ≈ 8.99 × 10⁹ N·m²/C²; force is attractive for opposite charges and repulsive for like charges.

Electric field E = F/q = kq/r²; field lines point away from positive charge and toward negative charge and never cross.

Potential difference V = W/q; for a point charge V = kq/r. Electric field points from higher to lower potential.

Ohm's law V = IR; power P = IV = I²R = V²/R. Resistivity relation R = ρL/A: longer or thinner wire means more resistance.

Series: R_eq = R₁ + R₂ + … and current is the same through each element. Parallel: 1/R_eq = 1/R₁ + 1/R₂ + … and voltage is the same across each branch.

Kirchhoff's rules: junction rule (current in equals current out) and loop rule (sum of potential changes around a closed loop is zero).

Capacitance C = Q/V; parallel-plate C = ε₀A/d; energy stored U = ½CV². Capacitors in parallel add; in series reciprocals add.

Magnetic force on a moving charge F = qvB sin θ; on a current-carrying wire F = BIL sin θ. Direction from the right-hand rule.

Faraday's law: induced emf ε = −N ΔΦ/Δt, where flux Φ = BA cos θ; Lenz's law states the induced current opposes the change in flux.

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

Transverse waves have displacement perpendicular to propagation; longitudinal waves (sound) have displacement parallel to propagation.

Sound speed in air ≈ 343 m/s at 20 °C; intensity level in decibels β = 10 log(I/I₀) with I₀ = 10⁻¹² W/m².

Doppler effect: observed frequency rises when source and observer approach, falls when they separate; for sound the medium provides a reference frame.

Standing waves on a string fixed at both ends: f_n = nv/(2L); pipes open at both ends behave the same way, while a pipe closed at one end supports only odd harmonics f_n = nv/(4L).

Reflection: angle of incidence equals angle of reflection. Refraction obeys Snell's law n₁ sin θ₁ = n₂ sin θ₂, with n = c/v.

Total internal reflection occurs only when light travels from a higher to a lower index and the incidence angle exceeds the critical angle 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 image distance means a virtual image.

Double-slit interference: bright fringes where d sin θ = mλ; single-slit minima where a sin θ = mλ. Diffraction limits resolution.

Temperature scales: T(K) = T(°C) + 273.15; a temperature change of 1 °C equals a change of 1 K.

Linear expansion ΔL = αL₀ΔT; heat transfer Q = mcΔT for a temperature change and Q = mL for a phase change at constant temperature.

First law of thermodynamics: ΔU = Q − W, where W is work done by the system. In an adiabatic process Q = 0; in an isothermal process ΔU = 0 for an ideal gas.

Ideal gas law PV = nRT with R ≈ 8.31 J/(mol·K); average kinetic energy per molecule is (3/2)k_BT, so temperature measures average molecular kinetic energy.

Thermal energy flows spontaneously from higher to lower temperature by conduction, convection, or radiation; radiation needs no medium.

Second law: the entropy of an isolated system never decreases; heat engines cannot convert all absorbed heat into work.

Efficiency of a heat engine e = W/Q_H = 1 − Q_C/Q_H; Carnot maximum e = 1 − T_C/T_H with temperatures in kelvin.

Conservation of energy: mechanical energy is conserved only when nonconservative forces such as friction do no work; otherwise ΔE_mech = W_nc.

Power P = W/t = Fv for constant force; energy units: 1 cal = 4.184 J, 1 kWh = 3.6 × 10⁶ J.

Photon energy E = hf = hc/λ, with h ≈ 6.63 × 10⁻³⁴ J·s and c ≈ 3.00 × 10⁸ m/s; shorter wavelength means higher energy per photon.

Photoelectric effect: electrons are emitted only above a threshold frequency; maximum kinetic energy KE_max = hf − φ, where φ is the work function.

de Broglie wavelength λ = h/p = h/(mv); matter waves become observable for very small masses or low momenta.

Bohr model: photon emitted when an electron drops between levels, with energy hf = E_high − E_low; the ground state of hydrogen is −13.6 eV.

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

Radioactive decay: N = N₀e^(−λt); half-life t₁/₂ = ln 2/λ ≈ 0.693/λ. Activity is measured in becquerels (decays per second).

Nuclear notation: alpha decay reduces mass number by 4 and atomic number by 2; beta-minus decay raises atomic number by 1; gamma emission changes neither.

Standard model: quarks and leptons are fundamental fermions; protons and neutrons are baryons made of three quarks; photons, gluons, and W/Z bosons carry forces.

Special relativity: γ = 1/√(1 − v²/c²); moving clocks run slow and moving lengths contract along the direction of motion.