OSAT Physics (OK114) cheat sheet

Scientific method sequence: observation, question, hypothesis, controlled experiment, analysis, conclusion, replication; a hypothesis must be falsifiable to be scientific.

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

A control group receives no treatment (or a placebo) and establishes the baseline against which the experimental group is compared.

Accuracy is closeness to the accepted value; precision is repeatability of measurements. Random error affects precision; systematic error shifts all readings in one direction and affects accuracy.

Significant figures: multiplication and division keep the least number of sig figs; addition and subtraction keep the least number of decimal places.

Unit prefixes: nano 10^-9, micro 10^-6, milli 10^-3, centi 10^-2, kilo 10^3, mega 10^6, giga 10^9; convert by moving the decimal three places per prefix step.

Dimensional analysis checks equations: both sides must reduce to identical base units (kg, m, s, A, K, mol, cd).

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

Peer review and reproducibility are the mechanisms by which scientific claims gain acceptance; anecdotal evidence and single trials do not establish causation.

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

Projectile motion separates into independent axes: horizontal velocity constant, vertical acceleration 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 is a force, while mass is an invariant measure of inertia.

Friction: static friction satisfies fs ≤ μsN and adjusts to applied force; kinetic friction is fk = μkN and opposes relative sliding.

Circular motion requires centripetal acceleration ac = v²/r directed toward the center; the net force is Fc = mv²/r, not a new outward force.

Newton's third law pairs act on different objects, so they never cancel each other in a single free-body diagram.

Inclined plane: the component of gravity along the incline is mg sin θ and the normal force is mg cos θ (frictionless surface).

Momentum form of Newton's second law: F = Δp/Δt; impulse J = FΔt = Δp equals the area under a force-time graph.

Kepler's third law: T² ∝ r³ for orbits about the same central body; orbital speed v = √(GM/r) for a circular orbit.

Work is W = Fd cos θ; only the force component along displacement does work, so forces perpendicular to motion do zero work.

Work-energy theorem: Wnet = ΔKE, with KE = ½mv²; the net work equals the change in kinetic energy.

Gravitational potential energy near Earth: PE = mgh; elastic potential energy of a spring: PE = ½kx².

Conservation of mechanical energy applies when only conservative forces act: KE + PE is constant; friction converts mechanical energy to thermal energy.

Power is P = W/t = Fv cos θ; measured in watts, where 1 W = 1 J/s.

Momentum p = mv is a vector; total momentum is conserved in any collision or explosion when external impulse is negligible.

Elastic collisions conserve both momentum and kinetic energy; perfectly inelastic collisions conserve momentum only and the objects stick together.

Coefficient of restitution e = (v2' − v1')/(v1 − v2); e = 1 for elastic, e = 0 for perfectly inelastic collisions.

Center of mass moves as if all external forces acted there; x_cm = Σmx/Σm, useful for explosions and recoil problems.

Temperature measures average kinetic energy of particles; average translational KE = (3/2)kBT per molecule for an ideal gas.

Ideal gas law: PV = nRT with R = 8.314 J/(mol·K); alternative form PV = NkBT with kB = 1.38 × 10^-23 J/K.

First law of thermodynamics: ΔU = Q − W, where W is work done by the system; sign conventions must be applied consistently.

Isothermal processes hold T constant (ΔU = 0 for ideal gas); adiabatic processes have Q = 0; isochoric processes have W = 0; isobaric processes have W = PΔV.

Second law: entropy of an isolated system never decreases; heat flows spontaneously from hot to cold, and no engine can exceed Carnot efficiency.

Carnot efficiency e = 1 − Tc/Th with temperatures in kelvin; real engines always fall short of this limit.

Heat transfer modes: conduction (molecular collisions, needs medium), convection (bulk fluid motion), radiation (electromagnetic, needs no medium).

Specific heat: Q = mcΔT; latent heat: Q = mL, with no temperature change during a phase change.

Kinetic theory: pressure arises from molecular collisions with walls; rms speed v_rms = √(3kBT/m) = √(3RT/M).

Wave relation: v = fλ; frequency is set by the source and stays constant across media, while speed and wavelength change.

Transverse waves oscillate perpendicular to propagation (light, string waves); longitudinal waves oscillate parallel (sound in air).

Sound speed in air is about 343 m/s at 20 °C and increases with temperature; it is faster in liquids and solids than in gases.

Standing waves on a string fixed at both ends: fn = nv/(2L); pipes open at both ends fn = nv/(2L); closed at one end only odd harmonics fn = nv/(4L).

Doppler effect: observed frequency rises as source and observer approach and falls as they separate; f' = f(v ± v_o)/(v ∓ v_s).

Snell's law: n1 sin θ1 = n2 sin θ2; light bends toward the normal entering a denser medium; total internal reflection occurs past the critical angle sin θc = n2/n1.

Thin lens and mirror equation: 1/f = 1/do + 1/di; magnification m = −di/do; real images form on the opposite side of a lens and are inverted.

Young's double slit: bright fringes at d sin θ = mλ; single-slit minima at a sin θ = mλ; diffraction limits resolution.

Electromagnetic spectrum ordered by increasing frequency: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma; all travel at c = 3.0 × 10^8 m/s in vacuum.

Coulomb's law: F = kq1q2/r² with k = 8.99 × 10^9 N·m²/C²; force is along the line joining charges and is repulsive for like signs.

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

Ohm's law: V = IR; resistance of a wire R = ρL/A, so resistance rises with length and falls with cross-sectional area.

Series circuits: same current, R_eq = ΣR, voltages add. Parallel circuits: same voltage, 1/R_eq = Σ1/R, currents add.

Electrical power: P = IV = I²R = V²/R; energy consumed is P × t, often billed in kilowatt-hours.

Kirchhoff's rules: junction rule (charge conservation, ΣI = 0) and loop rule (energy conservation, ΣV = 0 around a closed loop).

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

A changing magnetic flux induces an emf: Faraday's law ε = −NΔΦ/Δt; Lenz's law says induced current opposes the change that produced it.

Capacitance C = Q/V; parallel-plate C = ε0A/d; energy stored U = ½CV²; capacitors in series combine as 1/C = Σ1/C.

Photoelectric effect: light arrives in photons of energy E = hf; emission occurs only above a threshold frequency, and maximum KE = hf − φ.

Photon energy shortcut: E(eV) ≈ 1240/λ(nm); h = 6.63 × 10^-34 J·s and c = 3.0 × 10^8 m/s.

de Broglie wavelength λ = h/p = h/(mv); matter waves explain electron diffraction and the Bohr quantization condition.

Bohr model: En = −13.6 eV/n² for hydrogen; photon energy on transition equals the energy-level difference, ΔE = hf.

Heisenberg uncertainty principle: ΔxΔp ≥ h/(4π); position and momentum cannot both be known precisely.

Radioactive decay: N = N0e^(−λt); half-life t½ = 0.693/λ; activity in becquerels (1 Bq = 1 decay/s).

Nuclear notation: mass number A = protons + neutrons, atomic number Z = protons; 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 A nor Z.

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

Read analog scales to one-tenth of the smallest division; record the estimated digit and report uncertainty with correct units.

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

Linearize data before fitting: for T = 2π√(L/g), plot T² versus L so the slope is 4π²/g and g can be extracted.

Slope of a best-fit line carries units of y per x; R² near 1 indicates a good linear fit but does not prove causation.

Random uncertainty is reduced by averaging repeated trials; systematic uncertainty requires calibration or corrected procedure instead.

Graph rules: independent variable on the horizontal axis, dependent on the vertical; label axes with quantity and units and include uncertainty bars.

Safety: wear goggles and aprons, know eyewash and fire extinguisher locations, never point a heated test tube at anyone, and add acid to water, not water to acid.

Electrical safety: check insulation, avoid grounded metal contact, use low-voltage sources for student labs, and never exceed equipment ratings.

Handle radioactive sources with tongs, maximize distance, minimize exposure time, and store in shielded containers; dispose of chemical and biological waste per local regulations.