AEPA Physics (NT308) cheat sheet

Newton's second law: net force equals mass times acceleration (F = ma); weight is mg, distinct from mass.

Kinematics: v = v0 + at, x = v0t + ½at², and v² = v0² + 2ax apply only for constant acceleration.

Projectile motion separates into independent horizontal (constant velocity) and vertical (acceleration g) components.

Conservation of momentum: total momentum of an isolated system is constant; collisions conserve momentum, but kinetic energy is conserved only in elastic collisions.

Work-energy theorem: net work equals change in kinetic energy (W = ΔKE); gravitational PE near Earth is mgh.

Circular motion requires centripetal force F = mv²/r directed toward the center; it does no work because it is perpendicular to velocity.

Density = mass/volume; pressure in a static fluid depends only on depth (P = P0 + ρgh); Archimedes: buoyant force equals weight of displaced fluid.

Hooke's law: restoring force F = −kx for an ideal spring; elastic PE = ½kx².

Kepler's third law relates orbital period to radius: T² ∝ r³ for orbits about the same central body.

Coulomb's law: F = kq1q2/r²; force is along the line joining charges and is repulsive for like signs.

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

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

Series circuits share current and sum resistances; parallel circuits share voltage and add conductances (1/R_total = Σ1/Ri).

Kirchhoff's rules: junction rule conserves charge; loop rule conserves energy around any closed path.

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

Faraday's law: induced emf equals the negative rate of change of magnetic flux; Lenz's law gives the direction opposing the change.

Capacitance C = Q/V; energy stored in a capacitor is ½CV²; parallel-plate capacitance grows with area and shrinks with plate separation.

Wave speed equals frequency times wavelength (v = fλ); frequency is set by the source and does not change on entering a new medium.

Sound speed is highest in solids, lower in liquids, lowest in gases; it increases with temperature in air.

Doppler effect: observed frequency rises when source and observer approach and falls when they separate.

For standing waves on a string fixed at both ends, wavelengths are λ = 2L/n; for a pipe open at both ends the same rule applies, while a pipe closed at one end allows only odd harmonics.

Snell's law: n1 sinθ1 = n2 sinθ2; light bends toward the normal when entering a medium of higher index.

Total internal reflection occurs only when light travels from higher to lower index and the angle exceeds the critical angle, sinθc = n2/n1.

Thin lens and mirror equation: 1/f = 1/do + 1/di, with magnification m = −di/do; real images form on the same side as the outgoing light for mirrors and the opposite side for lenses.

Double-slit interference maxima occur where path difference equals mλ; single-slit minima occur where it equals mλ.

Electromagnetic waves travel at c ≈ 3 × 10⁸ m/s in vacuum; energy of a photon is E = hf.

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

Second law: entropy of an isolated system never decreases; heat flows spontaneously from hot to cold.

Absolute temperature must be used in gas laws and efficiency formulas; T(K) = T(°C) + 273.

Ideal gas law: PV = nRT; for a fixed amount of gas, PV/T is constant.

Isothermal processes hold T constant (ΔU = 0 for ideal gas); adiabatic processes exchange no heat (Q = 0); isochoric processes do no work.

Carnot efficiency of a heat engine is 1 − Tc/Th, the maximum possible between two reservoirs.

Specific heat: Q = mcΔT; latent heat for phase change is Q = mL with no temperature change during the transition.

Entropy change for reversible heat transfer is ΔS = Q/T, evaluated at the temperature of the transfer.

Photoelectric effect: electrons are emitted only above a threshold frequency; maximum kinetic energy is hf − φ, independent of intensity.

Photon energy E = hf = hc/λ; de Broglie wavelength is λ = h/p.

Mass-energy equivalence: E = mc²; nuclear binding energy appears as a mass defect.

Radioactive decay follows exponential law N = N0e^(−λt); half-life is the time for half the nuclei to decay.

Alpha decay reduces mass number by 4 and atomic number by 2; beta-minus decay converts a neutron to a proton, raising atomic number by 1.

The Bohr model quantizes angular momentum and explains hydrogen's discrete line spectrum; energy levels are negative and converge toward zero.

Special relativity: the speed of light is invariant; moving clocks run slow and moving lengths contract along the direction of motion.

Nuclear fission splits heavy nuclei and releases energy; fusion combines light nuclei and powers stars.

Independent variable is manipulated by the experimenter; dependent variable is measured; controlled variables are held constant.

A valid conclusion requires a control group and repetition or multiple trials to reduce random error.

Accuracy describes closeness to the true value; precision describes repeatability of measurements.

Random errors scatter results symmetrically and are reduced by averaging; systematic errors shift all results in one direction and require calibration.

Percent error = |measured − accepted| / accepted × 100%.

Significant figures in a result are limited by the least precise measurement; addition uses decimal places, multiplication uses significant figures.

A hypothesis must be testable and falsifiable; a theory is a well-supported explanatory framework, not a guess.

Correlation does not establish causation; a controlled experiment with random assignment supports causal claims.

SI base units include the meter, kilogram, second, ampere, kelvin, mole, and candela.

Dimensional analysis checks equations: both sides must have identical units.

Graphing the dependent variable against the independent variable reveals linearity; slope carries the units of y over x.

A linear fit y = mx + b gives slope as a rate and intercept as the value when x = 0.

Uncertainty propagates: for addition and subtraction, absolute uncertainties add; for multiplication and division, relative uncertainties add.

Scientific notation expresses values as a coefficient between 1 and 10 times a power of ten.

A model is a simplified representation; its predictions hold only within the assumptions used to build it.

Laboratory safety: identify hazards, use goggles and appropriate PPE, and know the location of eyewash and fire equipment.

Never taste or directly smell chemicals; waft vapors toward the nose.

Electrical safety: check insulation, avoid water near circuits, and disconnect power before adjusting wiring.

Dispose of chemical and biological waste according to labeled categories, not the sink or trash.

Read an instrument's scale before use and record to the smallest calibrated division plus one estimated digit.

Calibrate balances and meters with known standards before collecting data.

Report accidents and broken glass immediately to the instructor rather than cleaning hazardous material alone.

Ethical science requires honest data reporting, including reporting outliers and failed trials.

Peer review subjects claims to independent scrutiny before publication.

Informed consent and confidentiality govern research involving human subjects.

Proper citation credits prior work and avoids plagiarism; fabricated or altered data is misconduct.

Animal research requires justification, minimization of suffering, and review-board approval.

Replication by independent researchers strengthens confidence in a result.

Conflicts of interest must be disclosed so findings can be judged fairly.

A scientific claim is supported by empirical evidence, not by authority or popularity.

Anecdotal evidence lacks controls and cannot establish general cause and effect.

Sample size and random selection determine how well results generalize to a population.

Blinding reduces bias: single-blind hides treatment from subjects, double-blind hides it from both subjects and experimenters.

Placebo controls isolate the effect of the treatment from expectation effects.

Statistical significance does not equal practical importance; effect size matters.

Extraordinary claims require independent replication before acceptance.

The scientific method cycles: question, hypothesis, prediction, experiment, analysis, revision.

A prediction is a specific, testable consequence derived from a hypothesis.

Operational definitions specify exactly how a variable is measured.

Pilot studies refine procedures before full-scale data collection.

Data tables should label units and record raw values before any transformation.

Outliers should be investigated, not automatically deleted.

Conclusions should state limits of the design and suggest further tests.

Measurement uncertainty is expressed as ± a value with the same units as the measurement.

The mean of repeated measurements reduces random error by roughly the square root of the number of trials.

Standard deviation quantifies spread around the mean.

A best-fit line should pass near the data's central trend, not forced through every point.

Interpolation estimates within the data range; extrapolation beyond it is less reliable.

Unit conversions use dimensional reasoning so unwanted units cancel.

Reporting should match the precision of the instrument used.