NY Regents Physics cheat sheet

Average velocity equals displacement divided by elapsed time; speed uses distance and is a scalar, velocity is a vector.

Constant-acceleration kinematics: v = v0 + at, Δx = v0t + ½at², v² = v0² + 2aΔx.

Newton's second law: net force equals mass times acceleration (F_net = ma); weight equals mg with g ≈ 9.8 m/s² downward.

Friction force equals the coefficient of friction times the normal force; static friction adjusts up to a maximum value.

For projectiles, horizontal acceleration is zero and vertical acceleration is g downward; the two components are independent.

An object in equilibrium has zero net force and zero acceleration, so constant velocity or rest.

Centripetal acceleration equals v²/r directed toward the center; it changes direction, not speed.

Momentum p = mv is conserved in collisions when net external force is zero; impulse equals change in momentum (FΔt = Δp).

For a frictionless inclined plane, the component of gravity along the incline is mg sin θ.

Work equals force times displacement times cos θ; work is zero when force is perpendicular to motion.

Kinetic energy equals ½mv²; gravitational potential energy near Earth equals mgh.

The work-energy theorem: net work done on an object equals its change in kinetic energy.

Mechanical energy is conserved when only conservative forces act; friction converts mechanical energy to thermal energy.

Power equals work divided by time, or force times velocity (P = Fv); the unit is the watt (J/s).

A spring's elastic potential energy equals ½kx²; Hooke's law gives restoring force F = kx.

Efficiency equals useful output energy divided by total input energy, expressed as a fraction or percent.

Total energy is conserved in all processes; energy transforms among forms but is never created or destroyed.

Coulomb's law: electric force between point charges is kq1q2/r², attractive for opposite signs and repulsive for like signs.

Electric field strength equals force per unit positive charge (E = F/q); field lines point away from positive charges.

Ohm's law: V = IR for a conductor at constant temperature; resistance equals voltage divided by current.

For resistors in series, resistances add and current is the same through each; for parallel, reciprocals add and voltage is the same.

Electric power equals IV, I²R, or V²/R; the unit is the watt.

Current is the rate of charge flow (I = q/t), measured in amperes; conventional current is opposite electron drift.

A magnetic field exerts force on a moving charge (F = qvB sin θ) and on a current-carrying wire; force is zero when parallel to the field.

A changing magnetic flux through a loop induces an emf (Faraday's law); the induced current opposes the change (Lenz's law).

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

Period equals the reciprocal of frequency (T = 1/f).

Reflection: angle of incidence equals angle of reflection, measured from the normal.

Refraction occurs when wave speed changes at a boundary; bending toward the normal happens when speed decreases.

Sound is a longitudinal mechanical wave requiring a medium; light is an electromagnetic transverse wave needing none.

The Doppler effect is a frequency shift due to relative motion between source and observer; approaching raises observed frequency.

For a wave on a string, speed equals the square root of tension divided by linear mass density.

Standing waves form at fixed boundaries; the fundamental has a node at each end and an antinode in the middle.

Diffraction is the spreading of waves around obstacles and through openings; it is most noticeable when opening size is comparable to wavelength.

The photoelectric effect: light delivers energy in quanta E = hf; emission occurs only above a threshold frequency, regardless of intensity.

Photon energy relates to wavelength by E = hc/λ; shorter wavelength means higher energy.

The work function is the minimum energy to eject an electron; maximum kinetic energy equals hf minus the work function.

Atomic emission and absorption spectra are discrete because electrons occupy quantized energy levels; photon energy equals the level difference.

Wave-particle duality: electrons and other particles show interference and diffraction, and light shows particle behavior in the photoelectric effect.

Mass-energy equivalence: E = mc²; small mass defects correspond to large energy releases in nuclear reactions.

Radioactive decay is random and unaffected by temperature or pressure; half-life is the time for half the nuclei to decay.

Alpha decay emits a helium nucleus, beta decay converts a neutron to a proton with an electron emitted, and gamma decay releases a photon.