GRE Physics Subject Test flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Newton's second law

The net force equals the rate of change of momentum, F = dp/dt. For constant mass this becomes F = ma, valid only in inertial reference frames.

Parallel-axis theorem

The moment of inertia about any axis equals the moment about a parallel axis through the center of mass plus Md², where d is the separation between the axes.

Simple harmonic oscillator frequency

For a mass on a spring, angular frequency is the square root of k/m. For a small-angle pendulum it is the square root of g/L.

Kepler's third law

The square of an orbital period is proportional to the cube of the semi-major axis, with the constant of proportionality set by the central mass: T² = 4π²a³/(GM).

Gauss's law

The electric flux through any closed surface equals the enclosed charge divided by the permittivity of free space, allowing fields of symmetric charge distributions to be found easily.

Capacitor stored energy

A charged capacitor stores energy equal to one half CV², equivalently Q²/(2C). Inserting a dielectric of constant κ multiplies capacitance and stored energy at fixed voltage.

Faraday's law of induction

A changing magnetic flux through a loop induces an emf equal to the negative rate of flux change. Lenz's law gives the direction opposing the change.

Ampère–Maxwell law

The line integral of magnetic field around a closed loop equals μ₀ times the enclosed current plus μ₀ε₀ times the rate of change of electric flux through the loop.

Snell's law

At an interface, n₁ sinθ₁ equals n₂ sinθ₂. Light bends toward the normal entering a denser medium and can totally internally reflect leaving one.

Double-slit fringe spacing

For slit separation d, wavelength λ, and screen distance L much larger than d, adjacent bright fringes are separated by approximately λL/d.

Rayleigh resolution criterion

Two point sources are just resolved when the central diffraction maximum of one falls on the first minimum of the other, requiring angular separation near 1.22λ/D.

Thin lens equation

Object and image distances satisfy 1/f = 1/d_o + 1/d_i, with magnification m = −d_i/d_o. A negative image distance indicates a virtual image.

Carnot efficiency

The maximum efficiency of any heat engine operating between hot and cold reservoirs is one minus the ratio of cold to hot absolute temperatures.

First law of thermodynamics

The change in internal energy equals heat added to the system minus work done by the system. Work is the integral of pressure over volume change.

Equipartition theorem

In classical thermal equilibrium each quadratic degree of freedom carries average energy one half k_B T, giving monatomic gases three translational degrees and energy 3k_BT/2.

Entropy change of ideal gas

For an ideal gas, entropy change equals nC_V ln(T₂/T₁) plus nR ln(V₂/V₁). Free expansion into vacuum increases entropy while temperature stays constant.

de Broglie wavelength

A particle of momentum p has wavelength h/p. An electron accelerated through V volts has wavelength near 1.23 nm divided by the square root of V.

Infinite square well energies

A particle confined to a one-dimensional box of width L has energies n²π²ħ²/(2mL²). Energy levels scale as the inverse square of the box size.

Uncertainty principle

Position and momentum uncertainties satisfy ΔxΔp ≥ ħ/2, and energy and time satisfy ΔEΔt ≥ ħ/2. This follows from the wave nature of matter.

Hydrogen energy levels

The Bohr model gives E_n = −13.6 eV/n². Photon energies from transitions equal differences between these levels, matching observed spectral series.

Electric dipole selection rules

Allowed electric dipole transitions require the orbital angular momentum to change by exactly one unit and the magnetic quantum number to change by at most one.

Photoelectric threshold

Electrons escape a metal only when photon energy exceeds the work function. Maximum kinetic energy equals hf minus the work function, independent of intensity.

Lorentz factor

Defined as one over the square root of one minus v²/c², it equals one at rest and diverges as speed approaches c, governing time dilation and length contraction.

Relativistic energy–momentum relation

Total energy satisfies E² = p²c² + m²c⁴. For a particle at rest this reduces to mc²; for massless particles it gives E = pc.

Relativistic velocity addition

Velocities do not add simply. If a frame moves at v and an object moves at u within it, the observed speed is (u + v)/(1 + uv/c²).

Poisson counting uncertainty

For a counting experiment with N detected events, the standard deviation is the square root of N, so the fractional uncertainty decreases as one over the square root of N.

Propagation of independent errors

For a function of measured quantities, the variance equals the sum over variables of the squared partial derivative times that variable's variance, assuming independent random errors.

Least-squares slope

For a straight-line fit, the slope equals the covariance of x and y divided by the variance of x. Residual scatter gives the uncertainty in slope and intercept.

Radioactive decay law

Activity falls exponentially with time constant λ. Half-life equals ln2 divided by λ, and activity equals λ times the number of undecayed nuclei.

Quark charges

Up, charm, and top quarks carry charge +2/3 e; down, strange, and bottom carry −1/3 e. Observable hadrons combine them into integer-charge color singlets.

Hubble's law

Distant galaxies recede with speed proportional to distance, v = H₀d, with H₀ near 70 km/s per megaparsec, evidence for an expanding universe.

Schwarzschild radius

The radius of the event horizon of a non-rotating black hole equals 2GM/c², about 3 km for a solar-mass object.