Your FREE GRE Physics Flashcards 2026 – 200+ Cards

$\vec F = m\vec a$ — net force equals mass times acceleration (more generally $\vec F = d\vec p/dt$).

Net work equals the change in kinetic energy: $W_{net} = \Delta KE = \tfrac{1}{2}mv_f^2 - \tfrac{1}{2}mv_i^2$.

$KE = \tfrac{1}{2}mv^2$.

$U = mgh$.

$\vec p = m\vec v$; conserved when no net external force acts.

$\vec J = \int \vec F\,dt = \Delta \vec p$ — impulse equals change in momentum.

The velocities are exchanged: the incoming mass stops and the struck mass moves off at the original speed.

Objects stick together; momentum is conserved (they move at the center-of-mass velocity) but kinetic energy is not.

$a_c = \dfrac{v^2}{r}$, directed toward the center of the circular path.

$F_c = \dfrac{mv^2}{r} = m\omega^2 r$, pointing toward the center.

$a = g\sin\theta$ down the slope.

$F = -kx$ — the restoring force of an ideal spring, proportional to displacement.

$\omega = \sqrt{\dfrac{k}{m}}$.

$T = 2\pi\sqrt{\dfrac{L}{g}}$ (small oscillations).

Motion under a restoring force proportional to displacement: $x(t) = A\cos(\omega t + \phi)$.

$\vec\tau = \vec r\times\vec F$; the rotational analog of force, with $\tau = I\alpha$.

$I = \sum m_i r_i^2$ (or $\int r^2\,dm$) — rotational analog of mass.

$I = I_{cm} + Md^2$, where $d$ is the distance from the center-of-mass axis to the parallel axis.

$I = \tfrac{1}{3}ML^2$ (about its center it is $\tfrac{1}{12}ML^2$).

$I = \tfrac{2}{5}MR^2$; about a tangent axis it is $\tfrac{7}{5}MR^2$.

$\vec L = I\vec\omega$ (or $\vec r\times\vec p$); conserved when no external torque acts.

$KE_{rot} = \tfrac{1}{2}I\omega^2$.

Conservation of angular momentum $I\omega =$ constant — reducing $I$ raises $\omega$; her rotational KE increases (work done pulling in).

$F = \dfrac{Gm_1 m_2}{r^2}$.

$v_{esc} = \sqrt{\dfrac{2GM}{R}}$; independent of the escaping object's mass, $\sqrt{2}\times$ the surface orbital speed.

$T^2 \propto a^3$ — the square of the orbital period is proportional to the cube of the semi-major axis.

A planet sweeps equal areas in equal times — a consequence of angular-momentum conservation; it moves fastest at perihelion.

$L = T - V$ (kinetic minus potential energy) in generalized coordinates.

$\dfrac{d}{dt}\dfrac{\partial L}{\partial \dot q} - \dfrac{\partial L}{\partial q} = 0$ for each generalized coordinate.

$H = T + V$ — total energy in coordinates and momenta; Hamilton's equations $\dot q = \partial H/\partial p,\ \dot p = -\partial H/\partial q$.

$p_i = \dfrac{\partial L}{\partial \dot q_i}$ — conserved if $L$ does not depend on $q_i$ (a cyclic coordinate).

$\vec a_{Cor} = -2\,\vec\omega\times\vec v$ in a rotating frame; deflects motion to the right in the Northern Hemisphere.

$-\vec\omega\times(\vec\omega\times\vec r)$, pointing outward; magnitude $\omega^2 r$.

$\Delta v = v_e \ln\!\dfrac{m_i}{m_f}$ — change in speed from exhaust speed and the initial-to-final mass ratio.

$\mu = \dfrac{m_1 m_2}{m_1 + m_2}$ — converts a two-body problem into an equivalent one-body problem.

$T = 2\pi\sqrt{\dfrac{I}{mgd}}$, where $d$ is the pivot-to-center-of-mass distance.

$P = \dfrac{dW}{dt} = \vec F\cdot\vec v$.

A force whose work is path-independent and equals minus a potential-energy change; $\vec F = -\nabla U$.

$f_k = \mu_k N$, opposing motion; static friction satisfies $f_s \le \mu_s N$.

The constant speed where drag balances gravity, so net force and acceleration are zero.

$F = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1 q_2}{r^2}$ — force between two point charges.

$E = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r^2}$, directed radially.

$\oint \vec E\cdot d\vec A = \dfrac{Q_{enc}}{\varepsilon_0}$ — electric flux through a closed surface equals enclosed charge over $\varepsilon_0$.

Zero; any excess charge resides on the conductor's surface.

$U = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1 q_2}{r}$; potential of a point charge $V = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r}$.

$\vec E = -\nabla V$ — the field points down the steepest decrease of potential.

$C = \dfrac{\kappa\varepsilon_0 A}{d}$; inserting a dielectric $\kappa$ raises the capacitance.

$U = \tfrac{1}{2}CV^2 = \dfrac{Q^2}{2C} = \tfrac{1}{2}QV$.

$V = IR$.

$P = IV = I^2 R = \dfrac{V^2}{R}$.

Series: $R = R_1 + R_2 + \dots$. Parallel: $\dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dots$.

Parallel: $C = C_1 + C_2 + \dots$. Series: $\dfrac{1}{C} = \dfrac{1}{C_1} + \dfrac{1}{C_2} + \dots$ (opposite of resistors).

$\tau = RC$ — charge on the capacitor relaxes as $e^{-t/\tau}$.

$\tau = \dfrac{L}{R}$.

Junction rule: currents into a node sum to zero (charge conservation). Loop rule: voltages around a closed loop sum to zero (energy conservation).

$\vec F = q\vec E + q\vec v\times\vec B$ — force on a charge from electric and magnetic fields.

$B = \mu_0 n I$, where $n$ is turns per unit length.

$\oint \vec B\cdot d\vec l = \mu_0 I_{enc}$ — gives B from current with high symmetry.

$d\vec B = \dfrac{\mu_0}{4\pi}\dfrac{I\,d\vec l\times\hat r}{r^2}$ — field from a current element.

Attractive when the currents are in the same direction, repulsive when opposite.

$\varepsilon = -\dfrac{d\Phi_B}{dt}$ — a changing magnetic flux induces an EMF.

The induced current flows so as to oppose the change in magnetic flux that produced it (the minus sign in Faraday's law).

Proportional to the square of the number of turns, $L \propto N^2$ (also to area and core permeability).

$U = \tfrac{1}{2}LI^2$.

The weber (Wb); $1\ \text{Wb} = 1\ \text{T}\cdot\text{m}^2$.

Gauss's law, Gauss's law for magnetism ($\nabla\cdot\vec B = 0$), Faraday's law, and the Ampere-Maxwell law — the four laws of electromagnetism.

$c = \dfrac{1}{\sqrt{\mu_0\varepsilon_0}} \approx 3.0\times10^8$ m/s.

Transverse, require no medium, travel at $c$ in vacuum, consist of oscillating $\vec E$ and $\vec B$ fields perpendicular to each other and to the motion.

$\vec S = \dfrac{1}{\mu_0}\vec E\times\vec B$ — energy flux (power per area) carried by an EM field.

$X_C = \dfrac{1}{\omega C}$; in a capacitor, current leads voltage by 90°.

$X_L = \omega L$; in an inductor, current lags voltage by 90°.

$\omega_0 = \dfrac{1}{\sqrt{LC}}$ — where $X_L = X_C$ and the impedance is minimized.

$\Phi_B = \int \vec B\cdot d\vec A$ — the field component through a surface times its area.

$\omega = \dfrac{qB}{m}$ — angular frequency of a charge circling in a magnetic field.

The net electric (or magnetic) field at a point is the vector sum of the fields from each source.

$v = \lambda f$ — speed equals wavelength times frequency.

The frequency. The wavelength and speed change, but the frequency is fixed by the source.

$n_1\sin\theta_1 = n_2\sin\theta_2$ — governs refraction at an interface.

$n = \dfrac{c}{v}$; light slows ($v$ decreases) in a higher-index medium.

Occurs when light in a denser medium hits the boundary beyond the critical angle $\theta_c = \sin^{-1}(n_2/n_1)$; confines light in optical fibers.

$\dfrac{1}{f} = \dfrac{1}{d_o} + \dfrac{1}{d_i}$; magnification $m = -\dfrac{d_i}{d_o}$.

$d\sin\theta = m\lambda$ — constructive interference at integer path differences.

$a\sin\theta = m\lambda$ ($m = \pm1, \pm2, \dots$) — dark fringes for a slit of width $a$.

Proportional to the wavelength and inversely proportional to the slit separation: $\Delta y = \dfrac{\lambda L}{d}$.

$\theta_B = \tan^{-1}(n)$ — the incidence angle at which reflected light is fully polarized.

$I = I_0\cos^2\theta$ — intensity of polarized light through a polarizer at angle $\theta$.

Exactly half the intensity, $\tfrac{1}{2}I_0$, is transmitted (and the output is polarized).

Approaching source → blueshift (higher frequency); receding source → redshift (lower frequency).

Interference = superposition of waves from multiple sources; diffraction = bending/spreading of a single wave around edges or apertures.

The photoelectric effect. Interference, diffraction, and polarization are all explained by the wave theory.

$d\sin\theta = m\lambda$; a grating gives sharp, widely separated orders for spectroscopy.

$\theta \approx 1.22\dfrac{\lambda}{D}$ — minimum angular separation a circular aperture of diameter $D$ can resolve.

$\lambda_n = \dfrac{2L}{n},\ f_n = \dfrac{nv}{2L}$ — harmonics for $n = 1, 2, 3, \dots$.

Violet (refracted/dispersed most by a prism); red has the longest visible wavelength.

The index of refraction depends on wavelength (dispersion), so different colors bend by different amounts.

$\Delta U = Q - W$ — change in internal energy equals heat added minus work done by the system.

The entropy of an isolated system never decreases; heat does not spontaneously flow from cold to hot.

The entropy of a perfect crystal approaches zero as the temperature approaches absolute zero.

$PV = nRT$ (or $PV = Nk_B T$).

$T$ constant, so $\Delta U = 0$ and $Q = W$ for an ideal gas.

$P$ constant; work done by the gas is $W = P\,\Delta V$.

$V$ constant, so $W = 0$ and $Q = \Delta U$.

No heat exchange, $Q = 0$, so $\Delta U = -W$; for an ideal gas $PV^\gamma =$ constant.

No work and no heat, so $\Delta U = 0$; since $U$ depends only on $T$, the temperature stays constant.

$\eta = 1 - \dfrac{T_c}{T_h}$ (kelvin) — the maximum efficiency of any engine between two reservoirs.

$dS = \dfrac{dQ_{rev}}{T}$; for a reversible cycle the total entropy change of the universe is zero.

$S = k_B \ln \Omega$ — entropy in terms of the number of accessible microstates $\Omega$.

Each quadratic degree of freedom contributes $\tfrac{1}{2}k_B T$ to the average energy.

$\langle KE\rangle = \tfrac{3}{2}k_B T$ — independent of molecular mass.

$v_{rms} = \sqrt{\dfrac{3k_B T}{m}}$ — heavier molecules move slower at the same temperature.

The classical distribution of molecular speeds in an ideal gas; raising $T$ broadens it and shifts the peak to higher speed.

$P = \sigma A T^4$ — total power radiated by a blackbody is proportional to $T^4$.

$\lambda_{max} T =$ constant — a hotter blackbody peaks at a shorter wavelength.

$k_B \approx 1.38\times10^{-23}$ J/K — links temperature to energy ($k_B = R/N_A$).

$Q = mc\,\Delta T$; for a gas, $C_P - C_V = R$ per mole (Mayer's relation).

Moves heat from cold to hot using external work — a consequence (and demonstration) of the second law.

Fermi-Dirac governs fermions (one per state, Pauli); Bose-Einstein governs bosons (many can share a state).

Depends only on temperature; for a monatomic ideal gas $U = \tfrac{3}{2}nRT$.

$\hat H\psi = E\psi$ — gives the stationary states $\psi$ and their energies $E$.

$i\hbar\dfrac{\partial \psi}{\partial t} = \hat H\psi$.

$|\psi(x)|^2$ is the probability density; the probability in $[a,b]$ is $\int_a^b |\psi|^2\,dx$.

$\int_{-\infty}^{\infty} |\psi|^2\,dx = 1$ — total probability is one.

$E_n = \dfrac{n^2 h^2}{8mL^2} = \dfrac{n^2\pi^2\hbar^2}{2mL^2}$, $n = 1, 2, 3, \dots$

$\psi_n(x) = \sqrt{\dfrac{2}{L}}\sin\!\left(\dfrac{n\pi x}{L}\right)$.

$E_n = \left(n + \tfrac{1}{2}\right)\hbar\omega$ — evenly spaced levels with zero-point energy $\tfrac{1}{2}\hbar\omega$.

$[\hat x,\hat p] = i\hbar$ — position and momentum operators do not commute.

$\Delta x\,\Delta p \ge \dfrac{\hbar}{2}$; an energy-time form is $\Delta E\,\Delta t \ge \dfrac{\hbar}{2}$.

$\hat H$ represents the total energy of the system; its eigenvalues are the allowed energies.

$\hat p = -i\hbar\dfrac{\partial}{\partial x}$.

Energy eigenstates are orthogonal and normalized: $\int \psi_m^* \psi_n\,dx = \delta_{mn}$.

$\langle A\rangle = \int \psi^* \hat A\,\psi\,dx$ — the average measured value of observable $\hat A$.

A particle has a nonzero probability of passing through a potential barrier even when its energy is below the barrier height.

$s = \tfrac{1}{2}$; the electron is a spin-½ fermion with two spin projections $m_s = \pm\tfrac{1}{2}$.

No two identical fermions can occupy the same quantum state simultaneously.

$\lambda = \dfrac{h}{p}$ — every particle has a wave nature, demonstrated by electron diffraction.

Quantum expectation values obey the classical equations of motion ($m\,d\langle x\rangle/dt = \langle p\rangle$).

$\hat A\psi = a\psi$: a measurement of $\hat A$ on eigenstate $\psi$ yields the eigenvalue $a$ with certainty.

$L^2 = l(l+1)\hbar^2$ and $L_z = m_l\hbar$ — magnitude and projection are both quantized.

$E_n = -\dfrac{13.6\,\text{eV}}{n^2}$; the ground state is $-13.6$ eV.

$L = n\hbar$ — orbital angular momentum is an integer multiple of $\hbar$.

$E = hf = \dfrac{hc}{\lambda}$; emitted photon energy equals the gap between two atomic levels.

$\dfrac{1}{\lambda} = R\left(\dfrac{1}{n_1^2} - \dfrac{1}{n_2^2}\right)$ — wavelengths of hydrogen spectral lines.

Transitions ending at $n = 1$ (Lyman, UV), $n = 2$ (Balmer, visible), $n = 3$ (Paschen, IR).

The $n = 3 \to 2$ Balmer transition (H-alpha) — the smallest energy gap gives the longest wavelength.

Principal $n$, azimuthal $l$, magnetic $m_l$, and spin $m_s$ — they label every electron state.

$KE_{max} = hf - \phi$; below a threshold frequency no electrons are emitted, evidence for photons.

$\phi$, the minimum energy to free an electron from a metal surface.

Small spectral-line splitting from spin-orbit coupling — the electron's spin interacting with its orbital motion.

Even smaller splitting from the interaction between the nuclear spin and the electron cloud.

Splitting of atomic energy levels (and spectral lines) in an external magnetic field.

Shifting and splitting of spectral lines in an external electric field (the electric analog of the Zeeman effect).

An atomic beam splits into discrete components in a non-uniform magnetic field — proof that angular momentum (spin) is quantized.

$\Delta\lambda = \dfrac{h}{m_e c}(1-\cos\theta)$ — wavelength shift of an X-ray photon scattering off an electron; evidence for photon momentum.

Electrons form interference patterns, demonstrating their wave nature (wave-particle duality).

Electrons fill degenerate orbitals singly with parallel spins before pairing, to minimize energy.

Electrons fill the lowest-energy orbitals first when building up an atom's ground-state configuration.

$\Delta l = \pm1$ (and $\Delta m_l = 0, \pm1$) — allowed electric-dipole transitions.

An inner-shell vacancy filled by an outer electron emits a characteristic X-ray; K-alpha is $n=2 \to 1$.

The uncertainty principle: confining the electron more tightly raises its momentum (and energy), setting a minimum-energy ground state.

(1) The laws of physics are the same in all inertial frames. (2) The speed of light $c$ is the same for every observer.

$\gamma = \dfrac{1}{\sqrt{1 - v^2/c^2}}$ — scales time dilation, length contraction, and energy.

$\Delta t = \gamma\,\Delta t_0$ — a moving clock runs slow; $\Delta t_0$ is the proper time in the clock's rest frame.

$L = \dfrac{L_0}{\gamma}$ — a moving object is shortened along its direction of motion; $L_0$ is the proper length.

The time interval measured by a clock at rest relative to the two events — the shortest possible interval between them.

$x' = \gamma(x - vt),\ t' = \gamma\!\left(t - \dfrac{vx}{c^2}\right)$ — relates coordinates between inertial frames.

$E = \gamma mc^2$; rest energy is $E_0 = mc^2$.

$\vec p = \gamma m\vec v$.

$E^2 = (pc)^2 + (mc^2)^2$; for a photon $E = pc$, at rest $E = mc^2$.

$KE = (\gamma - 1)mc^2$ — reduces to $\tfrac{1}{2}mv^2$ at low speed and grows without bound as $v\to c$.

$u' = \dfrac{u + v}{1 + uv/c^2}$ — keeps the result below $c$.

$\Delta s^2 = (c\Delta t)^2 - \Delta x^2$ — the same for all inertial observers.

Includes time dilation, so it differs from the classical Doppler shift; receding source → redshift, approaching → blueshift.

The traveling twin accelerates and decelerates, breaking the symmetry, so that twin ages less.

Its kinetic energy $(\gamma-1)mc^2$ diverges as $v\to c$ — infinite energy would be required.

Random error scatters measurements (reduced by averaging); systematic error biases them in one direction (a calibration/offset problem).

They add in quadrature: $\sigma = \sqrt{\sigma_1^2 + \sigma_2^2}$.

A count of $N$ events has uncertainty $\sqrt{N}$; the fractional uncertainty $1/\sqrt{N}$ shrinks with more data.

Standard deviation measures spread; the standard error of the mean is $\sigma/\sqrt{N}$.

Extracts a small signal at a known reference frequency from heavy noise, by mixing and low-pass filtering, hugely improving signal-to-noise.

A conducting enclosure that shields its contents from external electric fields (charges redistribute to cancel the field inside).

Provides thermal insulation to reach and hold temperatures near absolute zero; liquid helium boils at 4.2 K.

Slows and cools atoms using laser light tuned just below an atomic transition, reducing their kinetic energy.

Trap and move microscopic particles using the radiation pressure (momentum) of a focused laser beam.

Measures the carrier density (and sign of charge carriers) in a material from the transverse Hall voltage in a magnetic field.

Determines an ion's mass-to-charge ratio from the time it takes to travel a known distance after acceleration.

Fourier-transform IR offers higher resolution, faster acquisition, and better signal-to-noise (Fellgett's advantage) over dispersive IR.

Displays voltage versus time, used to view waveforms, measure amplitude, frequency, and phase.

A computed result is limited by the least-precise input; report uncertainty to one or two significant figures.

Detects single photons by cascading secondary-electron emission, producing a measurable pulse from very weak light.

Detects ionizing radiation via gas ionization producing electrical pulses; counts follow Poisson statistics.

2, 8, 20, 28, 50, 82, 126 — proton or neutron counts that fill nuclear shells and give extra stability.

The energy released forming a nucleus from its nucleons; the mass defect times $c^2$. Iron-56 has the highest binding energy per nucleon.

Alpha emits a $\ce{^4_2He}$ nucleus; beta emits an electron/positron (plus a neutrino); gamma emits a high-energy photon.

$N(t) = N_0 e^{-\lambda t}$; the half-life is $t_{1/2} = \dfrac{\ln 2}{\lambda}$.

Quarks carry color charge and can never be isolated — only color-neutral hadrons (mesons, baryons) are observed.

Baryons are three quarks (e.g. proton = uud), mesons are a quark-antiquark pair; the six flavors are u, d, c, s, t, b.

Strong, electromagnetic, weak, and gravity — mediated by gluons, photons, W/Z bosons, and (hypothetically) gravitons.

Zero electrical resistance below a critical temperature; expels magnetic fields (Meissner effect).

Flow with zero viscosity, seen in liquid helium-4 below 2.17 K — particles flow without losing kinetic energy.

The maximum white-dwarf mass (≈ 1.4 solar masses) supported by electron degeneracy pressure; above it the core collapses.