Physics flashcards
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44 decks
- Units and Measurement (Physics)Recall cards on units and measurement: the scope and scale of physics (physics as a science, orders of magnitude, models, theories, and laws, and the length, mass, and time scales of the universe); units and standards (physical quantities, base versus derived quantities, the seven SI base quantities and units, the modern second and meter standards, and metric prefixes); unit conversion with conversion factors; dimensional analysis (the base-dimension symbols L, M, T, I, theta, N, and J, dimensionless quantities, dimensional consistency, and transcendental arguments); estimates and Fermi calculations; significant figures (accuracy versus precision, uncertainty versus discrepancy, percent uncertainty, counting significant figures, and the rules for arithmetic operations and exact numbers); and the three-stage strategy for solving physics problems.
- Vectors (Physics)Recall cards on vectors: scalars versus vectors (magnitude and direction, notation, displacement, equal, parallel, antiparallel, orthogonal, and negative vectors, scalar multiplication, resultants, the commutative, associative, and distributive laws, the parallelogram and tail-to-head rules, unit vectors, and vector subtraction); coordinate systems and components (vector and scalar components, the unit vectors i-hat, j-hat, and k-hat, component form, magnitude and direction angle from components, quadrant rules, polar coordinates, and right-handed axes); the algebra of vectors (the analytical component method, component-wise addition, subtraction, and scalar multiplication, equality, the null vector, and unit vectors from magnitude); and the products of vectors (the scalar or dot product and the vector or cross product, their properties, unit-vector identities, component forms, and the applications to work and torque).
- Motion Along a Straight Line (Physics)Recall cards on one-dimensional kinematics: position and frame of reference; displacement as the change in position (final minus initial), a vector measured in meters, and its distinction from distance traveled; average velocity as displacement over elapsed time; instantaneous velocity as the time derivative of position and the slope of a position-versus-time graph; speed as a scalar and instantaneous speed as the magnitude of velocity; average and instantaneous acceleration as the rate of change of velocity and the slope of a velocity-versus-time graph, with the sign conventions relating acceleration and velocity direction to speeding up or slowing down; the constant-acceleration kinematic equations and the notation behind them; free fall under gravity alone with acceleration g directed downward; and finding velocity and displacement by integrating acceleration and velocity over time.
- Motion in Two and Three Dimensions (Physics)Recall cards on kinematics in two and three dimensions: the position, displacement, and velocity vectors in unit-vector notation and their component forms; instantaneous velocity as the derivative of position and always tangent to the path; the acceleration vector as the first derivative of velocity and the second derivative of position; the independence of motion along perpendicular axes and the constant-acceleration equations applied per axis; projectile motion with zero horizontal acceleration and downward gravity, including the launch components, time of flight, maximum height, range, the 45-degree maximum, complementary launch angles, and the parabolic trajectory; uniform and nonuniform circular motion, centripetal acceleration expressed through speed, period, and angular frequency, and tangential and total acceleration; and relative motion, with the addition rules for position, velocity, and acceleration across reference frames and the invariance of acceleration between frames moving at constant relative velocity.
- Newton's Laws of Motion (Physics)Recall cards on Newton's laws of motion: force as a vector push or pull measured in newtons, external versus contact versus field forces, the four fundamental forces, and the net force as a vector sum; Newton's first law, inertia and its measure by mass, inertial reference frames, and equilibrium under zero net force; Newton's second law in scalar and vector form, F_net = m a and its momentum form F_net = dp/dt, with the proportionalities between force, mass, and acceleration; mass versus weight, w = m g, and how weight varies with local gravity while mass does not; Newton's third law and action-reaction pairs acting on different bodies, including thrust; common forces such as the normal force, tension, friction, Hooke's-law spring restoring force, and the real-versus-fictitious distinction; and how to draw and use free-body diagrams to apply Newton's second law.
- Applications of Newton's Laws (Physics)Recall cards on applying Newton's laws: the systematic problem-solving strategy of sketching the situation, drawing a free-body diagram of the external forces, applying Newton's second law per coordinate axis, and checking the result; static and dynamic equilibrium, tension in a massless string over a frictionless pulley, apparent weight and elevator problems, and connected objects. Friction as a contact force opposing relative motion, static versus kinetic friction, the laws f_s <= mu_s N and f_k = mu_k N, the dimensionless coefficients of friction, area independence, and the microscopic origins of friction. Centripetal acceleration and force in uniform circular motion, F_c = m v^2/r = m r omega^2, ideally banked curves with theta = arctan(v^2/rg), inertial versus noninertial reference frames, and the fictitious centrifugal and Coriolis forces. And drag force through a fluid, F_D = (1/2) C rho A v^2, the drag coefficient, terminal velocity v_T = sqrt(2mg/(rho C A)), and Stokes' law for small slow objects.
- Work and Kinetic Energy (Physics)Recall cards on work and kinetic energy: work as the transfer of energy when a force acts through a displacement, the infinitesimal work dW = F.dr, the constant-force result W = Fd cos(theta), the parallel-component rule, work as a line integral or the area under a force-versus-displacement curve, the sign of work, the joule and foot-pound, and the work done by friction, gravity, and a spring, including conservative versus dissipative forces and the zero work around a closed path. Kinetic energy K = (1/2)mv^2 as a non-negative scalar that depends on speed and reference frame, its joule unit, the momentum form K = p^2/(2m), and translational versus rotational kinetic energy. The work-energy theorem W_net = K_f - K_i derived from Newton's second law, its use for variable forces and curved frictionless paths, and the consequences of positive, negative, and zero net work. And power as the rate of doing work, average power W/t, instantaneous power dW/dt = F.v, the watt, and the horsepower.
- Potential Energy and Conservation of Energy (Physics)Recall cards on potential energy and the conservation of energy: potential energy as energy stored in a system because of the configuration of its interacting objects, the rule that the change in potential energy is the negative of the work done by the associated conservative force, the arbitrary additive constant and the choice of a zero reference, gravitational potential energy U = mgy near Earth's surface, and elastic potential energy U = (1/2)kx^2 for a spring. Conservative forces (path-independent work, zero work around a closed path) versus non-conservative dissipative forces such as friction and air resistance, recovering a conservative force from its potential energy by F = -dU/dx or the gradient, and the curl test. Mechanical energy E = K + U, its conservation when only conservative forces do work, W_nc = change in E when they do not, and the law of conservation of energy. Potential energy diagrams: the total-energy line, the condition K = E - U >= 0, turning points, allowed and forbidden regions, force as minus the slope, equilibrium points, stable versus unstable equilibria from the second derivative, maximum speed at a potential minimum, and the infinite potential well. And sources of energy: thermal, chemical, radiant, and nuclear energy, renewable versus nonrenewable sources, conversion losses, hydro, wind, and solar power, and the 2010 world energy shares.
- Linear Momentum and Collisions (Physics)Recall cards on linear momentum and collisions: linear momentum p = mv as a vector pointing along the velocity, measured in kg·m/s, characterizing an object's quantity of motion and depending linearly on mass and velocity. Impulse J as force times time, the infinitesimal and integral forms, the impulse-momentum theorem J = delta p, Newton's second law as F = dp/dt, and the average force in a collision. Conservation of linear momentum for a closed system, why internal Newton's-third-law pairs cancel while external forces change total momentum. Types of collisions: momentum always conserved, kinetic energy conserved only in elastic collisions, inelastic and perfectly inelastic collisions, and explosions. Collisions in multiple dimensions with per-direction conservation and component equations. The center of mass as the weighted average position of mass, r_CM and its component and integral forms, F_ext = M a_CM, and the constant center-of-mass velocity of a system with zero external force. And rocket propulsion as a variable-mass system, exhaust velocity, the Tsiolkovsky rocket equation delta v = u ln(m_0/m), and the effect of gravity on a launch.
- Fixed-Axis Rotation (Physics)Recall cards on the rotation of a rigid body about a fixed axis. Rotational variables: angular position theta = s/r in radians, angular displacement, angular velocity omega = d theta/dt, and angular acceleration alpha = d omega/dt, with the counterclockwise-positive sign convention and the right-hand rule for the direction of the angular velocity vector. Rotation with constant angular acceleration: the four rotational kinematic equations as direct analogs of the linear ones (theta for x, omega for v, alpha for a). Relating angular and translational quantities: tangential speed v_t = r omega, tangential acceleration a_t = r alpha, centripetal acceleration a_c = r omega^2, and the total linear acceleration. Moment of inertia and rotational kinetic energy: K = (1/2) I omega^2, I = sum m r^2 as the rotational analog of mass, and its dependence on the axis and the mass distribution. Calculating moments of inertia: the integral I = integral r^2 dm, the parallel-axis theorem I = I_cm + m d^2, and standard results for a rod (about center and end), a disk, and compound bodies. Torque tau = r x F, its magnitude r F sin theta, the lever arm, net torque, and its sign. Newton's second law for rotation, sum tau = I alpha, the rotational analog of F = ma. And work and power for rotational motion, W = integral tau d theta, the work-energy theorem, and P = tau omega.
- Angular Momentum (Physics)Recall cards on angular momentum and rolling motion. Rolling without slipping: the contact point is instantaneously at rest, v_CM = R omega, a_CM = R alpha, and d_CM = R theta; the acceleration down an incline a_CM = m g sin(theta)/(m + I_CM/r^2), the static-friction bound needed to prevent slipping, and the split of kinetic energy into translational (1/2) m v_CM^2 plus rotational (1/2) I_CM omega^2 with friction doing no work. Angular momentum of a particle: l = r x p, magnitude r p sin(theta), direction by the right-hand rule, the lever-arm form l = r_perp m v, and the unit kg m^2/s. The rotational form of Newton's second law, sum tau = dl/dt, and for a system sum tau_ext = dL/dt. Angular momentum of a rigid body, L = I omega, directed along the rotation axis. Conservation of angular momentum when the net external torque is zero: I omega = I' omega', the ice-skater effect, and the rise in rotational kinetic energy K'_rot = K_rot (I/I'). And the precession of a gyroscope: gravitational torque tau = r M g sin(theta) perpendicular to L, the precession rate omega_p = r M g/(I omega), nutation, and Earth's 26,000-year precession.
- Static Equilibrium and Elasticity (Physics)Recall cards on the static equilibrium of rigid bodies and on stress, strain, and elasticity. Static equilibrium requires zero linear and zero angular acceleration: the first condition sets the vector sum of external forces to zero (translational equilibrium), and the second sets the sum of external torques about any axis to zero (rotational equilibrium), both at once. For rotation about a fixed z-axis the six scalar equations reduce to three, torque magnitude is r F sin(theta), the pivot may be chosen freely, and weight acts at the center of gravity. Solving equilibrium problems: free-body diagrams with forces at their real points of application, choosing the pivot to cancel an unknown, statically indeterminate cases, and the normal, friction, tension, and hinge forces involved. Stress is force per unit area and strain is the dimensionless fractional deformation; within the linear limit stress = elastic modulus times strain, measured in pascals. Tensile, compressive, bulk, and shear stress and strain define Young's modulus, the bulk modulus, and the shear modulus. Elasticity, the proportionality and elastic limits, Hooke's law, the plastic region, permanent deformation, and the fracture (breaking) stress.
- Gravitation (Physics)Recall cards on Newtonian gravity and its consequences. Newton's law of universal gravitation gives an attractive, inverse-square force F = G m1 m2 / r^2 along the line joining two masses, with the universal constant G first measured by Cavendish; spherically symmetric bodies act as though their mass sits at the center, and net forces add by superposition. Gravitation near Earth's surface: g = GM/r^2, weight W = mg, the fall of all masses at the same rate, and the small corrections from altitude, Earth's rotation, and its equatorial bulge. Gravitational potential energy U = -GMm/r (zero at infinity), conservation of total mechanical energy, escape velocity sqrt(2GM/R), and gravitational binding. Satellite orbits: circular orbital speed and period, orbital energy E = -GMm/2r, geostationary orbits, and weightlessness in free fall. Kepler's three laws of planetary motion (ellipses, equal areas, and the period-axis relation) and their basis in angular momentum and the inverse-square force. Tidal forces, spring and neap tides, tidal locking, and Io's heating. Finally Einstein's theory of gravity: the equivalence principle, spacetime curvature, the Schwarzschild radius and black holes, gravitational lensing, and time dilation.
- Fluid Mechanics (Physics)Recall cards on the mechanics of fluids at rest and in motion. Density rho = m/V, specific gravity, and the states of matter. Pressure p = F/A as a scalar that acts equally in all directions and increases with depth as p = p0 + rho g h. Measuring pressure: gauge versus absolute pressure, the pascal and other units, and the barometer and manometer. Pascal's principle and how hydraulic systems multiply force without creating extra work. Archimedes' principle and buoyancy: the buoyant force equals the weight of displaced fluid, and floating, sinking, and apparent weight follow from density. Fluid dynamics: flow rate, the equation of continuity, laminar versus turbulent flow, and ideal fluids. Bernoulli's equation as energy conservation along a streamline, Bernoulli's principle relating speed and pressure, and entrainment. Finally viscosity, the Reynolds number, Poiseuille's law and its strong dependence on tube radius, and the onset of turbulence.
- Oscillations (Physics)Recall cards on oscillatory motion. Periodic motion, period and frequency, and amplitude. Simple harmonic motion (SHM) as the motion of a Hooke's-law restoring force: position x(t) = A cos(omega t + phi), its velocity and acceleration, angular frequency omega = sqrt(k/m), and the period T = 2 pi sqrt(m/k) that depends only on mass and spring constant. Energy in SHM: elastic potential and kinetic energy, the conserved total E = (1/2) k A^2 proportional to amplitude squared, and the speed at any position. SHM as the projection of uniform circular motion. Pendulums: the simple pendulum with T = 2 pi sqrt(L/g), the physical pendulum, and the torsional pendulum. Damped oscillations: the velocity-proportional damping force, exponential amplitude decay, and the underdamped, critically damped, and overdamped regimes. Forced oscillations: natural frequency, steady-state amplitude, and resonance when the driving frequency matches the natural frequency.
- Waves (Physics)Recall cards on traveling and standing waves. Mechanical waves in a medium versus electromagnetic and matter waves. Amplitude, wavelength, period, and frequency, and the wave-speed relations v = lambda/T = lambda*f. Transverse versus longitudinal (compressional) waves. The mathematics of waves: the sinusoidal wave function y = A sin(kx - omega t + phi), wave number k = 2 pi/lambda, angular frequency omega = 2 pi/T, the phase and phase constant, transverse velocity and acceleration of a medium element, and the linear wave equation. Wave speed on a stretched string v = sqrt(F_T/mu) and the general elastic-over-inertial form. Energy and power of a wave: P = (1/2) mu A^2 omega^2 v, the amplitude-squared and frequency-squared scaling, intensity I = P/A, and the inverse-square law for a point source. Interference and superposition: constructive and destructive interference and the resultant amplitude 2A cos(phi/2). Standing waves and resonance: nodes and antinodes, the standing-wave function y = 2A sin(kx) cos(omega t), allowed wavelengths lambda_n = 2L/n and resonant frequencies f_n = n f_1 on a string fixed at both ends, harmonics, overtones, normal modes, and resonance.
- Sound (Physics)Recall cards on sound as a longitudinal disturbance of matter that travels outward through a medium. Compressions and rarefactions, the sinusoidal pressure and displacement variations and their quarter-cycle phase difference, and the wave-speed relation v = omega/k = lambda*f. The speed of sound: about 331 m/s in dry air at 0 C, 343 m/s at 20 C, its dependence on absolute temperature v = 331*sqrt(T/273 K), and the forms v = sqrt(Y/rho) in a solid rod and v = sqrt(gamma R T/M) in an ideal gas. Sound intensity I = P/A, the inverse-square falloff, the pressure-amplitude relation, the threshold of hearing 10^-12 W/m^2, and the decibel scale beta = 10 log10(I/I0). Standing sound waves and normal modes: nodes and antinodes, tubes open at both ends (all harmonics, lambda_1 = 2L) versus closed at one end (odd harmonics only, lambda_1 = 4L), fundamentals, overtones, and harmonics. Sources of musical sound and timbre, the end correction, beats and the beat frequency |f1 - f2|, the Doppler effect for moving source and moving observer, and shock waves, the Mach number, the sonic boom, and the shock-cone half-angle sin(theta) = 1/M.
- Temperature and Heat (Physics)Recall cards on temperature, heat, and heat transfer. Temperature as what a thermometer measures and as a measure of average translational kinetic energy, thermal equilibrium, and the zeroth law of thermodynamics. The Celsius, Fahrenheit, and Kelvin scales, their fixed points, the conversion formulas, and absolute zero (0 K = -273.15 C). Thermal expansion: linear (delta L = alpha L delta T), area (delta A = 2 alpha A delta T), and volume (delta V = beta V delta T with beta = 3 alpha), thermal stress, and water's density maximum near 4 C. Heat, the calorie and the mechanical equivalent of heat (1 kcal = 4186 J), specific heat and Q = mc delta T, and calorimetry (Q_cold + Q_hot = 0). Phase changes: melting, vaporization, and sublimation, the pressure dependence of melting and boiling points, latent heats of fusion and vaporization (water 334 kJ/kg and 2256 kJ/kg), phase diagrams, the triple point, and the critical point. The three mechanisms of heat transfer: conduction (P = kA(T_h - T_c)/d and the R-factor), convection (forced and natural), and radiation via the Stefan-Boltzmann law P = sigma A e T^4.
- The Kinetic Theory of Gases (Physics)Recall cards on the kinetic theory of gases. The ideal gas law in molecular form (pV = N k_B T) and molar form (pV = nRT), the Boltzmann constant, Avogadro's number, the universal gas constant R = N_A k_B, moles and molar mass, and the empirical Boyle, Charles, and Amonton laws. Standard temperature and pressure, the 22.4 L molar volume, and the van der Waals equation for real gases. The molecular model: kinetic-theory assumptions, pressure from wall collisions (pV = (1/3) N m (v^2)avg), average translational kinetic energy K_avg = (3/2) k_B T, the rms speed v_rms = sqrt(3 k_B T / m) = sqrt(3 R T / M), monatomic internal energy (3/2) nRT, Dalton's law of partial pressures, and the mean free path and mean free time. Heat capacity and equipartition: C_V at constant volume, degrees of freedom, the equipartition theorem, C_V = (d/2) R for monatomic (3/2 R), diatomic (5/2 R), and polyatomic (3R) gases, the Dulong-Petit law for solids (3R), and temperature-activated degrees of freedom. The Maxwell-Boltzmann distribution of molecular speeds, the most probable, average, and rms speeds and their ordering (v_p < v_avg < v_rms), and how the distribution shifts with temperature and molecular mass.
- The First Law of Thermodynamics (Physics)Recall cards on the first law of thermodynamics. Thermodynamic systems: system, boundary, and surroundings; open, closed, and isolated systems; thermal equilibrium and the zeroth law; equations of state f(p, V, T) = 0 and pV - nRT = 0; extensive versus intensive variables; and pV diagrams. Work, heat, and internal energy: dW = p dV, W as the integral of p dV and the area under a pV curve, the sign of work in expansion and compression, the path dependence of work, and the work in isothermal (nRT ln(V2/V1)), isobaric (p(V2 - V1)), and isochoric (zero) processes; internal energy as the total molecular energy, E_int = (3/2) nRT for a monatomic ideal gas, and the quasi-static process. The first law itself: Delta E_int = Q - W, the sign conventions for Q and W, the differential form dE_int = dQ - dW, internal energy as a path-independent state function, and the isothermal, cyclic, and isolated-system cases. Thermodynamic processes: isothermal, adiabatic, isobaric, isochoric, cyclic, and non-quasi-static, with Q = W for a cycle. Heat capacities of an ideal gas: C_V and C_p, Q = n C_V Delta T and Q = n C_p Delta T, dE_int = n C_V dT, Mayer's relation C_p = C_V + R, the monatomic, diatomic, and polyatomic values, and C_V = (d/2) R. Adiabatic processes: Q = 0, Delta E_int = -W, pV^gamma = constant, TV^(gamma-1) = constant, the adiabatic index gamma = C_p/C_V > 1, the steeper adiabatic slope, free expansion at constant temperature, and engine knocking.
- The Second Law of Thermodynamics (Physics)Recall cards on the second law of thermodynamics. Reversible and irreversible processes: the definition of each, why nearly all real processes are irreversible, the quasi-static and dissipation-free requirements for reversibility, free expansion and spontaneous heat flow as irreversible processes, and the microscopic origin of irreversibility. Heat engines: the working substance, hot and cold reservoirs, the zero internal-energy change over a cycle, net work W = Q_h - Q_c, and thermal efficiency e = W/Q_h = 1 - Q_c/Q_h. Refrigerators and heat pumps as reversed heat engines: Q_h = Q_c + W, the coefficients of performance K_R and K_P, and why a coefficient of performance can exceed 1. Statements of the second law: the Kelvin and Clausius statements, the impossibility of a perfect heat engine or perfect refrigerator, and the equivalence of the two statements. The Carnot cycle: its four reversible steps (two isothermal, two adiabatic), the Carnot engine, Q_c/Q_h = T_c/T_h, the efficiency e = 1 - T_c/T_h, Carnot's principle, the equal efficiency of all reversible engines, and the Carnot coefficients of performance. Entropy: delta-S = Q/T for a reversible isothermal step, the integral form, entropy as a state function, the zero net entropy change over a reversible cycle, the joule-per-kelvin unit, phase-change entropy, and the entropy statement that total entropy never decreases. Entropy on a microscopic scale: entropy as disorder, the statistical second law, delta-S = nR ln(V2/V1) for isothermal expansion, the third law, and the approach to perfect order at absolute zero.
- Electric Charges and Fields (Physics)Recall cards on electric charge and the electric field. Electric charge: its two types, like-repels-unlike-attracts, the coulomb unit, the elementary charge e = 1.602 x 10^-19 C, quantization, conservation, and the charged constituents of the atom, plus what makes an ion positive or negative. Conductors and insulators: conduction electrons and free charge flow, why excess charge spreads on a conductor, why charge stays put on an insulator, polarization, why a charged object attracts a neutral one, charging by induction, and grounding. Coulomb's law: F = k q1 q2 / r^2, its proportionalities, the permittivity of free space epsilon_0 = 8.85 x 10^-12, Coulomb's constant k = 8.99 x 10^9, the line of action, Newton's third law, and superposition. The electric field: E as force per unit positive charge with F = QE, the newton-per-coulomb unit, the field of a point charge, its direction, its independence from the test charge, and superposition. Continuous charge distributions: linear, surface, and volume charge densities, field by integration, and the uniform field sigma / (2 epsilon_0) of an infinite charged plane. Electric field lines: tangency, where they begin and end, line density and count, why they never cross, and that they are only a visualization. Electric dipoles: the definition, the dipole moment p = q d, the coulomb-meter unit, the zero net force and the torque tau = p x E in a uniform field, the alignment tendency, and permanent versus induced dipoles.
- Gauss's Law (Physics)Recall cards on electric flux and Gauss's law. Electric flux: what it measures, its definition as the dot product of the electric field with an area vector, the symbol Phi, the unit N*m^2/C, its scalar nature, the area vector of flat and closed surfaces, the E*A*cos(theta) form for a uniform field, when flux is maximum or zero, the surface-integral form for a nonuniform field, the exit-positive/enter-negative sign convention, and why the net flux through a surface enclosing no charge is zero. Gauss's law: the statement that net flux equals enclosed charge over epsilon_0, its integral form, the meaning of q_enc, the Gaussian surface, that E is the total field from all charges, why outside charges add zero net flux, why the flux is independent of surface shape, the equivalence to Coulomb's law, the point-charge sphere result, and the role of superposition. Applying Gauss's law: identifying symmetry, matching the Gaussian surface to it, the spherical, cylindrical, and planar symmetry cases, and the field results for a sphere inside and out, an infinite line E = lambda/(2*pi*epsilon_0*r), an infinite plane E = sigma/(2*epsilon_0), parallel plates, and a spherical shell. Conductors in electrostatic equilibrium: the definition, conduction electrons, why the interior field is zero, why excess charge sits on the outer surface, the perpendicular field just outside E = sigma/epsilon_0, cavity induction, charge concentration at sharp points, and electrostatic shielding.
- Electric Potential (Physics)Recall cards on electric potential energy, electric potential, and their applications. Electric potential energy: that the Coulomb force is conservative and path-independent, the symbol U and its joule unit, W = -delta U, the zero reference at infinity, the two-charge result U = k*q*Q/r, Coulomb's constant, and the zero closed-loop line integral. Electric potential and potential difference: V = U/q, the symbol V, test-charge independence, the volt as J/C, delta V = delta U/q, V_B - V_A, voltage, delta U = q*delta V, E = -delta V/delta s in a uniform field, 1 N/C = 1 V/m, and the electron-volt. Calculations of potential: V = k*q/r for a point charge, the 1/r versus 1/r^2 falloff, the scalar nature and algebraic superposition of potential, the electric dipole and its moment p = q*d, the integral form for a continuous distribution, and the far-field dipole potential. Field from potential: E = -dV/ds, the steepest-descent direction, E = -grad V, the partial-derivative components, and the scalar-first method. Equipotential surfaces and conductors: the definition and lines, perpendicularity to field lines, zero work along a surface, a conductor as an equipotential, grounding, and charge concentration at small radii of curvature. Applications: the Van de Graaff generator, xerography and the photoconductor, laser and ink-jet printers, and the electrostatic precipitator.
- Capacitance (Physics)Recall cards on capacitors and capacitance. Capacitors and capacitance: what a capacitor is and stores, its two-conductor construction, the definition C = Q/V, the farad and its name, the practical range, geometry dependence, the constant Q/V ratio, the parallel-plate result C = eps0*A/d, the permittivity of free space, the field E = sigma/eps0, and the spherical, isolated-sphere, and cylindrical capacitance formulas. Capacitors in series and parallel: the reciprocal-sum series rule, equal series charge, the smaller-than-smallest result, series voltage adding, the parallel sum rule, equal parallel voltage, the larger-than-largest result, parallel charge adding, and network reduction. Energy stored: field storage, the three energy forms U = 1/2 C V^2, U = Q^2/2C, U = 1/2 Q V, energy persisting after disconnection, the energy density u = 1/2 eps0 E^2, and the defibrillator. Capacitor with a dielectric: what a dielectric is, the dielectric constant kappa, kappa = 1 for vacuum and kappa > 1 otherwise, C = kappa*C_0, the constant-charge and voltage/energy drops on a disconnected capacitor, dielectric strength, and the stud finder. Molecular model of a dielectric: polar versus nonpolar molecules, alignment and induced dipoles, surface induced charge, the opposing induced field, E = E_0/kappa, and breakdown.
- Current and Resistance (Physics)Recall cards on electric current, resistance, and superconductors. Electrical current: current as the rate of charge flow, I = dQ/dt, the ampere and its name, the need for a complete circuit, conventional current, electron carriers in metals, carriers in ionic solutions, and drift velocity. Model of conduction in metals: the free-electron sea, the zig-zag drift path, signal speed versus drift speed, I = nqAv_d, current as a scalar, current density J as a vector, J = nqv_d, E = rho J, and why good electrical conductors conduct heat. Resistivity and resistance: resistivity rho, its reciprocal conductivity, the ohm-meter, conductor versus insulator versus semiconductor, R = V/I, R = rho L/A, the ohm, the temperature dependence rho = rho_0[1 + alpha(T - T_0)], and the temperature coefficient alpha. Ohm's law: V = IR, Ohm's experiment, its empirical nature, ohmic versus nonohmic devices, and the diode. Electrical energy and power: P = IV, P = I^2 R, P = V^2/R, the watt, resistive heating, E = Pt, and the kilowatt-hour. Superconductors: zero resistance below a critical temperature, Onnes's discovery, mercury, the Meissner effect, Type I and Type II, YBCO, BCS theory and Cooper pairs, persistent currents, MRI magnets, SQUIDs, and the Josephson effect.
- Direct-Current Circuits (Physics)Recall cards on direct-current circuits. Electromotive force: emf as work per unit charge, the symbol epsilon, the volt, energy conversion, terminal voltage, internal resistance r, V_terminal = emf - I r, I = emf/(R + r), and ideal versus real batteries. Resistors in series and parallel: the same current in series, R_S as a sum, the source voltage as a sum of drops, the same voltage in parallel, 1/R_P as a sum of reciprocals, branch currents summing to the total, and combination circuits. Kirchhoff's rules: junctions, the junction rule from charge conservation, the loop rule from energy conservation, and the sign conventions for resistors and emf sources. Electrical measuring instruments: the ammeter in series, the voltmeter in parallel, the galvanometer, converting it to an ammeter or voltmeter, and analog, digital, and ohmmeter designs. RC circuits: charging and discharging of a capacitor, the time constant tau = RC, the 63.2% and 36.8% marks, and a full capacitor as an open circuit. Household wiring and safety: thermal and shock hazards, short circuits, P = I^2 R_w, fuses and breakers, the live, neutral, and ground wires, grounding, and the GFCI.
- Magnetic Forces and Fields (Physics)Recall cards on magnetic forces and fields. Magnets and Earth's field: the two poles, attraction and repulsion, the absence of magnetic monopoles, Earth as a bar magnet, compass behavior, field reversals, and the historical discoveries of Oersted, Ampere, Arago, and Faraday. The magnetic field: its definition through the force on a moving charge, F = qv x B, F = qvB sin(theta), the tesla and gauss, the right-hand rule, and field lines. Motion of a charged particle: circular and helical paths, why the magnetic force does no work, r = mv/(qB), the period T = 2 pi m/(qB), pitch, magnetic bottles, and the Van Allen belts. Force on a current-carrying conductor: RHR-2, F = IL x B, F = BIL sin(theta), and the zero net force on a closed loop. Force and torque on a current loop: the magnetic dipole moment mu = NIA, tau = mu x B, tau = IAB sin(theta), the potential energy U = -mu . B, electric motors, and the commutator. The Hall effect: Hall's experiment, the Hall voltage, the force balance, drift speed, velocity selectors, and identifying charge carriers. Applications: the mass spectrometer and the cyclotron.
- Sources of Magnetic Fields (Physics)Recall cards on the sources of magnetic fields. The Biot-Savart law: the field of a current element, the permeability of free space, the right-hand rule for the direction, and the field of a circular arc and a full loop. The magnetic field of a thin straight wire: B = mu_0 I/(2 pi R), concentric circular field lines, and the right-hand rule. The force between two parallel currents: attraction and repulsion, the historical ampere definition, and the pinch effect. The magnetic field of a current loop: the magnetic dipole moment, the on-axis field, and the inverse-cube dipole falloff. Ampere's law: the line integral of B, the enclosed current, the Amperian loop, when to use it versus the Biot-Savart law, and the field inside and outside a thick wire. Solenoids and toroids: the uniform interior field of a solenoid, the zero exterior field, and the toroid field. Magnetism in matter: atomic dipole moments, paramagnetism, diamagnetism, ferromagnetism, magnetic domains, hysteresis, susceptibility, and permeability.
- Electromagnetic Induction (Physics)Recall cards on electromagnetic induction. Faraday's law: magnetic flux and the weber, the induced emf as the negative rate of change of flux, and the N-turn coil form. Lenz's law: the induced current opposes the flux change, the negative sign, the like-pole repulsion of an approaching magnet, and the energy-conservation basis. Motional emf: epsilon = Blv, the induced current and retarding force on a moving rod, and the mechanical-to-electrical power balance. Induced electric fields: the line-integral form of Faraday's law, the nonconservative character with no associated potential, and the field around a circular path. Eddy currents: magnetic damping, slotted plates, metal detectors, eddy-current braking, and induction cooktops. Electric generators and back emf: the rotating-coil emf, peak emf, motor-versus-generator energy conversion, and how back emf sets a motor's current. Applications: hard disk read heads, giant magnetoresistance, magnetic stripes, graphics tablets, regenerative braking, and transcranial magnetic stimulation.
- Inductance (Physics)Recall cards on inductance. Mutual inductance: the henry, the M = N Phi / I definition, its symmetry and geometry dependence, and the induced emf epsilon = -M dI/dt. Self-inductance: Phi = LI, the self-induced emf -L dI/dt, its Lenz's-law polarity, the inductor as a circuit element, and the solenoid formula. Energy in a magnetic field: U = (1/2) L I^2, the energy density B^2/(2 mu0), and inductor power. RL circuits: the asymptotic rise and decay of current, the time constant L/R, the 63% rule, and the initial and steady-state conditions. LC oscillations: omega = 1/sqrt(LC), the electric-to-magnetic energy exchange, the charge and current solutions and their 90-degree phase, and the mass-spring analogy. RLC series circuits: damped oscillations, the governing differential equation, and the underdamped, critically damped, and overdamped regimes.
- Alternating-Current Circuits (Physics)Recall cards on alternating-current circuits. AC sources: DC versus AC, the v = V0 sin(omega t) and i = I0 sin(omega t) forms, peak versus instantaneous notation, and US and European mains values. Simple AC circuits: the resistor in phase, the capacitor's current leading and the inductor's current lagging by pi/2, capacitive reactance XC = 1/(omega C), inductive reactance XL = omega L, their frequency dependence, and phasors. Series RLC circuits: impedance Z = sqrt(R^2 + (XL - XC)^2), the AC Ohm's law I0 = V0/Z, the phase angle, and the element voltages. Power: rms current and voltage, the average-power formulas, the power factor cos(phi), and why only resistors dissipate. Resonance: XL = XC, omega0 = 1/sqrt(LC), minimum impedance, maximum current and power, and the quality factor. Transformers: the voltage and current turns ratios, step-up and step-down, power conservation, and high-voltage transmission.
- Electromagnetic Waves (Physics)Recall cards on electromagnetic waves. Maxwell's equations: the displacement current that completes Ampere's law, the four laws (Gauss, Gauss for magnetism, Faraday, Ampere-Maxwell), how changing fields generate each other, the prediction of waves at the speed of light, and Hertz's confirmation. Plane waves: transverse fields perpendicular to each other and to propagation, E/B = c, the wave equation, c = 1/sqrt(epsilon0 mu0), and the E cross B direction. Energy: energy density, the Poynting vector, intensity, and the field amplitude relation E0 = c B0. Momentum and radiation pressure: p = U/c, absorber versus reflector pressure, comet tails, and light sails. The electromagnetic spectrum: c = f lambda, and radio, microwave, infrared, visible, ultraviolet, X-ray, and gamma-ray bands.
- The Nature of Light (Physics)Recall cards on the nature of light. The propagation of light: the speed of light in vacuum, its invariance for all observers, the index of refraction n = c/v, and the ray model. The law of reflection: angle of reflection equals angle of incidence, specular versus diffuse reflection, corner reflectors, and retroreflectors. Refraction and Snell's law: bending toward or away from the normal, and representative indices for air, water, and diamond. Total internal reflection: the critical angle theta_c = arcsin(n2/n1) and optical fibers. Dispersion: white light spread into a spectrum, wavelength-dependent index, prisms, and rainbows. Huygens's principle: wavelets, wave fronts, refraction, and diffraction. Polarization: Malus's law, polarizing filters, Brewster's angle, birefringence, optical activity, and liquid-crystal displays.
- Geometric Optics and Image Formation (Physics)Recall cards on geometric optics and image formation. Plane mirrors: same-size, upright, virtual images located as far behind the mirror as the object is in front, and the real-versus-virtual image distinction. Spherical mirrors: concave and convex geometry, center of curvature, vertex, optical axis, focal point, f = R/2, the mirror equation 1/d_o + 1/d_i = 1/f, magnification m = -d_i/d_o, and sign conventions. Images formed by refraction: apparent depth h_i = (n2/n1) h_o and the single-spherical-surface equation. Thin lenses: converging and diverging behavior, the thin-lens equation, the lensmaker's equation, ray tracing, and image types. The eye: cornea and lens, accommodation, near and far points, optical power in diopters, and correction of myopia and hyperopia. The camera, the simple magnifier and angular magnification, and compound microscopes and telescopes.
- Interference (Physics)Recall cards on the wave interference of light. Young's double-slit experiment: coherence versus incoherence, constructive and destructive interference, fringes, and the historical evidence for the wave nature of light. The mathematics of interference: path length difference delta-l = d sin(theta), bright fringes at d sin(theta) = m*lambda, dark fringes at d sin(theta) = (m + 1/2)*lambda, order m, and the fringe position y_m = m*lambda*D/d. Multiple-slit interference: principal maxima, the N minus 2 secondary maxima, secondary-maximum amplitude 1/N and intensity 1/N^2, and the diffraction grating. Interference in thin films: the 180-degree phase change on reflection off a higher-index medium, the in-film wavelength lambda_n = lambda/n, and the soap-film constructive and destructive conditions. The Michelson interferometer: the beam splitter, the fringe-shift relation 2*delta-d = m*lambda_0, the compensator plate, and its use in precision measurement.
- Diffraction (Physics)Recall cards on the diffraction of light. Single-slit diffraction: the bright central maximum and dimmer secondary maxima, the dark-fringe condition a sin(theta) = m*lambda, and why a narrower slit spreads the pattern. Intensity in single-slit diffraction: the phasor derivation, I = I0 (sin(beta)/beta)^2 with beta = (pi a sin(theta))/lambda, and the faint 0.045 and 0.016 secondary maxima. Double-slit diffraction as an interference pattern under a single-slit envelope, and missing orders. Diffraction gratings: d sin(theta) = m*lambda, sharp principal maxima, and spectroscopy. Circular apertures and resolution: the Rayleigh criterion theta = 1.22 lambda/D, microscope resolution x = 0.61 lambda/NA, and the diffraction limit. X-ray diffraction and Bragg's law m*lambda = 2d sin(theta). Holography: recording amplitude and phase by the interference of laser light.
- Relativity (Physics)Recall cards on special relativity. Einstein's two postulates: the laws of physics are the same in all inertial frames, and light travels at the same speed c in all inertial frames regardless of the motion of source or observer. Relativity of simultaneity. Time dilation Delta t = gamma * Delta tau, proper time, and the Lorentz factor gamma = 1/sqrt(1 - v^2/c^2). The twin paradox. Length contraction L = L0*sqrt(1 - v^2/c^2) along the direction of motion. The Lorentz transformation, the invariant spacetime interval, and light cones. Relativistic velocity addition. The relativistic Doppler effect, redshift, and blueshift. Relativistic momentum p = gamma*m*u. Relativistic energy E = gamma*m*c^2, rest energy E0 = m*c^2, kinetic energy K = (gamma - 1)*m*c^2, the energy-momentum relation E^2 = (pc)^2 + (mc^2)^2, and mass-energy equivalence.
- Photons and Matter Waves (Physics)Recall cards on the birth of quantum physics. Blackbody radiation, the Stefan-Boltzmann law P = sigma*A*T^4, Wien's displacement law, the ultraviolet catastrophe, and Planck's quantization E_n = n*h*f. The photoelectric effect and Einstein's photon explanation, the photoelectric equation K_max = h*f - phi, the work function, and the cutoff frequency. The Compton effect and the photon momentum p = h/lambda. Bohr's model of the hydrogen atom, the Rydberg formula, quantized angular momentum, the Bohr radius, and the energy levels E_n = -13.6 eV/n^2. De Broglie's matter waves lambda = h/p and the Davisson-Germer experiment. Wave-particle duality and Heisenberg's uncertainty principle Delta x * Delta p >= h-bar/2.
- Quantum Mechanics (Physics)Recall cards on nonrelativistic quantum mechanics. The wave function and the Born interpretation |Psi|^2 as a probability density, normalization, expectation values, and the position and momentum operators. The Heisenberg uncertainty principle in its position-momentum and energy-time forms. The time-dependent and time-independent Schrodinger equations, stationary states, and separation of variables. The quantum particle in a box with quantized energies E_n = n^2 pi^2 h-bar^2/(2mL^2) and zero-point energy. The quantum harmonic oscillator with evenly spaced levels E_n = (n + 1/2) h-bar omega. Quantum tunneling through potential barriers, the transmission probability, and applications from alpha decay to the scanning tunneling microscope.
- Atomic Structure (Physics)Recall cards on the quantum structure of atoms. The hydrogen atom and its three quantum numbers n, l, and m, the quantized energy E_n = -13.6 eV/n^2, orbital angular momentum L = sqrt(l(l+1)) h-bar, space quantization, and spectroscopic s, p, d, f notation. The orbital magnetic dipole moment, the Bohr magneton, and the Zeeman effect. Electron spin with s = 1/2, the Stern-Gerlach experiment, the Pauli exclusion principle and the building-up of the periodic table. Atomic spectra and selection rules, characteristic X-rays and Moseley's law, bremsstrahlung, and the physics of lasers including stimulated emission, population inversion, and gain media.
- Condensed Matter Physics (Physics)Recall cards on condensed matter physics. Molecular bonding by ionic, covalent, and van der Waals forces, the energetics of NaCl and H2 formation, and molecular rotational and vibrational spectra. Bonding in crystalline solids, the Madelung constant, and dissociation energy. The free electron model of metals, the Fermi energy, the Fermi factor, and the density of states. Band theory, valence and conduction bands, and the energy gaps that distinguish conductors, insulators, and semiconductors. Doping, n-type and p-type material, holes, the p-n junction, diodes, and transistors. Superconductivity, the Meissner effect, critical fields, Cooper pairs and BCS theory, and high-temperature superconductors.
- Nuclear Physics (Physics)Recall cards on nuclear physics. Properties of nuclei: protons, neutrons, nucleons, atomic and mass numbers, isotopes, the atomic mass unit, nuclear radius and density, and the strong nuclear force. Nuclear binding energy, the mass defect, binding energy per nucleon, and the stability of iron-56. Radioactive decay, the decay law and decay constant, half-life, activity, the becquerel and curie, and carbon-14 dating. Alpha, beta, and gamma decay with their changes in Z and A and their penetrating power. Nuclear fission, chain reactions, critical mass, and the liquid drop model. Nuclear fusion, the proton-proton chain in the Sun, and the deuterium-tritium reaction. Medical applications and biological effects: technetium-99m, PET imaging, the gray, the rad, relative biological effectiveness, and the sievert.
- Particle Physics and Cosmology (Physics)Recall cards on particle physics and cosmology. The four fundamental forces and their ranges and relative strengths. Fermions and bosons; the six quarks and their fractional charges; hadrons, mesons, and baryons; the six leptons; force carriers (photon, gluons, W and Z bosons, graviton) and the Higgs boson; antiparticles and annihilation. Conservation laws: baryon number, the three lepton numbers, strangeness, and neutrino oscillations. Quarks: spin, color charge, confinement, gluons, and the deep-inelastic-scattering evidence. Particle accelerators (Van de Graaff, linac, cyclotron, synchrotron, colliding beams, the LHC) and detectors. The Standard Model: electroweak theory, quantum electrodynamics, quantum chromodynamics, Feynman diagrams, virtual particles, and grand unified theories. Cosmology: Hubble's law, the Hubble constant, the Big Bang as expanding space, cosmological redshift, the age of the universe, the epochs of the early universe, Big Bang nucleosynthesis, the cosmic microwave background, and dark energy and dark matter.