Physics - Personal Study Sheet for All Modules

Mechanics v = v_0 + at (no acceleration) x = x_0 + v_0 t + 1/2 a t^2 (constant acc) v^2 = v_0^2 + 2a(x - x_0) (constant acc) Kinematics Review s = d/t (avg speed) v = d/t (avg velocity) a = Delta v / Delta t g = 9.8 m/s^2 (gravity) v = dx/dt (limit of x/t at one moment) a = dv/dt (limit of v/t at one moment) Horizontal KINEMATICS: v_x = v_0 cos theta x = (v_0 cos theta)t Falling Objects (Free Fall) Independant of mass constant "a" due to gravity air resistance affects if object is light Vertical KINEMATICS: v_y = v_0 sin theta - gt y = (v_0 sin theta)t - 1/2 gt^2 v_y^2 = (v_0 sin theta)^2 - 2g(y - y_0) Dynamics FORCES (Vectors) F_net = ma (Newton's 2nd Law) Sum of Forces = ma Forces Applied F = mg (weight) F_friction = u_k N (kinetic friction) F_friction = u_s N (static friction) (u_s is greater than u_k) F_centripetal = mv^2/r (centripetal force) F_T = (m1 m2 g) / (m1 + m2) (Atwood machine) Work and Energy W = Fd cos theta (Work) Work-Energy Thm: W_net = Delta KE PE_g = mgh (gravitational potential energy) PE_s = 1/2 kx^2 (spring potential energy) KE = 1/2 mv^2 (kinetic energy) Conservation of Energy Sum of PE + KE is constant if isolated system Sum of PE + KE = Sum of PE' + KE' Momentum P = mv (momentum) F = Delta p / Delta t Impulse = F Delta t = Delta p Collisions Elastic (KE conserved) Inelastic (KE not conserved) Circular Motion a_c = v^2/r (centripetal acc) v = 2 pi r / T (orbital speed) w = v/r (angular velocity) w = 2 pi f (angular freq) w = 2 pi / T Simple Harmonic Motion x(t) = A cos (wt + phi) (position) v(t) = -wA sin (wt + phi) (velocity) a(t) = -w^2 A cos (wt + phi) (acceleration) T = 2 pi sqrt(m/k) (period of mass on a spring) T = 2 pi sqrt(L/g) (period of pendulum) w = sqrt(k/m) (angular frequency) w = sqrt(g/L) Waves v = lambda * f (wave speed) v = sqrt(Tension/ (m/L)) (wave speed on string) v = sqrt(B/rho) (wave speed in fluid) I = P/A (intensity) Intensity is proportional to A^2 and w^2 Sound Loudness (decibels) beta = 10 log(I/I_0) where I_0 = 10^-12 W/m^2 Doppler Effect f' = f (v +/- v_d) / (v +/- v_s) Beat Frequency f_beat = |f1 - f2| Thermodynamics Q = mc Delta T (heat transfer) Q = mL (latent heat) W = P Delta V (work done by gas) Delta U = Q - W (first law of thermodynamics) PV = nRT (ideal gas law) W = -P Delta V Fluids P = F/A (pressure) rho = m/V (density) P = rho g h (pressure in a fluid) Archimedes' Principle Buoyant Force = rho_fluid V_submerged g Continuity Equation A1 v1 = A2 v2 Bernoulli's Equation P1 + 1/2 rho v1^2 + rho g h1 = P2 + 1/2 rho v2^2 + rho g h2 Optics 1/f = 1/d_o + 1/d_i (thin lens equation) M = -d_i / d_o (magnification) n1 sin theta1 = n2 sin theta2 (Snell's Law) f = R/2 (focal length of spherical mirror) Refraction n = c/v (index of refraction) Electricity and Magnetism F = kq1q2/r^2 (Coulomb's Law) E = F/q (electric field) E = kQ/r^2 (electric field of point charge) V = PE/q (electric potential) V = kQ/r (electric potential of point charge) U = k q1q2/r (electric potential energy) Delta V = -E d (uniform electric field) C = Q/V (capacitance) C = epsilon_0 A/d (parallel plate capacitor) U = 1/2 CV^2 = 1/2 QV = 1/2 Q^2/C (energy stored in capacitor) I = Delta Q/Delta t (current) V = IR (Ohm's Law) P = IV = I^2 R = V^2/R (power) R_eq = R1 + R2 + ... (series resistors) 1/R_eq = 1/R1 + 1/R2 + ... (parallel resistors) B = mu_0 I / (2 pi r) (magnetic field of long straight wire) F = I L B sin theta (force on current-carrying wire in magnetic field) F = qvB sin theta (force on moving charge in magnetic field) phi_B = BA cos theta (magnetic flux) E = -N Delta phi_B / Delta t (Faraday's Law of Induction) V_rms = V_max / sqrt(2) (RMS voltage) I_rms = I_max / sqrt(2) (RMS current) Absolute Pressure P_abs = P_gauge + P_atm P = rho g h (pressure as a function of depth in a fluid) P = F/A (pressure definition) V = m/rho (volume from mass and density) Buoyancy FB = rho_fluid V_disp g FB is the force on an object as if the weight of the displaced fluid. FB = m_fluid_disp g Fully submerged If FB > mg, object floats up If FB < mg, object sinks If FB = mg, object is suspended Continuity Equation (fluids) A1 v1 = A2 v2 For incompressible fluids, the flow rate is constant through a pipe of varying diameter. v is faster in smaller area. Bernoulli's Principle (fluids) P + 1/2 rho v^2 + rho g h = constant Viscous Fluids Poiselle's Equation Q = (pi r^4 Delta P) / (8 eta L) (volume flow rate in a viscous pipe) Delta P = Q (8 eta L) / (pi r^4) (pressure drop due to viscosity) eta is the viscosity coefficient Reynolds Number (fluid flow) Re = (rho v D) / eta Re < 2000 --> laminar flow Re > 3000 --> turbulent flow Diffusion Flux = -DA (dC/dx) (Fick's Law of Diffusion) F = D A (Delta C / Delta x) (simplified form of Fick's Law) Delta x is the distance D is the diffusion coefficient Thermal Physics Thermodynamics Delta U = Q - W (First Law of Thermodynamics) Q = mc Delta T (heat transfer - specific heat) Q = mL (latent heat - phase change) P = W/t (power) Rate of Heat Transfer Q/t = kA (Delta T / L) (conduction) P_cond = kA (Delta T / L) P_rad = sigma A T^4 (radiation, Stefan-Boltzmann Law) P_conv = hA Delta T (convection) Conversions 1 atm = 101325 Pa 1 atm = 760 mmHg 1 atm = 101.3 kPa 1 cal = 4.184 J 1 K = 1 C (change in temperature) F = 9/5 C + 32 (Fahrenheit to Celsius) Ideal Gas Law PV = nRT (n is moles, R is gas constant) PV = NkT (N is number of molecules, k is Boltzmann constant) U = (3/2) nRT (internal energy of monoatomic ideal gas) Kinetic Theory of Gases KE_avg = (3/2) kT (average kinetic energy per molecule) v_rms = sqrt(3RT/M) (root-mean-square speed) Electric Field Coulomb's Law F = k q1 q2 / r^2 (magnitude of force between two point charges) k = 8.99 x 10^9 Nm^2/C^2 Electric Field E = F/q (electric field definition) E = kQ/r^2 (electric field of point charge) Electric Field Lines (properties) Lines begin on positive charges and end on negative charges. Lines never cross. Density of lines indicates strength. Electric Potential Energy U = k q1 q2 / r (potential energy of two point charges) Delta U = q Delta V (change in potential energy) Potential V V = U/q (potential definition) V = kQ/r (potential of point charge) Delta V = -E d (for uniform electric field) Capacitance C = Q/V (capacitance definition) C = epsilon_0 A/d (parallel plate capacitor) U = 1/2 CV^2 = 1/2 QV = 1/2 Q^2/C (energy stored in capacitor) Circuits I = Delta Q/Delta t (current) V = IR (Ohm's Law) P = IV = I^2 R = V^2/R (power) R_eq = R1 + R2 + ... (series resistors) 1/R_eq = 1/R1 + 1/R2 + ... (parallel resistors) tau = RC (time constant for RC circuit) I(t) = I_0 e^(-t/RC) (current decay in RC circuit) V(t) = V_0 e^(-t/RC) (voltage decay in RC circuit) Magnetism F = qvB sin theta (force on moving charge in magnetic field) F = I L B sin theta (force on current-carrying wire in magnetic field) B = mu_0 I / (2 pi r) (magnetic field of long straight wire) B = mu_0 n I (magnetic field in solenoid) phi_B = BA cos theta (magnetic flux) E = -N Delta phi_B / Delta t (Faraday's Law of Induction) V_rms = V_max / sqrt(2) (RMS voltage) I_rms = I_max / sqrt(2) (RMS current) Optics c = speed of light f = frequency lambda = wavelength c = lambda f Reflection theta_i = theta_r (law of reflection) 1/f = 1/do + 1/di (mirror equation) M = -di/do (magnification) f = R/2 (focal length of spherical mirror) Refraction n1 sin theta1 = n2 sin theta2 (Snell's Law) n = c/v (index of refraction) Critical angle: sin theta_c = n2/n1 (for n1 > n2) Lenses 1/f = 1/do + 1/di (thin lens equation) M = -di/do (magnification) Diffraction d sin theta = m lambda (single slit diffraction) a sin theta = m lambda (single slit diffraction - minima) For a single slit, the width of the central maximum is 2 lambda L / a Interference d sin theta = m lambda (double slit interference - maxima) d sin theta = (m + 1/2) lambda (double slit interference - minima) Bright fringes occur when path difference is integer multiple of wavelength. Dark fringes occur when path difference is half-integer multiple of wavelength. Modern Physics Photoelectric Effect KE_max = hf - phi (maximum kinetic energy of emitted electron) phi = work function Atomic Structure E_n = -13.6 eV / n^2 (energy levels of hydrogen atom) Delta E = hf (energy of photon) h = 6.626 x 10^-34 J s (Planck's constant) c = 3.00 x 10^8 m/s (speed of light) lambda = h / p (de Broglie wavelength) Radioactivity N(t) = N_0 e^(-lambda t) (radioactive decay law) T_1/2 = ln(2) / lambda (half-life) A = lambda N (activity) Activity: decay rate. Nuclear Reactions E = mc^2 (mass-energy equivalence, Einstein) Mass defect: Delta m = (Z mp + N mn) - M_atom Binding Energy: BE = Delta m c^2 Quantum Mechanics Heisenberg's Uncertainty Principle: Delta x Delta p >= h / (4 pi) Schrodinger Equation (conceptual, not explicitly written out) Semiconductors N-type: doped with donors (extra electrons) P-type: doped with acceptors (electron holes) PN junction diode: allows current flow in one direction (forward bias) and blocks in reverse (reverse bias).