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Physics C Formulas Kinematics Rotational Dynamics Uniform Acceleration: τ = rFsinθ V= Δ x / t I = mr2 (point mass) = ( ) mr2 a= Δ v / t I = Icm + mh2 x = xo + vo + 1/2at2 I = ∫ dmr2 = ∫ (m/L) dx x2 v = vo + at α = τ net / I vf2 = vo2 + 2a Δ x k = ½ I ω2 x = v t = [ (v + vo)/2 ] t Angular Momentum Non uniform Acceleration: L=Iω v = dx/dt L = m v r closest a = dv/dt Li = Lf Δ x = ∫ v(t) dt SHM ∆ v = ∫ a(t) dt x = A sin ωt Newton’s Laws v = A ω cos ωt Fnet = ma (2nd law) a= - A ω2 sin ωt Ff = μ Fn ω= 2π / T Fs = k x Mass on a Spring Differential Equations d2x/dt2 = - kx/m a = Fnet / m à dv/dt = Fnet / m ω = √ k/m Work T = 2π √ m/k w = Fd cos θ = F ∙ x Total Energy = k + Us = ½ KA2 w = area under F- x curve Pendulum w = ∫ F(x) dx T=2π √ L/g Power “rate of change of energy” Torsion Pendulum Pavg = w / t T = 2π √ I/κ P = dw /dt Gravitation w = ∫ P(t) dt outside planet P = F v cos θ Fg = (Gm1m2)/r2 Energy g = (Gm) / r2 k = ½ mv2 Ug = - (Gm1m2) /r Ug = mgh inside planet Us = ½ k x2 g = (4/3) Gρπ rinside ∆k=w Circular Orbits ∆ u = w = - ∫ F(x) dx Fc = Fg à mv2/r = Gm1m2/r2 Energy i = Energy f ac = g à v2/r = GM/r2 Potential Energy Curve v = √ GM/r F = - du/dx = - slope of u function Elliptical Orbits Center of Mass T2= (4π2/GM) r3 Xcm = (X1m1 + X2m2 + …) / (m1+m2+…) ki + Ugi = Kf + Ugf Xcm = (1/m) ∫ λ x dx λ = mass/ length at extremities Impulse Li = Lf à mvr = mvr p = mv J = ∆p J = Favg t J = area under F-t curve J = ∫ F(t) dt Momentum Conservation Kirchhoff’s Rule Pi = Pf isolated system Junction: Iin = Iout Rotational Kinematics Loop: Σ ∆V = 0 ω = θ / t = dθ/dt Charging Capacitors α = ∆ω/ t = dω/dt q= ξ C (1- e–t/RC) θ = θo + ωot + ½ αt2 I = (ξ / R ) e–t/RC ω = ωo + αt τ = RC ω2 = ωo2 + 2 α ∆θ Discharging Capacitors θ = s/r q = Qo e–t/RC ω = v/r I = (V/R) e–t/RC α = a/r I = dq/dt à q = ∫ I(t) dt Electrostatics Magnetism F = KQ1Q2/r2 on particles Fe = qE FB = q v B sinθ = q v x B Point Charge on short wires E = KQ/r2 FB = BIL sinθ Smooth Charge Distribution on long wires dE = (Kλdx) / (x2+R2) à dEx = dEcosθ B = μo I / 2π r Guass’s Law Biot-Savart Law: Short Wires Φ = ∫ E dA dB = (μo I ds / 2π r2) sinθ ∫ E dA = qenc/ εo Ampere’s Law Potential vs. Potential Energy ∫ B ds = μo Ienc ∆ v = Eavgd Flux ∆ v = - ∫ E ds Φ = BconsA cosθ = B ∙ A E = - dv/dx Φ = ∫ B(x) w dx ∆ Ue = qV Induction Charge Distribution ξ = -dΦ/dt V = KQ/r (pt. charge) ξ = BLv Ue = KQ1Q2/r (pt. charge) Inductance (smooth) ξ = -L (dI/dt) V = KQ/R L=NΦ/I Capacitor Solenoid C = Q/V L/l = μo n2 A Uc = ½ QV = ½ CV2 = ½ Q2/C RL Circuits Parallel Plate I = (ξ/R )(1- e–Rt/L) à with emf E = - σ / εo = Q/A εo I = Io e–Rt/L à without emf V = Ed τ = L/R C = A εo / d Maxwell’s Equations…4/3 notes Circuits I = ∆ q / t = dq/dt R = ρ L / A = L/ σ A à ρ = 1/σ Ohm’s Law V = IR J = I/A= σE P = IV = I2R = V2/R
