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

Document Info

Posted By:

Joy Tseng

Date:

Wednesday, January 2, 2008

School:

Clarkstown High School South

Class:

AP Physics C

Tags:

• forces
• maxwell
• mechanics
• study guide
• formula sheet
• formulas
• Electromagnetism
• kinematics
• physics

About this Document

This is a general formula sheet for all of the sections of the AP Physics C exams, both electromagnetism and mechanics.