Physics 131 Equation Sheet: Fall 2007 - Prof. Andrew J. Dougherty, Quizzes of Mechanics

Download Physics 131 Equation Sheet: Fall 2007 - Prof. Andrew J. Dougherty and more Quizzes Mechanics in PDF only on Docsity! Phys 131 Equation Sheet Fall 2007 Kinematics: v = v0 + at x = x0 + v0t + 1 2 at2 v2 = v20 + 2a(x− x0) arad = v2 r ~vP/A = ~vP/B + ~vB/A Forces and Potentials: ~F = d~p dt Ffr,s ≤ µsFN Ffr,k = µkFN Fs = −k(x−xR) Us = 1 2 k(x− xR)2 ~Fg = − GM1M2 r2 r̂ Ug = − GM1M2 r T 2 = 4π2r3 GM Work-Energy: W = ∫ r2 r1 ~F · d~r W = ~F · ~r Ki + Wtot = Kf P = ~F · ~v ∆UAB = − ∫ B A ~F · d~r Fx = − dU dx Systems of Particles: ~p = m~v ~F = d~p dt Mxcm = m1x1 + m2x2 + · · · = ∑ i mixi∑ ~Fext = M~acm v2f − v1f = −(v2i − vi1) Rotation: θ = θ0 + ω0t + 1 2 αt2 ω = ω0 + αt ω2 = ω20 + 2α(θ − θ0) v = ωr atan = αr arad = ω2r ~L = ~r × ~p (particle) L = Iω (rigid body) ~τ = ~r × ~F I = ∑ i mir 2 i K = 1 2 Iω2 ∑ ~τext = d~L dt ∑ τext = Iα I = Icm + Md2 K = 1 2 MV 2cm + 1 2 Icmω 2 Electric Force and Potential Energy: ~F = k q1q2 r2 r̂ U = k q1q2 r Vectors: Ax = A cos θ Ay = A sin θ A = √ A2x + A2y ~A · ~B = AB cos φAB ~A · ~B = AxBx + AyBy + AzBz ~A× ~B = n̂AB sinφAB Math: ax2 + bx + c = 0 x = −b± √ b2 − 4ac 2a (1 + x)n ≈ 1 + nx for x  1 Constants: g = 9.8m/s2 G = 6.67 × 10−11Nm2/kg2 REarth = 6.37 × 106m MEarth = 5.98× 1024kg MSun = 1.99× 1030kg c = 2.998× 108m/s e = 1.602× 10−19 C k = 1/4π0 = 8.988× 109 Nm2/C2 0 = 8.854× 10−12 C2/Nm2 me = 9.109× 10−31 kg