Fg = Gm1 m2 /r2 , G = 6.67 × 10−11 Nm2 /kg2 2 U = −Gm1 m2 /r, g = GmE /RE √ T = 2πa3/2 / Gm ω = k/m = 2πf = 2π/T x = A cos(ωt + φ) 2 A = x2 + v0 /ω 2 ), φ = arctan(−v0 /(x0 ω)) 0 ω = g/L = mgd/I x = Ae−(b/2m)t cos ω t, ω = k/m − b2 /4m2 2 2 A = Fmax / (k − mωd )2 + b2 ωd y(x, t) = A cos[ω(x/v − t)] = A cos(kx − ωt) λ = 2π/k, v√ ω/k = λf = F/µ = 2 2 Pav = (1/2) µF ω 2 A2 , I1 /I2 = r2 /r1 y(x, t) = ASW sin kx sin ωt fn = nv/(2L) p = mv J = Fdt = ∆p F = dp/dt Fext = dP/dt = M aCM p1i + p2i = p1f + p2f rCM = ( mi ri )/( mi ) ω = dθ/dt, α = dω/dt = d2 θ/dt2 = rθ, v = rω, atan = rα, arad = ω 2 r θ = θ0 + ω0 t + 1 αt2 2 ω = ω0 + αt 2 ω 2 = ω0 + 2α∆θ 1 ∆θ = 2 (ω + ω0 )t 2 I = mi ri IP = Icm + M d2 K = 1 Iω 2 2 Moments of inertia: Slender rod, about center Slender rod, about end Rectangular plate, about center Rectangular plate, about edge Hollow cylinder Solid cylinder Thin-walled hollow cylinder Solid sphere Thin-walled hollow sphere τ =F , τ =r×F τ = Iα 2 K = 1 M vcm + 1 Icm ω 2 2 2 W = τ dθ, P = τ ω L = r × p = r × mv L = Iω τ = dL/dt Fx = 0, Fy = 0, τ =0
1 2 12 M L 1 2 3ML 2 2

1 12 M (a + b ) 1 2 3Ma 1 2 2 2 M (R1 + R2 ) 1 2 2MR 2

MR

2 2 5MR 2 2 3MR

|A × B| = AB sin φ = AB⊥ = A⊥ B

ˆ i j A × B = (Ay Bz − Az By )ˆ + (Az Bx − Ax Bz )ˆ + (Ax By − Ay Bx )k F = ma FB on A = −FA on B w = mg fs ≤ µs n, fk = µk n K = 1 mv 2 2 W = F · s = F s cos φ x P W = x12 Fx dx = P12 F · d Wtot = K2 − K1 = ∆K P = dW/dt W = −∆U U = mgh, U = 1 kx2 2 K2 + U2 = K1 + U1 + Wother Fx (x) = −dU (x)/dx ˆ i j F = − ∂U ˆ + ∂U ˆ + ∂U k
∂x ∂y ∂z

vx = dx/dt, vav−x = (x2 − x1 )/(t2 − t1 ) ax = dvx /dt, aav−x = (v2x − v1x )/(t2 − t1 ) t x(t) = x0 + 0 vx (t) dt t vx (t) = v0x + 0 ax (t) dt v = dr/dt a = dv/dt x = x0 + v0x t + 1 ax t2 2 vx (t) = v0x + ax t 2 vx (t)2 = v0x + 2ax ∆x v0x +vx (t) ∆x = t 2 r = r0 + v0 t + 1 at2 2 v = v0 + at ˆ A = Axˆ + Ayˆ + Az k i j Ax = A cos θ, Ay = A sin θ A= A2 + A2 , x y tan θ = Ay /Ax A · B = AB cos θ = Ax Bx + Ay By + Az Bz arad = v 2 /R = 4π 2 R/T 2 vP/A = vP/B + vB/A g = 9.80 m/s2 , 1 hr = 3600 s, 1 km/hr = 0.278 m/s
√ b If at2 + bt + c = 0, then t = −b± 2a −4ac . n n−1 If x = at , then dx/dt = nat . t a If x = atn , then t12 x(t) dt = n+1 tn+1 − tn+1 . 2 1
2