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equation_sheet

# equation_sheet - VECTORS Ax = Acos Ay = Asin and Ay r =(A2...

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VECTORS: A x = Acos ( θ ), A y = Asin ( θ ), and r = ( A 2 x + A 2 y ) 1 / 2 , and tan ( θ ) = A y A x . KINEMATICS: x f = x i + v xi t + 1 2 a x t 2 , θ f = θ i + ω i t + 1 2 αt 2 v xf = v xi + a x t , ω f = ω i + αt v 2 xf = v 2 xi + 2 a x ( x f - x i ), ω 2 f = ω 2 i + 2 α ( θ f - θ i ) x f = x i + 1 2 ( v xi + v xf ) t , θ f = θ i + 1 2 ( ω i + ω f ) t ω = dt , α = dt , v = , s = , a t = NEWTON’S LAWS: F = m a , τ = F 12 = - F 21 , F = d p dt , τ = d L dt = r × F FRICTION: f k = μ k N f s μ s N WORK: W = F · d = Fdcos ( θ ) ENERGY: E i + W = E f U s = 1 2 kx 2 s U g = mgh = - Gm 1 m 2 R K = 1 2 mv 2 K = 1 2 2 MOMENTUM and IMPULSE: p = m v , L = = r × p , Δ p = I = F Δ t , INERTIA: I = mr 2 , I disk = 1 2 mR 2 I sphere = 2 5 mR 2 SIMPLE HARMONIC MOTION: d 2 x dt 2 = - cx , x = Acos ( ωt + φ ), f = 1 T = ω 2 π , ω = q k m = p g L v max = ωA , a max = ω 2 A WAVES: v = q T μ = λf , ω = 2 πf = 2 π T , k = 2 π λ , y = Acos ( kx - ωt + φ ) y = 2 Asin ( kx ) cos ( ωt ), Δ r = λ Δ φ 2 π , f n = n 2 L q T μ for string with both ends fixed
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• Winter '08
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