Eqn Sheet

Eqn Sheet - ME 270 EQUATIONS (You probably will not need...

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ME 270 EQUATIONS (You probably will not need all of these equations) u = r r , r = r T 2 T 1 = e μ s β A B = AB cos θ v = v o + a c t = A x B x + A y B y + A z B z s = s o + v o t + 1 2 a c t 2 A = A u v 2 = v o 2 + 2 a c ( s s o ) M o = r × F , M o = Fd Σ F = m a Σ F = 0 Σ M / P = 0 M o = i r x F x j r y F y k r z F z v = xi + y j + zk M a = u a M o v = ru r + r u + z k M a = u a ( r × F ) v = vu t M a = u ax r x F x u ay r y F y u az r z F z a =  + y j + M a = M a u a a = v u t + v 2 ρ u n m = W g , g = 32.17 ft / s 2 = 9.807 m / s 2 a = ( r r θ 2 ) u r + ( r θ + 2 r θ ) u θ + z k ρ = 1 + dy dx 2 d 2 y dx 2 Σ F x = m x , Σ F y = m y , Σ F z = m z v = ds dt , a = dv dt = v dv ds Σ F r = m ( r r θ 2 ) , Σ F θ = m ( r θ + 2 r θ ) , Σ F z = m z Σ F t = m v , Σ F n = m v 2 ρ , Σ F b = 0
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n B / A = r B / A r B / A F = Fn F f static μ S N f slide = K N x = x dm dm y = y dm dm z = z dm dm x = m i x i m i y = m i y i m i z = m i z i m i P = ρ gh w = ghd If β = βα ( ) , then: d dt = d d α d dt (chain rule of differentiation) v = ˙ x i + ˙ y j = ˙ r e r + r ˙ θ e = v e t a = ˙ ˙ x i + ˙ ˙ y j = ˙ ˙ r r ˙ 2 ( ) e r + r ˙ ˙ + r ˙ ( ) e = ˙ v e t + v 2 e n Trigonometric Identities
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Eqn Sheet - ME 270 EQUATIONS (You probably will not need...

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