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# Equations - 2 2 sin 2 i i v h g = f i average x x x v t t...

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) ( 2 v ) ( 2 / 1 , 2 1 2 2 xf 2 i f x xi xf xi i f x xi i f x x a v t v v x x t a t v x x + = + + = + + = = a m F arrowrightnosp arrowrightnosp Useful equations: t a v v x xi xf + = x = r cos θ , y = r sin θ ƒ s ≤ µ s n, ƒ k = µ k n R = - b v R = ½ DρAv 2 A . B = A B cos θ F s = - kx W = F Δ r cos θ, K = ½ mv 2 U g = mgy U s = ½ kx 2 Σ W = K f K i Δ E mech = Δ K + Δ U = -ƒ k d + Σ W other forces F = Δ p / Δ t p 1i + p 2i = p 1f + p 2f Parallel axis theorem: I = I CM + Md 2 For a rigid body: L=Iω, τ = Iα, rotational K.E. = (1/2)Iω 2 Moment of inertia Moment of inertia around of center of mass of (i) a solid disk = (ii) a rod = (iii) a ring = MR 2 Center of Mass: ω r v = α r a = tan r r v a rad 2 2 ω = = 2 2 tan rad a a a + = 0 lim x t x dx v t dt Δ → Δ = = Δ 2 2 0 lim x x x t v dv d x a t dt dt Δ → Δ = = = Δ 2 sin2 i i v R g θ = 2 2 sin 2 i i v h g θ = f i average x x x v t t Δ = = Δ Δ xf xi x x v v v a t t Δ = = Δ Δ 2 2 tan y
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Unformatted text preview: 2 2 sin 2 i i v h g = f i average x x x v t t − Δ = = Δ Δ xf xi x x v v v a t t − Δ = = Δ Δ 2 2 tan y x r x y = = + j y i x r ⌢ ⌢ a + = t d a dt = v 2 r C v a a r = − = − 2 2 r t a a a = + 2 c v F ma m r = = ∑ ∑ = = % i i i r m 1 2 I 2 2 1 MR 2 12 1 ML F x r P x r L a a a a a a = = τ i i i i i CM m x m x ∑ ∑ = ext tot L dt d a a = f f i i I I = v m p a a = f i x x x W F dx = ∫ r F W a a Δ = ....
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