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exam_2_eqsheet_Fall06

# exam_2_eqsheet_Fall06 - Some Equations for Exam 2 For this...

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Some Equations for Exam 2 For this exam, use the approximation that g =10m / s 2 . For a function f ( x )= ax n , where n is an integer, df dx = nax n - 1 . Work by ± F moving from i to f : W = ± f i ± F · d±s Power: P = dW dt Kinetic energy: K = 1 2 mv 2 ; for rotating bodies, K = 1 2 2 . Potential energy: Δ U = - ± f i ± F · for a conservative force; and F x = - ∂U ∂x , etc. Gravitational potential energy near the Earth’s surface: U = mgh . For an ideal spring, force: F = - kx ; potential energy: U = 1 2 2 . For a system, W ext E mec K U . For an isolated system, W ext = 0, so E mec is constant and Δ K U =0 . Momentum: ±p = m±v ; Newton’s 2 nd Law: ± F = d±p dt . For a system with Σ ± F ext , tot = const . Position of the center of mass: ±r cm = 1 M Σ m i i , where M m i . Angular velocity: ω = dt . Angular acceleration: α = dt . For a constant angular acceleration, ω = ω 0 + αt and φ = φ 0 + ω 0 t + 1 2 αt 2 . For circular motion, the tangential component of acceleration is a t = αr ; the radial (centripetal) component is a r = v 2 /r = ω 2 r . Rotational inertia, or moment of inertia: I = ± r 2 dm . for a solid sphere about any diameter:
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