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General Physics(ppt) Ch 10 - Chapter 10 Rotation A rigid...

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Chapter 10 Rotation A rigid object is one that is nondeformable---that is, it is an object in which the separations between all pairs of particles remains constant. θ r s = Polar coordinates (r, θ ) r s = θ unit : radian (rad) (deg) 180 ) ( 0 θ π θ = rad Chapter 10 Rotation Angular displacement, Velocity and Acceleration Angular displacement i f θ θ θ - = Δ Average angular speed Δ - θ θ θ Instantaneous angular speed d θ θ Δ t t t i f i f Δ = - ω dt t t ω = Δ Δ 0 lim Average angular acceleration t t t i f i f Δ Δ = - - ω ω ω α Instantaneous angular acceleration dt d t t ω ω α = Δ Δ Δ 0 lim Right-hand rule for determining the direction of the angular velocity vector
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Chapter 10 Rotation Rotational kinematics : Rotational Motion with Constant Angular Acceleration Rotational Motion About a Fixed Axis Linear Motion t i f α ω ω + = at v v i f + = 2 2 1 t t i i f α ω θ θ + + = 2 2 1 at t v x x i i f + + = ) ( 2 2 2 i f i f θ θ α ω ω - + = ) ( 2 2 2 i f i f x x a v v - + = Chapter 10 Rotation Angular and Linear Quantities ω θ r dt d r dt ds v = = = θ r s = α ω r d r dv a = = = dt dt 2 2 ω r r v a r = = α r a t = 4 2 4 2 2 2 2 2 ω α ω α + = + = + = r r r a a a r t
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Chapter 10 Rotation Rotational Energy = = = i i i i i i i i
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