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lec08-203-011rot-kin-post

lec08-203-011rot-kin-post - Rotational motion[radians...

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Δθ ω= Δt θ Δω α= Δt o t ω ω α = + 2 1 2 o o t t θ θ ω α = + + 2 2 2 ( - ) o o ω ω α θ θ = 0 [ ] t Lim t θ ω Δ → Δ = Δ 0 [ ] t Lim t ω α Δ → Δ = Δ 0 [ ] t v a Lim t Δ → Δ = Δ 0 [ ] t x v Lim t Δ → Δ = Δ 2 2 2 ( - ) o o v v a x x = 2 1 2 o o x x v t at = + + o v=v +at Δv a= Δt x Δx v= Δt 1 [ ] sec sec rev Hz = = 1 f T = 2 f ω π = Rotational motion Translational Motion + ccw - cw [radians] rad 1 [ = ] sec s 2 rad s const. acceleration instantaneous quantities 8-0 [m] [m/s] [m/s 2 ] direction
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8-1 CM moves at constant v along dotted line. Rotation about CM at constant angular speed ω . in general rotation + translation every where consider just rotation about an axis CM moves with parabolic trajectory. Rotation about CM at constant angular speed ω .
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Axis of rotation r object Rotational Kinematics 8-2a ω
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l Δ t Δ l r θ Δ Δ = θ Δ radians l 1 t r t θ ω Δ Δ = = Δ Δ 1 v r ω = v r ω = C. Clockwise (+) Clockwise (-) l 1 d d v dt r dt r θ ω = = = 0 t Δ → r rotates object In time ave. angular vel. (rad./s) ω = instant. angular vel. ω = l d v dt = v 8-2b ω
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ω ω
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