lec08-203-08rot-kin-mod1

lec08-203-08rot-kin-mod1 - in general rotation translation...

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8-0 CM moves at constant v along dotted line. Rotation about CM at constant angular speed ω . in general rotation + translation every where consider first just rotation about an axis
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8-1 sign convention 1 t r t θ ω Δ Δ = = Δ Δ ω ω π α π = = = Δ 2 - 44 -0 14.7 3 f i rad t s Rotational Kinematics ω =angular velocity (rad./sec) ω ω α = Δ - f i t ave. angular acceleration (rad/s 2 ) ω α = d dt instantaneous angular acceleration (rad/s 2 ) ω α Δ Δ = = Δ = = Δ Δ Δ 1 1 ( ) v v a t r t r t r α = a r α a= r
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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 8-2 [m] [m/s] [m/s 2 ] direction
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Direction matters – Right Hand Rule 8-3
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Fan demo/example fan at full speed (stroboscope observation) rev 1340 rev min 1340 = min 60 min sec rev f=22 sec frequency 1 f= T ω π π = = = 2 44 (0.1) 4.4 v s r m m s r=0.1 m 1 2 2 (22) 44 sec rad f s ω π π π = = = angular velocity linear velocity (at radius r) 8-4
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Initially fan at rest i ω =0 observe fan reaches final speed in ~ 3 sec.
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