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304_Physics ProblemsTechnical Physics

# 304_Physics ProblemsTechnical Physics - 306 Rotation of a...

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306 Rotation of a Rigid Object About a Fixed Axis Additional Problems P10.57 mg m A A 2 1 3 2 sin θ α = α θ θ = = F H G I K J 3 2 3 2 g a g r t A A sin sin Then 3 2 g r g A F H G I K J > sin θ for r > 2 3 A About 1 3 the length of the chimney will have a tangential acceleration greater than g sin θ . a t t g g sin t θ θ θ FIG. P10.57 P10.58 The resistive force on each ball is R D Av = ρ 2 . Here v r = ω , where r is the radius of each ball’s path. The resistive torque on each ball is τ = rR , so the total resistive torque on the three ball system is τ total = 3 rR . The power required to maintain a constant rotation rate is P = = τ ω ω total 3 rR . This required power may be written as P = = = τ ω ρ ω ω ω ρ total 3 3 2 3 3 r D A r r DA a f e j With ω π π = F H G I K J F H G I K J = 2 10 1 1 000 3 rad 1 rev rev 1 min min 60.0 s 30.0 rad s P = × F H G I K J 3 0 100 0 600 4 00 10 1 000 30 0 3 4 3 . . . . m m s 2 a f a f e j π ρ or P = 0 827 . m s 5 3 e j ρ , where ρ is the density of the resisting medium. (a) In air,
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