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 θα = αθ θ = = F H G I K J 3 2 3 2 g a g r t A A sin sin Then 3 2 g rg A F H G I K J > sin for r > 2 3 A About 1 3 the length of the chimney will have a tangential acceleration greater than g sin . a t t g sin t FIG. P10.57 P10.58 The resistive force on each ball is RDA v = ρ 2 . Here vr = 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 total = 3 rR . The power required to maintain a constant rotation rate is P == τω total 3 rR . This required power may be written as = ρω total 33 2 rD Ar rDA af ej With π = F H G I K J F H G I K J = 21 0 1 1000 3 rad 1 rev rev 1 min min 60.0 s 30.0 rad s F H G I K J 3 0 100 0 600 4 00 10 30 0 3 4 3 .. . . m m s 2 a f or = 0827 . m s 53 , where is the density of the resisting medium. (a) In air, = 120 k gm 3 , and = 0992 .
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