314_Physics ProblemsTechnical Physics

314_Physics ProblemsTechnical Physics - 316 P10.79 Rotation...

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316 Rotation of a Rigid Object About a Fixed Axis P10.79 (a) ∆∆ KK U rot trans ++ = 0 Note that initially the center of mass of the sphere is a distance hr + above the bottom of the loop; and as the mass reaches the top of the loop, this distance above the reference level is 2 Rr . The conservation of energy requirement gives mg h r mg R r mv I += + + a f a f 2 1 2 1 2 22 ω r m h R P FIG. P10.79 For the sphere Im r = 2 5 2 and vr = so that the expression becomes gh gr gR v + 7 10 2 (1) Note that hh = min when the speed of the sphere at the top of the loop satisfies the condition Fm g mv == 2 a f or vg R r 2 =− af Substituting this into Equation (1) gives hR r R r min + 20 7 0 0 . or r R min .. = 270 (b) When the sphere is initially at = 3 and finally at point P , the conservation of energy
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