302_Physics ProblemsTechnical Physics

302_Physics ProblemsTechnical Physics - 304 Rotation of a...

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304 Rotation of a Rigid Object About a Fixed Axis Section 10.9 Rolling Motion of a Rigid Object P10.51 (a) Km v trans kg m s J == = 1 2 1 2 10 0 10 0 500 2 2 .. bg b g (b) KI m r v r rot kg m s J F H G I K J F H G I K J 1 2 1 2 1 2 1 4 10 0 10 0 250 22 2 2 2 ω b g (c) KKK total trans rot J =+ = 750 P10.52 WK K K K K K fi =− = + + trans rot trans rot W Mv I Mv MR v R F H G I K J F H G I K J 1 2 1 2 00 1 2 1 2 2 5 2 2 2 or WM v = F H G I K J 7 10 2 P10.53 (a) τα = I mgR I mR a mgR Im R a mgR mR g a mgR mR g CM sin sin sin sin sin sin θα θ = + 2 2 2 2 2 2 3 2 2 2 1 2 2 3 ej CM hoop disk The disk moves with 4 3 the acceleration of the hoop. (b) Rf I = α fnm g f mg mg gm R Rm g I R === = µµ µ θθ cos cos cos sin cos tan 2 3 1 2 2 2 1 3 ch R m g f n FIG. P10.53 P10.54 v I m I R v =+= + L N M O Q P 1 2 1 2 1 2 2 2 where = v R since no slipping. Also, Um g h i = , U f
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