Unformatted text preview: 10.76: (a) mgh = 1 2 1 2 mv + I (1) 2 2 1 I = I rim + I spokes = M r R 2 + 6 m s R 2 3 Uniform density means: m r = 2R and m s = R. No slipping means that = v R. Also, m = mr + ms = 2R + 6 R = 2 R( + 3) substituting into (1) gives 2 R( + 3) gh = = 1 ( 2 R ) ( + 3)( R) 2 + 1 2RR 2 + 6 1 RR 2 2 2 2 3 ( + 3) gh R 2 ( + 2) = ( + 3) (9.80 m s 2 )( 58.0 m ) ( 0.210 m ) 2 ( + 2) = 124 rad s and v = R = 26.0 m s (b) Doubling the density would have no effect because it does not appear in the answer. 1 R , so doubling the diameter would double the radius which would reduce by half, but v = R would be unchanged. ...
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