ch11-p071 - 71. We denote the cat with subscript 1 and the...

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71. We denote the cat with subscript 1 and the ring with subscript 2. The cat has a mass m 1 = M/ 4, while the mass of the ring is m 2 = M = 8.00 kg. The moment of inertia of the ring is 22 12 () / 2 Im RR =+ (Table 10-2), and I 1 = m 1 r 2 for the cat, where r is the perpendicular distance from the axis of rotation. Initially the angular momentum of the system consisting of the cat (at r = R 2 ) and the ring is 2 2 2 21 111 2 2 1 0 2 2 1 2 0 1 2 0 2 11 1 1 . ii i i mR Lm v rI mRR m R ωω ω ªº §· = + + = + + «» ¨¸ ©¹ ¬¼ After the cat has crawled to the inner edge at 1 rR = the final angular momentum of the system is 2 2 1 1 2 1 1. ff f f R m R R m R + = + + Then from L f = L i we obtain 2 2 2 2 2 2 01 2 1 2 1 2(0.25 1) (2.0) 1.273 ( 14 ) 1 2 f R R ++ == = . Thus, 0 1.273 f = . Using 0 =8.00 rad/s, we have f =10.2 rad/s. By substituting I = L / into 2 /2 KI = , we obtain KL = . Since L i = L f , the kinetic energy ratio becomes 0 1.273. f f i = which implies 0.273 f KK K K Δ= − = . The cat does positive work while walking toward
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This note was uploaded on 05/17/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.

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