Shows an overhead view of a ring that can rotate about its center like a merry-g

Question

Shows an overhead view of a ring that can rotate about its center like a merry-go-round. Its outer radius R2 is 0-9 m, its inner radius R1 is R2/2, its mass M is 7.1 kg, and the mass of the crossbars at its center is negligible. It initially rotates at an angular speed of 6.3 rad/s with a cat of mass m = M/4 on its outer edge, at radius R2. By how much does the cat increase the kinetic energy of the cat-ring system if the cat crawls to the inner edge, at radius R1? The number of significant digits is set to 2; the tolerance is +/-2%

Explanation / Answer

I1 1 = I2 2

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I1 = 0.5 * 7.1* (0.9*0.9 + 0.45*0.45) + 1.775 * 0.9*0.9 = 5.032125
I2 = 0.5 * 7.1* (0.9*0.9 + 0.45*0.45) + 1.775 * 0.45*0.45 = 3.9538125

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I1 1 = I2 2

5.032125 * 6.3 = 3.9538125 * 2

2 = 8.018182 rad/sec

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K = 0.5 I2 2^2 - 0.5 I1 1^2

     = 0.5*3.9538125*8.018182*8.018182 - 0.5*5.032125*6.3*6.3

     = 27.2 J

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