Rotational Kinetic Energy Question

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SUMMARY

The discussion centers on calculating the change in kinetic energy of a rotating ring system when a cat moves from the outer radius (R2 = 0.7 m) to the inner radius (R1 = R2/2). The ring has a mass (M) of 7.3 kg and initially rotates at an angular speed of 6.0 rad/s. Participants clarified that the kinetic energy (KE) increases when the cat, with a mass (m) of 1.825 kg (M/4), moves inward, resulting in a positive change in KE despite initial calculations yielding a negative value. This indicates that the final kinetic energy is indeed greater than the initial kinetic energy.

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Homework Statement


The picture shows an overhead view of a ring that can rotate about its center like a merry-go-round. Its outer radius R2 is 0.7 m, its inner radius R1 is R2/2, its mass M is 7.3 kg, and the mass of the crossbars at its center is negligible. It initially rotates at an angular speed of 6.0 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?

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The Attempt at a Solution



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I'm not sure I did this right. Is it possible for the answer to be negative.
THanks is advance.
 
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You've calculated the initial KE minus the final KE, and it turned out negative. So the final KE must be greater than the initial KE. That's fine! The KE increased by the magnitude of your calculated value.
 
gneill said:
You've calculated the initial KE minus the final KE, and it turned out negative. So the final KE must be greater than the initial KE. That's fine! The KE increased by the magnitude of your calculated value.

Thanks for the help. I was confused at first of why I got a negative number but you made it clear. Thanks once again.
 

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