Another rotational motion problem.

Sep 2008
7
0
An overhead view of a ring that can rotate about its center like a merry go round. Its outer radius R is 0.8 m, its inner radius r is 0.4 m, its mass is 8 kg, and the mass of the crossbars in the ring is negligible. It initially rotates at an angular speed of 8rad/s with a cat of mass 2 kg on its outer edge, at radius R. By how much does the cat increase kinetic energy of the cat-ring system if the cat crawls to the inner edge, at radius r? (The answer is 39.1J --- From textbook)

I don't know the solution.

I tried to find initial and final moment of inertia (I)

I-initial = (0.5)(8)((0.8^2)+(0.4^2)) + 2(0.8^2) = 4.48 kgm^2

I-final = (0.5)(8)((0.8^2)+(0.4^2)) + 2(0.4^2) = 3.52 kgm^2

Then I don't know how to do it.

Please help.
Thank you.
 

topsquark

Forum Staff
Apr 2008
3,106
659
On the dance floor, baby!
An overhead view of a ring that can rotate about its center like a merry go round. Its outer radius R is 0.8 m, its inner radius r is 0.4 m, its mass is 8 kg, and the mass of the crossbars in the ring is negligible. It initially rotates at an angular speed of 8rad/s with a cat of mass 2 kg on its outer edge, at radius R. By how much does the cat increase kinetic energy of the cat-ring system if the cat crawls to the inner edge, at radius r? (The answer is 39.1J --- From textbook)

I don't know the solution.

I tried to find initial and final moment of inertia (I)

I-initial = (0.5)(8)((0.8^2)+(0.4^2)) + 2(0.8^2) = 4.48 kgm^2

I-final = (0.5)(8)((0.8^2)+(0.4^2)) + 2(0.4^2) = 3.52 kgm^2

Then I don't know how to do it.

Please help.
Thank you.
Rotational kinetic energy is
\(\displaystyle K = \frac{1}{2}I \omega ^2\)

-Dan