Halliday, Resnick & Walker — Rolling, Torque, and Angular Momentum: Problem 54

Figure 11-45 shows an overhead view of a ring that can rotate about its center like a merry-go-round. Its outer radius \( R_2 \) is \( 0.800 \text{ m} \), its inner radius \( R_1 \) is \( R_2/2.00 \), its mass \( M \) is \( 6.00 \text{ kg} \), and the mass of the crossbars at its center is negligible. It initially rotates at an angular speed of \( 8.00 \text{ rad/s} \) with a cat of mass \( m = M/4.00 \) on its outer edge, at radius \( R_2 \). 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 \( R_1 \)?