Cockroach of mass m lies on the rim of a uniform disk of mass 4m that can rotate freely about its center like a merry-go-round. initially the cockroach and disk rotate together with an angular velocity of?0. then the cockroach walks halfway to the center of the disk. (a what then is the angular velocity of the cockroach-disk system? (b what is the ratio k/k0 of the new kinetic energy of the system to its initial kinetic energy? state your answer in terms of the given variables.

Question

Physics

Amirah Pham

6 February, 22:58

Cockroach of mass m lies on the rim of a uniform disk of mass 4m that can rotate freely about its center like a merry-go-round. initially the cockroach and disk rotate together with an angular velocity of?0. then the cockroach walks halfway to the center of the disk. (a what then is the angular velocity of the cockroach-disk system? (b what is the ratio k/k0 of the new kinetic energy of the system to its initial kinetic energy? state your answer in terms of the given variables.

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Morgan Valenzuela · Answer 1

The angular velocity of the cockroach does not change as long as it rotates with the disk it has the same angular velocity as the disk but by changing the distance from the center of the disk the linear velocity changes (V=r*ω) because the radius changes.

in order to find the kinetic energy you can use this formula k=1/2 * m * V²

so k/k0 = (V/V0) ² = (r/r0) ²

where the subscripts 0 denotes to the initial position of the cockroach so r0=2*r then we have k/k0=1/4