(a) What then is the angular velocity of the cockroach A cockroach of mass m lie

Question

(a) What then is the angular velocity of the cockroach

A cockroach of mass m lies on the rim of a uniform disk of mass of 3m that can rotate freely about its center like a merry-go-round. Initially the cockroach and disk rotate together with an angular velocity of omega = (b) What is the ratio K/K0 of the new kinetic energy of the system to its initial kinetic energy? K K0 = omega0. Then the cockroach walks halfway to the center of the disk. (Use any variable or symbol stated above as necessary.) (a) What then is the angular velocity of the cockroach disk system?

Explanation / Answer

The system will obey conservation of momentum

Ii*wi=Io*wo

Ii=.5*3*m*R^2+m*R^2
=m*R^2*4
and wi=0.261

Io=.5*3*m*R^2+m*R^2/4
=m*R^2*3.25

so
wo=4*0.261/3.25
0.321 rad/s

Kinetic energy is
.5*I*w^2

I will solve for Ko/Ki
(3.25*0.321^2)/(4*0.261^2)
=1.22
The increase in energy came from the work done by the cockroach to move inward.

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