What is the angular velocity and kinetic energy of a cockroach-disk system?

[cd80187]

A cockroach of mass m lies on the rim of a uniform disk of mass 4.29m that can rotate freely about its center like a merry-go-round. Initially the cockroach and disk rotate together with an angular velocity of 0.271 rad/s. 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?




I am not even sure how to begin this problem. I thought you could set up a ratio using v= r times omega. But that didn't work out, so I'm not sure where to even begin, even though the book says it relates to angular momentum.

 

[arildno]

Consider conservation of angular momentum.

 

[cd80187]

I figured it had something to do with that, but how am I supposed to figure out the rotational inertia, and for it, do i find the rotational inertic from the cockraoch using the parallel axis theorem and then add it to the rotational inertia of the disk, and then do it once again for the new placement of the cockraoch?

 

[cd80187]

I'm still having trouble figuring this one out

 

[Doc Al]

I figured it had something to do with that, but how am I supposed to figure out the rotational inertia, and for it, do i find the rotational inertic from the cockraoch using the parallel axis theorem and then add it to the rotational inertia of the disk, and then do it once again for the new placement of the cockraoch?

That will work. You can treat the cockroach as a point mass.

 

[cd80187]

So should I treat it as a particle with it as its own axis, or should I still do the parallel axis theorem and count r as the distance between the cockraoch and the center?

 

[Doc Al]

Either way will give you the same answer. Try it and see.