This question really has me stumped. Am I right to just ignore the fact that there is an inner control room ring?

This is what I think I will need:
We haven't gotten to inertia yet, but I think this is an inertia problem.
I = MR^2 (if I take out the inner ring and say it is a thin-walled hollow cylinder).
K = (1/2)*I*(omega)^2

I am not sure what I am suppose to do with the density of the core without a volume or mass. I am also not quite sure where I would bring in value of earth's gravity to solve with. Am I missing something to be able to start this?

It does seem that they forgot to tell you how much neutron star matter is at the center. Assuming you can get that info, figure out the net force on a mass that is moving with the outer ring. (Hint: What kind of acceleration does that mass undergo?)

Well, it looks like there is an alternative version of this problem with everything the same except it asks you to find out the rate of rotation and the mass of the generator. So there must be a way somehow to find the mass. Or this problem is just really weird.

But it would be centripetal acceleration right? a_rad = v^2/r = (omega)^2 *r
So omega would be my rate of rotation... if there was no mass at the center? Wouldn't a mass that is on the outside ring just equal it's weight?