Designing a Space Station: Calculate Rotational Motion

[PascalPanther]

"While listening to your professor drone on, you dream about becoming an engineer helping to design a new space station to be built in deep space far from any planetary systems. This state-of-the-(future) art station is powered by a small amount of neutron star matter which has a density of 2 x 10^14 g/cm^3. The station will be a large light-weight wheel rotating about its center which contains the power generator. A control room is a tube which goes all the way around the wheel and is 10 meters from its center. The living space and laboratories are located at the outside rim of the wheel and are another tube which goes all the way around it at a distance of 200 meters from the center. To keep the environment as normal as possible, people in the outer rim should experience the same “weight” as they had on Earth. That is if they were standing on a bathroom scale, it would read the same as if they were on Earth. This is accomplished by a combination of the rotation of the station and the gravitational attraction of the neutron star matter in the power generator. Calculate the necessary rate of rotation to accomplish this task.

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?

 

[Doc Al]

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?)

 

[PascalPanther]

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?

 

[Doc Al]

I strongly suspect that essential information is missing from the problem statement. Why were you told:

"A control room is a tube which goes all the way around the wheel and is 10 meters from its center."​

since that control room is never mentioned again?