Designing a Space Station: Calculate Rotational Motion

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Homework Help Overview

The discussion revolves around a problem related to the design of a space station, specifically focusing on calculating the necessary rotational motion to simulate Earth-like gravity for occupants in the outer rim of the station. The context includes the use of neutron star matter as a power source and the configuration of the station's structure.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the implications of the station's design, questioning the relevance of the inner control room and its distance from the center. There are discussions about inertia, centripetal acceleration, and the need for mass information to solve the problem. Some participants express uncertainty about how to incorporate the density of the neutron star matter and Earth's gravity into their calculations.

Discussion Status

The discussion is ongoing, with participants raising various questions about missing information and the relationships between the components of the problem. Some guidance has been offered regarding the need to consider net forces and accelerations, but no consensus has been reached on how to proceed with the calculations.

Contextual Notes

Participants note that essential information, such as the mass of the neutron star matter, is not provided, which complicates the problem. There is also uncertainty about the relevance of the control room's specifications.

PascalPanther
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"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?
 
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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. :bugeye:

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?
 
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?
 

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