How Long Should Rockets Fire to Rotate a Space Station?

[ft92]

Homework Statement

A space station of mass 6.0 × 104-kg is to be constructed in the shape of a thin annular cylinder (or ring). The inner radius of the annular cylinder is 100-m, and the outer radius (and location of the floor) is 105-m. Artificial gravity equivalent to free-fall acceleration, g, will be implemented by rotating the hoop through its central axis. Once the space station is constructed, two small rockets attached tangentially to opposite points on the hoop will be fired to set the space station into rotation. If each of the rockets produces a thrust of 102-N, for what time interval, in minutes, must they be fired to achieve the desired rotation? Assume the mass of the space station will be distributed uniformly within the annular ring.

I'm asked to find t in minutes.

Homework Equations

The Attempt at a Solution

 

[TSny]

The floor is at the outer radius. So it seems to me that you need to set the acceleration equal to g at the outer radius rather than the inner radius. This would not make a big difference.

Did you account for the fact that there are two rockets?

Otherwise, your work looks good to me.

 

[gneill]

Can you explain your calculation of the moment of inertia of the space station in more detail? In particular, why do you add the squares of the two radii?

 

[Shadrach Hepner]

The inertia calculation assumes that there is equal mass on both the inner and the outer tube. Thus, the total inertia is (1/2)MR_1^2 + (1/2)MR_2^2, which he factored. That assumption should be valid, since the difference in mass wouldn't be much. ft92, what is the actual issue here? How far off are you from the correct answer?

 

[BvU]

Torus moment of inertia is a bit more subtle (there is more mass at the outside), but it doesn't make a big difference. Do the rockets deliver 102 N or 10² N of thrust ?