A space station is constructed in the shape of a hollow ring of mass 5.70 104 kg

Question

A space station is constructed in the shape of a hollow ring of mass 5.70 104 kg and radius 110 m. The station has 100 crew members (each with average mass 70 kg), who can walk on a deck formed by the inner surface of the outer cylindrical wall of the ring. Artificial gravity is produced when the ring rotates (that is, the crew members experience a normal force from the floor pushing them inward).
(a) Assume the station is initially not rotating, and assume that the entire mass of the space station is concentrated in the outer ring. Also assume that the crew is initially on the outer rim. Rockets on the outside of the outer rim are fired tangentially to get the station spinning up to a speed such that the crew experiences a centripetal acceleration equal to g. What is the total angular momentum of the space station (plus crew) when it is up to maximum speed?
231143689 kg*m^2/s
(b) How much work is done to get the space station spinning?
34495768 J
(c) How long must the rockets be fired if there are 6 rockets, and each exerts a thrust of 125 N?
2801.73 s
(d) The rockets are no longer thrusting. The entire crew moves to the very center of the space station. What acceleration does an ant experience on the outer rim?
Incorrect: .02344 m/s^2
Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully.

Just need help with part d

Explanation / Answer

Centripetal acceleration is 2r, and since L = I is conserved, we know the ratio by which I decreases is the reciprocal of the ratio by which increases.

I from the station is 6.897 * 108 kg m2 and from the crew is 8.47 * 107 kg m2, so dividing (crew + station)/station I get 1.1228.

That's the amount increases, but we really care about 2, which increases by 1.2607.

Since the rim of the station did have centripetal acceleration of g, now it has 1.2607g which is 12.37 m/s2.

One possible hook to the problem is that if the ant is on the outer rim, the acceleration is -12.37 m/s2. Not sure if the question writer means for the minus sign to be there or not.

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