You’re an astronaut in the first crew of a new space station. The station is sha

Question

You’re an astronaut in the first crew of a new space station. The station is shaped like a wheel 18 m in diameter, with essentially all its 9*10^5-kg mass at the rim. When the crew arrives, it will be set rotating at a rate that requires an object at the rim to have radial acceleration g, thereby simulating Earth’s surface gravity. This will be accomplished using two small rockets, each with 140-N thrust, mounted on the station’s rim. Your job is to determine how long to fire the rockets and the number of revolutions the station will make during the firing.

Explanation / Answer

centripetal acc. a = w^2 r

9.81 = w^2 (9)

w = 1.044 rad/s

Torque = I alpha

2 ( 140 x 9) = (9x 10^5 x 9^2) alpha

alpha = 3.456 x 10^-5 rad/s^2

w = w0 + alpha t

1.044 = 0 + (3.456 x 10^-5) t

t = 3.02 x 10^4 sec ........Ans

theta = w0t + alpha t^2 / 2 =15765 rad Or 2509 rev

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