(a) Assume the station is initially not rotating, and assume that the entire mas

Question

(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?

(b) How much work is done to get the space station spinning?

(c) How long must the rockets be fired if there are 6 rockets, and each exerts a thrust of 200 N?

(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?

Explanation / Answer

Accoring to the given problem,

(a) 1 "g" = 9.8 m/s² = ²r = ²(145m) = 0.26 rad/s
L = I = mr² = (5.90*104 + 300*75)kg * (145m)² * 0.26rad/s = 4.455*108 kg·m²/s

(b) KE = ½I² = ½(mr²)² = ½(5.90*104 + 300*75)(145m)²(0.26rad/s)² = 57.9 MJ
The work that must be done to achieve this KE, assuming no losses, is 57.9 MJ

(c) torque = F*r = 6 * 200N * 145m = 174000 N·m
But also = I, so 174000 N·m = mr² = (5.90*104 + 300*75)kg * (145m)² *
= 1.015*10-4 rad/s²
Finally, t = / = 0.26rad/s / 1.015*10-4 rad/s² = 2560.46 s

(d) conservation of momentum: (I)i = (I)f
(5.90*104 + 300*75)kg * 0.26rad/s = 5.90*104kg * f
f = 0.36 rad/s
centripetal a = (f)²*r = (0.36rad/s)² * 145m = 18.7 m/s²

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