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 23 m in diameter, with essentially all its 9.0×105 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 100 N thrust, mounted on the station’s rim.

Part A

Determine how long to fire the rockets.

t=[ ] s

Part B

Determine the number of revolutions the station will make during the firing.

=[ ] rev

Explanation / Answer

Moment of inertia, I = mr² = 9*10^5kg x (23m)²

I = 4.76*10^7 kg.m²

Angular acceleration, d/dt = Torque / I

(equivalent to a = F/m)
d/dt = 2 [100 x 23m] / (4.67*10^7 kg.m²)

d/dt = 9.8*10^-5 rad/s²

Centripetal accel, 9.80m/s² = r ²
Final angular vel required, = (9.80 / 23m) = 0.652 rad/s

= d/dt x t
t = / (d/dt) .. .. 0.652/ 9.85*10^-5

t = 6619.28s =6.61*10^4 =110.19hr

Distance, rad = ½.(d/dt).t²

(equivalent to d = ut + ½ at².. .. u = o)
= ½ x (9.8*10^-5) x (6.61*10^4)² = 2.14*10^4 rad
Revs = / 2

= 2.14*10^4 / 2

=3.4*10^3 rev

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