Thread: how long are the rockets fired? How many revolutions does the station make during the firing?

You?re an astronaut in the first crew of a new space station. The station is shaped like a wheel 21 m in diameter, with essentially all its 5.5×10^5 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 130 N thrust, mounted on the station?s rim.

Moment of inertia, I = mr² = 5.50^5kg x (10.5m)² .. .. I = 6.06^7 kg.m²

Angular acceleration, d?/dt = Torque / I .. .. (equivalent to a = F/m)
d?/dt = 2 [130N x 10.50m] / (6.06^7 kg.m²) .. .. d?/dt = 4.5^-5 rad/s²

Centripetal accel, 9.80m/s² = r ?² ..
Final angular vel required, ? = ?(9.80 / 10.5m) = 0.966 rad/s

? = d?/dt x t
t = ? / (d?/dt) .. .. 0.966 / 4.5^-5 .. .. .. ?t = 2.15^4 s .. (5.96 hr)

Distance, ? rad = ½.(d?/dt).t² .. .. (equivalent to d = ut + ½ at².. .. u = o)
? = ½ x (4.5^-5) x (2.15^4)² = 1.04^4 rad
Revs = ? / 2? .. .. .. 1.04^4 / 2? .. .. .. ?1.66^3 rev