Question

Humans typically can withstand accelerations up to 40.0g. Suppose alien creatures install a rocket possessing 327470 N of thrust to the outside of the rotating space station, as shown. How long would it take (in days) for the artificial gravity to exceed 40.0g? Assume that the artificial gravity was g before the rocket was installed, and that the inside and outside diameters of the space station are 1.25 km and 1.26 km (respectively), its height is 55.0 m, and that the station is largely aluminum alloy of density 2.72 g/cm3.

Answer 1

initial angular velocity

9.8 = wi^2 * 625

wi = 0.125 rad/s

final angular velocity

40 * 9.8 = wf^2 * 625

wf = 0.792 rad/s

mass of space station

m = density * vol = 2.72* 10^3* 3.14* 55* ( 630^2 - 625^2)

m =2.947* 10^9 kv

moment of inertia

I = 0.5 m r1^2 + 0.5 m r2^2

I = 1.16* 10^15 kgm^2

now as we know from torque

T = I ( wf - wi) / t

537610 * 630* t = 1.16* 10^15* (0.792 - 0.125)

t = 2.285* 10^6 s

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