Rotation question angular velocity, and angular displacement?

Question

The empire's space station is a long way from any star. It is circular and has a radius of 5 km. Calculate the angular velocity that is needed to give the station an artificial gravity of 9.80 m/s^2 at its circumference. If the space station is initially stationary and it is accelerated at rate of 8x10^-5 rad/s^2 , then how long does it take for the space station to reach this angular velocity? What angular displacement does it rotate through during this time?

Answer 1

a= w^2*r
w=sqrt(9.8/5000)
w=0.0443 rad/s

w=α*t
t=w/α
t=0.443*100000/8
t=5537.5 sec
92 min and 17.5 seconds

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