cant calculate w/o the figures so here is how it should be done:
first calculate the moment of inertia for the 3 bodies shown
then torque = F(t) x Rs
so use the eqn Torque = MI x angular acceleration
n express the angular acceleration in term of F(t)
u can calculate the angular velocity from acceleration
for b) as there is no friction in the space station, velocity at t=30 is the same as t=10
good luck!