(Solved):   A giant toroidal space station is being evacuated. Model the \( 1.0 \times 10^{10}-\mathrm ...

 

A giant toroidal space station is being evacuated. Model the \( 1.0 \times 10^{10}-\mathrm{kg} \) station as a cylindrical hoop of radius \( 1.5 \mathrm{~km} \) rotating at a rate of \( 2 \pi \mathrm{rad} / \mathrm{min} \). If each wave of evacuees consists of one thousand \( 7.0 \times 10^{5}-\mathrm{kg} \) escape pods whose launchers are pointed radially outward from the station rim, what is the change in the angular speed \( \Delta \omega \) of the station as a result of the first \( \Delta \omega= \) wave? Express your answer in radians per second (rad/s).