$10\mathrm{.}14**$ A stationary space station can be approximated as a hollow spherical shell of mass $6$ tonnes $(6000$ kg$)$ and inner and outer radii of $5$ m and $6$ m$.$ To change its orientation, a uniform flywheel $($radius $10$ cm$,$ mass $10$ kg$)$ at the center is spun up quickly from rest to $1000$ rpm$.($a$)$ How long will it take the station to rotate by $10$ degrees? $($b$)$ What energy was needed for the whole operation? $[$To find the necessary moment of inertia, you could do Problem $10\mathrm{.}11.]$