$7-35.$ Initially a disk of mass m and radius r is balancing vertically at the top of a fixed sphere of radius $2$r$.$ It is disturbed slightly from rest and rolls with planar motion down the sphere without slipping.

$($a$)$ At what angle $0,$ measured from the vertical, does the disk leave the sphere? $($b$)$ Find the tangential friction force F$,$ as a function of $0$ during the rolling motion.