Q$6-$ A thin, cylindrical rod $,l=24\mathrm{.}0cm$ long with mass $m=1\mathrm{.}20kg$ has a

ball of diameter $d=8\mathrm{.}00cm$ and mass $M=2\mathrm{.}00kg$ attached to one end.

The arrangement is originally vertical and stationary, with the ball at the

top as shown in Figure. The combination is free to pivot about the

bottom end of the rod after being given a slight nudge.

$($a$)$ After the combination rotates through $90$ degrees, what is

its rotational kinetic energy?

$($b$)$ What is the angular speed of the rod and ball?

$($c$)$ What is the linear speed of the center of mass of the ball?