A solid disk is spinning in a horizontal plane at $8$ rev$/$s$.$ A non$-$rotating rod of equal mass to the disk is

dropped onto it from a negligible height. The rod$$s length equals the diameter of the disk. They begin to turn as

one, with their centers coincident.

$($a$)5$ points: What is the final rate of revolution in rev$/$s$?$

$($b$)5$ points: What is the ratio of the final to initial kinetic energy of the system?