A solid disk of mass M$=3\mathrm{.}39$ kg and radius R$=1\mathrm{.}3$ m is initially at rest on a frictionless horizontal axel. A blob of putty of mass m$=0\mathrm{.}3$ kg strikes the edge of the disk and stick to it at a point level with the axis after falling from rest at a height h$=4\mathrm{.}32$ m$.$

$($a$)$ What is the angular speed of the disk immediately after the putty sticks to it$?$

rad$/$s

$($b$)$ What is the lowest angular speed the disk subsequently attains.

rad$/$s

$($c$)$ What is the minimum value of h such that the disk will continue to rotate rather than simply oscillate back and forth after the putty hits?

m