A solid disk of mass $\backslash ($ M$=3\mathrm{.}51\backslash$mathrm$\{$~kg$\}\backslash )$ and radius $\backslash ($ R$=1\backslash$mathrm$\{$~m$\}\backslash )$ is initially at rest on a frictionless horizontal axel. A blob of putty of mass $\backslash ($ m$=0\mathrm{.}33\backslash$mathrm$\{$~kg$\}\backslash )$ strikes the edge of the disk and stick to it at a point level w the axis after falling from rest at a height $\backslash ($ h$=3\mathrm{.}16\backslash$mathrm$\{$~m$\}\backslash ).$

$($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.

$(0$

$\backslash (\backslash$checkmark $\backslash$mathrm$\{$rad$\}/\backslash$mathrm$\{$s$\}\backslash )$

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

m