A uniform solid disk of radius $\backslash ($ R $\backslash )$ and mass $\backslash ($ M $\backslash )$ is free to rotate on a frictionless pivot through a point on its rim $($see figure below$).$ The disk is released from rest in the position shown by the coppercolored cirrle

$($a$)$ What is the speed of its center of mass when the disk reaches the position indicated by the dashed circle? $($Use any variable or symbol stated above along with the following as necessary:

g$.)$

$\backslash [$

v$\_\{\backslash$mathrm$\{$CM$\}\}=$

$\backslash ]$

$($b$)$ What is the speed of the lowest point on the disk in the dashed position? $($Use any variable or symbol stated above along with the following as necessary: $\backslash ($ g $\backslash ).)$

$\backslash [$

v$\_\{\backslash$mathrm$\{$L$\}\}=$

$\backslash ]$

$($c$)$ Repeat part $($a$)$ using a uniform hoop of mass $\backslash ($ M $\backslash ).($Use any variable or symbol stated above along with the following as necessary: $\backslash ($ g $\backslash ).)$

$\backslash [$

v$\_\{\backslash$mathrm$\{$CM$\}\}=$

$\backslash ]$