Homework H$\mathrm{.}5.$I

Given: A homogeneous disk of mass $m$ and outer radius $R$ is able to rotate about a frictionless bearing at its center O$.$ A thin, homogeneous bar of mass $m$ and length $2R$ is welded to the disk with the bar aligned with a radial direction on the disk and one end at O$.$ A block of mass $2m$ is able to slide along a smooth, vertical wall, with the block being in no$-$slip contact with the outer surface of the disk, as shown in the figure. The system is released from rest with $=90.$

Find: Determine the angular velocity of the disk after the disk has rotated through an additional angle of $90$ after release.

Use the following parameters in your analysis: $m=5kg$ and $R=0\mathrm{.}1m.$