PROBLEM $4$:

An angular velocity control fuse is being considered for a satellite. When the spin about the axis O reaches the maximum $\backslash (\backslash$omega$\_\{1\}\backslash )$ a very thin tether connecting two masses snaps, releasing the arms and the arms will deploy as shown. The thin circular disk at the center, the $2$ slender arms $($rods$)$ and the $2$ balls $($considered as point masses$)$ all have the same mass $\backslash ($ m $\backslash ).$ Length of each rod and the diameter of the disk is d$.$ Determine the angular velocity $\backslash (\backslash$omega$\_\{2\}\backslash )$ as percentage of $\backslash (\backslash$omega$\_\{1\}\backslash )?$