Problem $17\mathrm{.}035-$ The angular velocities of a falling combined bar$-$gear systemThe $2\mathrm{.}500-$kg uniform slender bar AB is connected to the $3-$kg gear B that meshes with the stationary outer gear C$.$ The centroidal radius of gyration of gear B is $30$ mm$.$ Assume that the system is released from rest in the position shown in the figure. Determine the angular velocity as it passes through the vertical position. The angular velocity of the bar as it passes through the vertical position is $...$rad$/$s