A rod $($mass mp and length Lp$)$ is pinned at point O and a moveable

weight $($mass mw and diameter dw$)$ is attached to it as shown. The

system is released from rest in the horizontal position $($labeled

$$Initial$),$ and a sensor $($diameter ds and negligible mass$)$ is attached

to the top of the rod to measure its angular position. The pendulum

rod is mounted flush with the top of the sensor$,$ and the moveable

weight is rigidly attached to the pendulum rod as it swings. Obtain

an expression for the pendulum$$s angular speed w when it reaches the

bottom of its swing $($the vertical position labeled $$Final$)$ as a

function of the weight$$s center$-$of$-$gravity location, Lcg$.=\sqrt[\phantom{2}]{\frac{m_{p}g(\frac{L_p-d_s}{2})+m_{w}g{L}_{cg}}{\frac{1}{2}(\frac{1}{12}{m}_p{L}_p^2+m_p(\frac{L_p-d_s}{2}{)}^2+\frac{1}{2}{m}_w(\frac{d_w}{2}{)}^2+m_w{L}_{cg}^2)}}$