$(26$ points$)A6-k$g uniform disk welded to the $9-$ kg slender rodAB is pivoted at pin at A $.$ At the instant shown, rod AB is in a horizontal position and the assembly has an angular velocity of $=4\frac{\text{r}\text{a}\text{d}}{s}.$ Using the Energy Methods, calculate the angular velocity of the assembly when AB is in a vertical position right below pivot A when a$)$ is clockwise, and b$)$ when $$ is counterclockwise., Given: The moment of inertia of the rod with respect to $G=I_G=0\mathrm{.}1875kg*m^2,$ and the moment of inertia of the disc with respect to $C=I_D=0\mathrm{.}12kg.m^2.$

energy method: $T_1+V_1+S_1+U_{1-2}=T_2+V_2+S_2$