$(15$ points$)$ Rod $\backslash ($ A B $\backslash )$ has a weight of $\backslash (7\backslash$mathrm$\{$lb$\}\_\{\backslash$mathrm$\{$f$\}\}\backslash )$ and is attached to two smooth collars at its end points by ball$-$and$-$socket joins. If collar $\backslash ($ A $\backslash )$ is moving downward at a speed of $\backslash (8\backslash$mathrm$\{$ft$\}/\backslash$mathrm$\{$s$\}\backslash ),$ determine the kinetic energy of the rod at the instant show. Hint: This is determined from the angular velocity component of the rod that is directed perpendicular to the rod's axis.