A $77$ gg $,30-$cmcm$-$long rod hangs vertically on a frictionless, horizontal axle passing through its center. A $12$ gg ball of clay traveling horizontally at $2\mathrm{.}7$ m$/$sm$/$s hits and sticks to the very bottom tip of the rod. To what maximum angle, measured from vertical, does the rod $($with the attached ball of clay$)$ rotate? $$