solid wood door $1\mathrm{.}00$ m wide and $2\mathrm{.}00$ m high is hinged along one side and has a total mass of $40\mathrm{.}0$ kg$.$ Initially open and at rest, the door is struck at its center by a handful of sticky mud with mass $0\mathrm{.}500$ kg$,$ traveling perpendicular to the door at $12\mathrm{.}0$ m$/$s just before impact. Find the final angular speed of the door. Does the mud make a significant contribution to the moment of inertia?