A solid wood door $1\mathrm{.}00$ mm wide and $2\mathrm{.}00$ mm high is hinged along one side and has a total mass of $44\mathrm{.}0$ kgkg$.$ Initially open and at rest, the door is struck at its center by a handful of sticky mud with mass $0\mathrm{.}300$ kgkg$,$ traveling perpendicular to the door at $11\mathrm{.}0$ m$/$sm$/$s just before impact.

Part A

Find the final angular speed of the door.

Express your answer in radians per second.

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rad$/$srad$/$s

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Part B

Does the mud make a significant contribution to the moment of inertia?

yesno