# Problem: A solid wood door 1.00 m wide and 2.00 m high is hinged along one side and has a total mass of 43.0 kg . Initially open and at rest, the door is struck at its center by a handful of sticky mud with mass 0.600 kg , traveling perpendicular to the door at 13.0 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?

###### FREE Expert Solution

In this problem, we're going to use the law of conservation of angular momentum, stated as:

$\overline{){{\mathbf{L}}}_{{\mathbf{i}}}{\mathbf{=}}{{\mathbf{L}}}_{{\mathbf{f}}}}$

$\overline{)\begin{array}{rcl}\mathbf{m}\mathbf{v}\mathbf{r}& {\mathbf{=}}& \mathbf{\left(}{\mathbf{I}}_{\mathbf{d}\mathbf{o}\mathbf{o}\mathbf{r}}\mathbf{+}{\mathbf{I}}_{\mathbf{m}\mathbf{u}\mathbf{d}}\mathbf{\right)}\mathbf{\omega }\end{array}}$

The moment of inertia of the door is given by:

Idoor = (1/3)Mr2 = (1/3)(43.0)(12) = 14.33 kg•m2 ###### Problem Details

A solid wood door 1.00 m wide and 2.00 m high is hinged along one side and has a total mass of 43.0 kg . Initially open and at rest, the door is struck at its center by a handful of sticky mud with mass 0.600 kg , traveling perpendicular to the door at 13.0 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?