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

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

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

The moment of inertia of the door is given by:

I_{door} = (1/3)Mr^{2} = (1/3)(43.0)(1^{2}) = 14.33 kg•m^{2}

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?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Intro to Angular Collisions concept. You can view video lessons to learn Intro to Angular Collisions. Or if you need more Intro to Angular Collisions practice, you can also practice Intro to Angular Collisions practice problems.