# Bullet stuck into a ball and rotates it

1. Aug 17, 2015

### Karol

1. The problem statement, all variables and given/known data
A ball of mass M and radius R can rotate round an axis through it's center. a bullet of mass m travels with speed v, hits the ball near the surface and gets stuck in it.
What's their angular velocity after the collision.

2. Relevant equations
Moment of inertia of a ball round it's axis: $I=\frac{2}{5}MR^2$
Conservation of angular momentum: $mvR+MVR=0$

3. The attempt at a solution
Conservation of angular momentum:
$$mvR=(M+m)\omega R^2\Rightarrow \omega=\frac{mv}{(m+M)R}$$

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2. Aug 17, 2015

### stockzahn

Why didn't you use the ball's moment of inertia?

3. Aug 17, 2015

### Karol

$$mvR=\left( \frac{2}{5}MR^2+mR^2 \right)\omega\Rightarrow \omega=\frac{mv}{R\left( \frac{2}{5}M+m \right)}$$

4. Aug 17, 2015

### stockzahn

To understand it correctly: Does the statement imply that the ball is turning around an axis or is it lying on the ground and rolls away after getting hit by the bullet?

5. Aug 17, 2015

### stockzahn

Sorry, ignore this post (wrong thread)

Last edited: Aug 17, 2015
6. Aug 18, 2015

### haruspex

I'm struggling to picture how it could have hit it anywhere except near the surface.
(It's ok, I understand what they were trying to say.)