# Collision of particle with plate

1. Feb 8, 2014

### utkarshakash

1. The problem statement, all variables and given/known data
A uniform square plate of mass m and side a can freely rotate about a vertical axis passing through one edge. It is initially at rest. A particle of mass m is moving horizontally and perpendicular to the plane of the plate with velocity u. The particle collides with the plate elastically at the centre of the plate. Find the angular velocity of the plate just after collision.

3. The attempt at a solution

Applying conservation of angular momentum about the vertical axis,

$mua/2 = mu'a/2 + \dfrac{ma^2}{12} \omega$

Since the particle elastically collides with the center of plate,

$\omega \dfrac{a}{2} - u' = u$

where u' is velocity of particle after collision.

Doing this way gives me wrong answer! Any ideas where I'm going wrong?

2. Feb 8, 2014

### Saitama

Hi utkarshakash!

The moment of inertia seems to be incorrect.

3. Feb 8, 2014

### utkarshakash

Should it be (ma^2)/3?

4. Feb 8, 2014

### Saitama

Yes, looks correct to me. :)