Collision of particle with plate

[utkarshakash]

Homework Statement

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.

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?

 

[Saitama]

Homework Statement

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.

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?

Hi utkarshakash!

The moment of inertia seems to be incorrect.

 

[utkarshakash]

Hi utkarshakash!

The moment of inertia seems to be incorrect.

Should it be (ma^2)/3?

 

[Saitama]

Should it be (ma^2)/3?

Yes, looks correct to me. :)

 

[HalfLostAndSearching]

I would suggest checking your calculations and equations for any mistakes. It is important to double check all steps and ensure that the equations used are appropriate for the scenario. Additionally, it may be helpful to draw a diagram of the situation to better visualize the problem and identify any potential errors. It is also important to consider any external forces or factors that may affect the collision and the resulting angular velocity of the plate.