# Collision of particle with plate

• utkarshakash
In summary, 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. Using conservation of angular momentum, the correct moment of inertia (ma^2)/3 should be used to find the angular velocity of the plate just after collision.
utkarshakash
Gold Member

## 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?

utkarshakash said:

## 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.

Pranav-Arora said:
Hi utkarshakash!

The moment of inertia seems to be incorrect.

Should it be (ma^2)/3?

utkarshakash said:
Should it be (ma^2)/3?

Yes, looks correct to me. :)

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.

## 1. What is a collision of particle with plate?

A collision of particle with plate refers to the event where a small, subatomic particle interacts with a larger, solid object such as a plate. This interaction can result in a transfer of energy and momentum between the particle and the plate.

## 2. What causes a collision of particle with plate to occur?

A collision of particle with plate can occur due to various factors such as the movement and velocity of the particle, the surface properties of the plate, and external forces acting on the particle. In some cases, collisions may also be intentionally induced for scientific experiments or technological applications.

## 3. What are the effects of a collision of particle with plate?

The effects of a collision of particle with plate can vary depending on the properties and energies involved. Some possible effects include changes in the trajectory or speed of the particle, deformation or damage to the plate, and the release of heat or radiation. These effects can also be used to study the properties of particles and materials.

## 4. How is a collision of particle with plate studied or observed?

Collisions of particles with plates can be studied through various experimental techniques such as particle accelerators, detectors, and high-speed cameras. These tools allow scientists to measure and analyze the interactions between particles and plates, providing insights into the fundamental properties of matter.

## 5. What applications can a collision of particle with plate have?

Collisions of particles with plates have a wide range of applications in fields such as particle physics, materials science, and engineering. They can be used to study the behavior of fundamental particles, test the properties of materials, and develop new technologies such as particle accelerators and nuclear reactors.

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