Coefficient of restitution in rotation motion

[iitjee10]

Homework Statement

Suppose A ball of mass m moving with a speed v collides with a rod of mass M and length L placed horizontally on a smooth floor. The coefficient of restitution is 0.5.

Homework Equations

The Attempt at a Solution

In this case how do we utilise the information of COR.

If it were given COR is 1 then we could conserve kinetic energy. But in this case how do we how about it?

 

[fluidistic]

According to wikipedia the coefficient of restitution is worth $$\frac{v_{2f}-v_{1f}}{v_{1}-v_2}$$. (http://en.wikipedia.org/wiki/Coefficient_of_restitution) so it might be helpful.

 

[thomate1]

The coefficient of restitution (COR) in rotation motion is a measure of the elasticity of a collision between two objects in rotational motion. In this scenario, the COR of 0.5 suggests that the collision between the ball and the rod is not perfectly elastic, meaning that some energy is lost during the collision. This can be taken into account by using the conservation of energy principle, where the initial kinetic energy of the ball is equal to the final kinetic energy of the ball and the rod after the collision. However, since the COR is less than 1, the final kinetic energy of the system will be less than the initial kinetic energy, indicating that some energy was lost during the collision. This can be further analyzed using the equations for rotational kinetic energy and the moment of inertia of the rod. By incorporating the COR into these equations, we can determine the final angular velocity of the rod and the ball after the collision. Overall, the COR is an important factor to consider in rotational motion collisions as it provides information about the energy transfer and elasticity of the collision.