- #1

nerdvana101

- 8

- 0

I have a problem which I can't figure out.

Let us take a sphere which is rolling purely at a constant velocity v

_{o}.

Now, if the sphere were to collide inelastically with a wall, with coeff. of restitution = e.

Then what is the time after which the sphere starts pure rolling again?

Given coeff, friction = μ

I went about by considering that after the collision, the particle will have ev

_{o}velocity, but the same angular velocity ω=v

_{o}/r.

Now, since the sphere is translating, the angular velocity is in the opp. direction. So the frictional force will cause a torque to change ω.

So, if the body was initially moving rightwards, with clockwise ω, it's new velocity will be leftwards, but ω will remain clockwise. So the frictional force must act towards right to apply a counter-clockwise torque.

After this, I couldn't figure out which way to go.

Any help appreciated.!