# Collision of two rolling bodies

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1. Dec 1, 2015

### Arka420

1. The problem statement, all variables and given/known data
A solid sphere is rolling without slipping on rough ground with an angular velocity w and linear velocity v. It collides elastically with an another identical sphere at rest. Radius of each sphere is R and mass m. What is the linear velocity of the first sphere after it starts pure rolling again?
2. Relevant equations
The equations for the conservation of angular momentum.

3. The attempt at a solution
The basic idea is conserving angular momentum about the point of contact. Once that is done,the problem will be solved easily. Framing the equation for the conservation of momentum appears to be a problem (for me).

2. Dec 1, 2015

### haruspex

You have to assume no friction between the balls.
The first thing to do is analyse the collision ignoring the ground. This is ok because the collision is considered to be very brief, so any strictly limited force (gravity, normal force from ground, friction from ground) has negligible impulse during the collision. The impulse between the colliding balls is non-negligible, regardless of the brevity.

3. Dec 2, 2015

### Arka420

Pretty much OK. And is it OK to say,that after collision,second sphere acquires linear velocity v?

4. Dec 2, 2015

### haruspex

Yes, but is that relevant?