# Determing angular velocity after a collision

1. Dec 15, 2008

### fluidistic

1. The problem statement, all variables and given/known data
Suppose we are in deep space and there's a particle of mass $$m$$ and a sphere of radius $$R$$ of mass $$M$$. Suppose also that the sphere is initially at rest while the particle is moving with a constant velocity $$v_0$$. The particle collide with the sphere in a position such that the point of collision on the sphere is situated at R/8 over the center of mass of the sphere. But there's a constraint : the sphere can only move in the direction of the coming particle before the impact. (For this, you can imagine an object making a resistance on the sphere if it tries to move in a direction which differs from the coming particle).
The particle leaves the sphere forming an angle of $$60$$° with the sphere' surface.
Find the angular velocity of the sphere.
2. The attempt at a solution
I could easily find the velocity of the center of mass' sphere. I know that the linear momentum is conserved (in the direction of the particle before the impact), that the energy is likely not to be conserved and that the angular momentum is probably not conserved despite the fact that the collision is almost instantaneous. It's due to the fact that the sphere cannot move freely so that the object making a constraint suffers a great force in a small amount of time.
Hence I don't know how I can proceed. I don't want a clear solution but rather a tip about how I can start.

2. Dec 15, 2008

### Mthees08

I am not entirely sure of the constraint part, but angular momentum is always conserved the same as linear momentum. So my hint to you is to find the angular momentum of the particle initial and final and the difference is what the large ball should have, however THEN apply the constraints as you see fit. So certain aspects may be lost due to a loss of motion but the momentum was still transfered (or is not the equivalent of an angular impact occurred.)

3. Dec 15, 2008

### fluidistic

Thank you. Yeah you're right, I realized it some hours after having posted.