Angular-Linear Momentum Collisions

[JWA]

Hi there,

A friend of mine is creating a physics engine in java (mostly as a challenge I believe).

Today he asked me a question about the results of collisions between objects. For example, imagine that these 2 objects collide:

The results of such a collusion would be something like this:

where w_1 and w_2 are angular velocities, a_1 and a_2 are final velocities in the x,y plane.

The question really is, how do you calculate the values of a_1, a_2, w_1 and w_2?

Then does the method/answer change when you have initial angular velocities as well?

I would love to have a method for finding these values, but from what I've searched online, I can't find anything...

P.S. I would assume this is graduate level physics. I did a degree in physics and have honestly no clue but that might also be because I was never much good with physics :P

Thanks,
~jwa

 

[drvrm]

The question really is, how do you calculate the values of a_1, a_2, w_1 and w_2?

Then does the method/answer change when you have initial angular velocities as well?

I would love to have a method for finding these values, but from what I've searched online, I can't find anything...

By common sense one can say that the angular momentum before the collision and after the collision will be same...as the angular momentum is moment of momentum and simple momentum is being conserved.
the equations governing the conservation of momentum as well as angular momentum for closed
systems can give you the values of the angular velocities as well as the linear velocities if the initial conditions are given.
if you wish to see a simulation pl. visit <http://www.myphysicslab.com/collision.html>