When two circles collide, the angle of collision will NOT matter as they both will be met tangential to one another assuming that gravity is not a factor.

The topics you want to study is torque, angular momentum, and friction.

For friction, typically what will happen is that the ball will be launched off using the static friction coefficient between the two surfaces in a perfect world. In an imperfect world, there will be an amount of "slippage" changing the static coefficient of friction to it's weaker cousin kinetic coefficient of friction.

During this time, a large amount of rotational energy will be gained by the circle, but it will not be equal to the one that gave it unless it happens to be fixed in place.

It can be difficult to calculate this. So what you can do instead is approximate it.

For instance, on contact you can say that the initial energy gain is going to be about 87% before kinetic friction kicks in, and then it slowly ramps up to maybe 89% before it disconnects.

Thanks for all your feedback folks, really appreciated.

I will follow all the links and work through all your suggestions, and I WILL post back with the solution I end up with.

I really must get my nose into some physics books. I was pretty good at it during my years of education, sadly ladies and beer have taken their toll on my poor brain!

Thanks again.