# I Angular Momentum of colliding balls

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1. Oct 16, 2016

### Aaron Barnard

I am currently trying to model collisions of rigid balls. I have successfully been able to calculate collisions that only deal with linear momentum, but have run into trouble when I want to calculate angular momentum (e.g. when ballA glances the top of ballB, both balls should start spinning a little). The balls have a coefficient of friction as well. Although the collisions are inelastic, in my model, all translational kinetic energy that is lost to friction is turned into rotational kinetic energy. Is there anyway to calculate the resultant angular and linear momentums of each ball?

2. Oct 16, 2016

### CWatters

You cant turn translational kinetic energy that is lost to friction into rotational kinetic energy. It's lost as heat.

I think collisions between near rigid balls (eg pool/snooker) are normally modelled as elastic collisions. In general it's much easier to solve problems involving elastic or totally inelastic collisions than something between the two. I've never actually tried to solve the latter (other than simple bouncing balls with a coefficient of restitution).

The thing to remember is that momentum (both linear and angular) is always conserved. It's also separately conserved so linear angular momentum isn't converted to angular momentum. Applying conservation of momentum is likely to be the way forward.

Googling can find an example of the maths for elastic collisions with friction. I've not read it all but it covers linear then angular momentum under the sub-heading "COLLISIONS"..

http://archive.ncsa.illinois.edu/Classes/MATH198/townsend/math.html

3. Oct 17, 2016

### jbriggs444

If you assume a coefficient of restitution for motion perpendicular to the contacting surfaces then you can calculate a perpendicular impulse for each collision. If you multiply by the coefficient of kinetic friction then the product can be interpreted as an upper bound on the amount of tangential impulse that could result.

All that remains is deciding whether the associated impulsive torques are enough to lock the balls together so that their spins are coordinated or are insufficient to do so.

Edit: I assume here an inelastic model for the tangential component. Unlike a vintage "superball" which can bounce tangentially as well as radially.