# Perfectly Elastic Collisions in 2 Dimensions with Round Objects

1. Aug 22, 2010

### pacojoe

My friend is programming a curling application for the Android. He needs a way of calculating the results of perfectly elastic collisions in 2 dimensions with perfectly round objects (curling stones in this case, naturally).

I know what the basic formula for the conservation of momentum is for perfectly elastic collisions, and I remember doing some problems with it in my college physics course, but I don't remember doing problems in which the objects are moving toward one another at strange angles.

All the problems that I remember doing with this involved one of the objects staying put while the other one ran into it. Come to think of it, I don't think we ever had to consider the effects that the curvature of the objects would have on one another.

I've been trying to find decent resources for this just by Googling it, but I haven't found much that's of any use.

Does anyone know where I can find this kind of information? Any help is greatly appreciated.

2. Aug 23, 2010

### AJ Bentley

If the objects are perfectly elastic you can still use the method you are familiar with, you just resolve the momentum into components (x and y)

That gives you angles and speeds, the only problem remaining is the purely geometric one of working out the position of the centre of each object at collision.

3. Aug 23, 2010

### georgir

The general solution is to view a reference frame in which the center of masses of the objects is immobile, and then its the same as if they each hit an immovable wall at their point of contact.
[STRIKE]But in your case it is much simpler because you have two objects of equal mass and size, so they will just trade their velocities around. Each one starts to move in exactly the same way as the other was moving before the impact.[/STRIKE]
EDIT: I was wrong, oversimplifying it for a central collision. Sorry if I confused you with this.

Last edited: Aug 24, 2010