How does the zero momentum frame work in 2D collisions?

[joker_900]

Could anyone quickly explain how the zero momentum frame works in 2 dimensional collision problems? I really don't understand at all.
Thanks

 

[Shooting Star]

There exists such a frame in which the vector sum of the momenta of all the particles is zero. If the ith particle has mass mi and velocity vi, then let v = ∑mivi/∑mi. A frame of reference traveling at this velocity v wrt the lab frame would be such a frame.

For more convenience, you can consider it to be the non-rotating frame with origin at the centre of mass of the whole system and traveling at v.

The total momentum in this frame is zero both before and after a collision.