Zero Momentum Frame Explained: 2D Collision Problem

[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.

 

[Moetasim]

for asking about the zero momentum frame (ZMF) in 2-dimensional collision problems. The ZMF is a reference frame that is used to simplify the analysis of collisions by eliminating the effects of momentum. In this frame, the total momentum of the system is always zero, which makes it easier to track the changes in kinetic energy during a collision. To use the ZMF, you first need to calculate the total momentum of the system before and after the collision. Then, you can use this information to transform to the ZMF, where the initial and final momenta are equal but opposite in direction. This allows you to focus solely on the changes in kinetic energy and determine the outcome of the collision. I hope this helps in your understanding of the ZMF.