Collisions in the Center Mass Frame:
* To solve a collision problem using the center of mass frame:
(1) Jump to the cm-frame and determine the velocity of the particles in the cm-frame.
(2) Solve the problem in cm-frame using the fact the final velocity of a particle is just the negative of the initial velocity multiplied by the coefficient of restitution.
(3) Jump back to the original frame of reference, the lab frame, to determine the requested velocities in the lab frame.
Center of Mass Frame:
*The center of mass frame is a frame of reference moving at the velocity of the center of mass vcm of the system.
* In the cm-frame the velocity of each particle is found by subtracting vcm from each particle's speed in the "lab" frame of reference.
* In cm-frame the total momentum of all the particles in this frame is always zero both before and after the collision. Using a prime to indicate the velocity after collision,
* The coefficient of restitution is a measure of the elasticity of the collision. The value of the coefficient of restitution does not depend upon the frame of reference, i.e. ehas the same value in all frames moving at a constant speed. For objects that rebound off each other, it can be shown that,
