REACTIONS 

Remember that the total momentum  of a system of particles was given by  or

Up to now we have been measuring velocities with respect to the ''Lab" reference frame, which is the name for the reference frame associated with a stationary target. The Lab does not move, or in other words _Lab = 0. We can also measure velocities with respect to the center of mass frame where _cm = 0. This is also often called the center of momentum frame because if _cm = 0 then . If  = velocity in Lab frame and  = velocity in cm frame then

Example A red billiard ball of mass m_R moving at a speed v_R collides head on with a black billiard ball of mass m_B at rest. (A) What is the speed of the center of mass ? (B) What is the speed of both balls in the cm frame ?

Solution

which is the speed of the center of mass. Now get the speed of the red ball via

and the speed of the black ball is