I have never understood why it's beneficial to do a collision in the cm frame, but then I did an example for myself and it was easier. I just don't understand why. I had two objects with masses m1 and m2 and velocities v1 and v2. I found the velocity of the centre of mass: vcm = (m1v1+m2v2)/(m1+m2) And found the velocities of the two objects relative to the cm. u1 = v1-vcm u2 = v2 - vcm And used conservation of momentum in the center of mass frame. And magically I got that: m1u1 + m2u2 = 0 which I am guessing is the nice property of carrying out the math in the cm-frame. I just don't understand what leads to the above. Why should the equation: mu1 + mu2 = m1v1 + m2v2 - m1vcm - m2vcm = 0 It is surely pretty obvious for you, so try to explain it for me :) And try to explain why it is obvious physically in terms of the center of mass being the point where only external forces work.