center-of-mass frame
The center-of-mass frame is the point of view of an observer who rides along with a system's center of mass. From this moving vantage point a collision or explosion looks symmetric and simple, because in this frame the total momentum of the whole system is exactly zero — everything that moves one way is balanced by something moving the other way.
A reference frame is just the viewpoint (and coordinate system) from which you measure positions and velocities; switching frames means adding or subtracting a constant velocity from everything. Choose the frame moving at the center-of-mass velocity, v_cm = p_total / M_total, and by construction the total momentum becomes zero. In this frame two colliding objects always approach with equal and opposite momenta and, if the collision is elastic, simply bounce straight back with their speeds unchanged — the algebra practically melts away.
Physicists lean on this frame constantly, especially in particle physics, where the center-of-momentum frame is the natural stage for describing collisions and the energy available to create new particles. You solve the problem in the simple frame, then add v_cm back to translate the answer into the lab's point of view.
A 2 kg ball at 6 m/s approaches a 1 kg ball at rest (lab frame). The center of mass moves at v_cm = (2 times 6 + 1 times 0) / 3 = 4 m/s. Viewed from a frame gliding at 4 m/s, the 2 kg ball comes in at +2 m/s and the 1 kg ball at -4 m/s: their momenta are +4 and -4 kg m/s, summing to zero — the hallmark of the center-of-mass frame.
Subtract v_cm from every velocity and the total momentum vanishes.
The center-of-mass frame is a valid inertial frame only when v_cm is constant — that is, when no net external force acts. It simplifies the math but does not change the physics: any real, frame-independent result (like who ends up moving how fast in the lab) is the same once you transform back.