 Perfectly inelastic collision

For two point masses, a perfectly inelastic collision is an inelastic collision in which they stick and share one outgoing velocity. In the absence of appreciable external impulse, momentum conservation givesThe centre of mass decomposition of kinetic energy shows exactly how much translational energy is lost:At fixed total momentum, the common outgoing velocity minimizes translational kinetic energy. Thus sticking removes all relative translational motion for these two point masses; the energy can become deformation, heat or other internal motion.

Extended rigid bodies may remain joined while the combined object rotates. Their different material points then need not share one velocity, and angular momentum and rotational kinetic energy must also be included. Zero normal coefficient of restitution alone likewise does not assert sticking in every tangential direction.