An inelastic collision changes total kinetic energy. In the dissipative case it decreases, transferring energy to internal energy, including deformation and microscopic motion. Isolated colliding bodies still obey momentum conservation; conservation of energy requires accounting for the transferred energy. Bodies need not stick in every inelastic collision. The decrease in translational kinetic energy drives dissipative spreading of a planetary ring.
For the incoming masses and velocities in the elastic collision example, stipulate that the bodies stick. This perfectly inelastic collision has a shared outgoing velocityThe outgoing momenta are and , totaling . The outgoing kinetic energies are and , totaling . Thus of kinetic energy becomes internal energy within the isolated pair. Nothing in momentum conservation requires this to remain as kinetic energy. [ref]
https://openstax.org/books/university-physics-volume-1/pages/9-4-types-of-collisions. OpenStax University Physics Volume 1, section 9.4: elastic and perfectly inelastic outcomes
Two uniform discs of mass m and radius a stick at first edge contact. One initially translates at speed v and the other rests, with neither initially spinning. If the incoming velocity makes angle to the line of centres, the composite axial moment of inertia about its centre of mass is . Conserved angular-momentum magnitude is , so the angular velocity magnitude is . The centre-of-mass speed is v/2. Splitting kinetic energy into translation and rotation gives . The difference from is dissipated internally; it cannot be removed from angular-momentum conservation.
A perfectly inelastic collision is an inelastic collision in which the bodies stick and share one outgoing velocity. For two isolated point masses, momentum conservation gives . At fixed total momentum, common velocity minimizes the outgoing translational kinetic energy, so sticking gives the greatest loss of that kinetic energy for the specified incoming state.
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An inelastic collision is a type of collision in which the total kinetic energy of the system is not conserved, although the total momentum is conserved. Inelastic collisions occur when two objects collide and become deformed, stick together, or otherwise interact in a way that some of the kinetic energy is transformed into other forms of energy, such as heat, sound, or internal energy. In perfectly inelastic collisions, the colliding objects stick together after the collision and move as a single entity.