In an inelastic collision, the total momentum of the system is conserved, while the kinetic energy is not.

In physics, an inelastic collision is defined as a type of collision in which the total kinetic energy is not conserved, although the total momentum is. This contrasts with an elastic collision, where both momentum and kinetic energy are conserved. The principle of conservation of momentum states that the total momentum of a system remains constant if no external forces are acting on it. This principle is valid for all types of collisions, including inelastic collisions.

During an inelastic collision, the objects involved do not rebound off one another with the same speed and direction they had prior to the collision. Instead, they may either stick together and move as a single entity after the collision or separate and move in different directions at varying speeds. Despite these changes, the total momentum of the system remains unchanged both before and after the collision. This occurs because the momentum lost by one object is gained by another.

The reason kinetic energy is not conserved in an inelastic collision lies in the nature of these interactions. Inelastic collisions often involve some degree of deformation or alteration in the shape of the colliding objects, which consumes energy. This lost energy originates from the kinetic energy of the objects, resulting in a decrease in the total kinetic energy after the collision.

To calculate the momentum before and after an inelastic collision, you can use the formula:

$p = mv$

where $p$ represents momentum, $m$ represents mass, and $v$ represents velocity. By summing the momentum of all objects prior to the collision and comparing it to the total momentum afterward, you can confirm that they are equal, thereby demonstrating the conservation of momentum.

In summary, while inelastic collisions may alter the speed and direction of the involved objects and lead to a reduction in total kinetic energy, they do not affect the total momentum of the system. This fundamental principle of physics is applicable to all types of collisions, regardless of their characteristics.