Explain why total linear momentum is conserved in an elastic collision,and define inelastic collision and perfectly inelastic collision.

(N/A) In all collisions,the total linear momentum is conserved,meaning the initial momentum of the system is equal to the final momentum of the system.
When two objects collide,the mutual impulsive forces acting over the collision time $\Delta t$ cause a change in their respective momenta.
Change in momentum of the first object: $\Delta \overrightarrow{p_{1}} = \overrightarrow{F_{12}} \Delta t$
Change in momentum of the second object: $\Delta \overrightarrow{p_{2}} = \overrightarrow{F_{21}} \Delta t$
where $\overrightarrow{F_{12}}$ is the force exerted on the first particle by the second,and $\overrightarrow{F_{21}}$ is the force exerted on the second particle by the first.
From Newton's third law,$\overrightarrow{F_{12}} = -\overrightarrow{F_{21}}$.
Therefore,$\Delta \overrightarrow{p_{1}} = -\Delta \overrightarrow{p_{2}}$,which implies $\Delta \overrightarrow{p_{1}} + \Delta \overrightarrow{p_{2}} = 0$.
Thus,the total change in momentum of the system is zero,confirming conservation.
Elastic Collision: $A$ collision in which both total linear momentum and total kinetic energy are conserved. This occurs under conservative forces.
Inelastic Collision: $A$ collision in which total linear momentum is conserved,but total kinetic energy is not conserved. This occurs under non-conservative forces.
Perfectly Inelastic Collision: $A$ collision in which the two particles stick together and move with a common velocity after the collision.