The velocity of the system's center of mass.

$$v_{cm} = \frac{\sum \vec{p}}{\sum m}$$ where $\sum \vec{p}$ is the sum of all individual object momenta and $\sum m$ is the total mass of the system.

Sum of all individual momenta in a system.

Impulse ($j$) is the change in momentum ($\Delta p$) of a system: $$j = \Delta p$$

Any change in momentum for one object is balanced by an equal and opposite change in momentum for another object (Newton's Third Law).

Impulse is equal to the change in momentum: $$j = \Delta p$$

The change in momentum of the system will equal the impulse of that force.

The total momentum of that system stays constant.

Impulse causes a change in momentum.

Zero Net External Force: Total momentum of the system stays constant. Nonzero Net External Force: Momentum is transferred between the system and its surroundings.

Elastic Collision: Kinetic energy is conserved. Inelastic Collision: Kinetic energy is not conserved.