Momentum is defined as $\vec{p} = m\vec{v}$. It is a vector and is conserved in isolated systems when the net external impulse is negligible.

Impulse is $\vec{J} = \int \vec{F}\,dt$, and it equals the change in momentum: $\vec{J} = \Delta \vec{p}$. This connects force over time to motion changes, especially in collisions.

If the net external force on a system is zero or negligible, total momentum is conserved: $\vec{p}_{\text{i}} = \vec{p}_{\text{f}}$. This is especially useful in collisions and explosions.

In an elastic collision, both momentum and kinetic energy are conserved. In an inelastic collision, momentum is conserved but kinetic energy is not fully conserved. A perfectly inelastic collision is one in which objects stick together.