Definition

Momentum is a measure of how much "oomph" a moving object has, depending on both how heavy the object is and how fast it is going. It is the product of mass and velocity, $p = mv$, with units of $\text{kg}\cdot\text{m/s}$, a vector pointing in the direction of the velocity; a force applied over time changes momentum, and in a collision the total momentum before equals the total momentum after. In vector form $\vec{p} = m\vec{v}$, and Newton's second law in its fundamental form is $\vec{F}_{\text{net}} = d\vec{p}/dt$, which integrates to the impulse-momentum theorem, $\vec{J} = \int \vec{F}\, dt = \Delta\vec{p}$. When the net external force on a system is zero, total momentum is conserved, a result that follows from Newton's third law and, more deeply, from the translational symmetry of space. Momentum is conserved in every collision, elastic or not; kinetic energy is conserved only in elastic collisions.