Total Momentum and Center of Mass Velocity

The total linear momentum, denoted $\vec{P}_\text{total}$, of a collection of objects is defined as the sum of the individual momenta of each object.

For a collection of $n$ objects with masses $m_1, m_2, \dots, m_n$ and velocities $\vec{v}_1, \vec{v}_2, \dots, \vec{v}_n$, the total momentum calculation sums the products of mass and velocity for each object:

This means a collection of masses can have total momentum

$$\vec{P}_\text{total} = 0$$

even if masses within the collection are moving, as long as the sum of the momenta from each mass is zero

...