Conservation of Momentum

If an external force is not applied to a system, then momentum is conserved.

For example, consider one dimensional motion, and suppose there are two objects $A$ and $B$ with masses $m_A$ and $m_B$, respectively. If the initial velocity of object $A$ is $v_{A_i}$ and the initial velocity of object $B$ is $v_{B_i}$, then

$m_A v_{A_i} + m_B v_{B_i} = m_A v_{A_f} + m_B v_{B_f}$.

Here, $v_{A_f}$ is the final velocity of object $A$ and $v_{B_f}$ is the final velocity of object $B$. The system consists of objects $A$ and $B$.

If the masses of both objects are zero, then this equation reduces to the trivial statement,

$0=0$.