Law of conservation of momentum

This law gives us the quantitative analysis of the momentum of the two bodies present in an isolated system.

STATEMENT:

The law of conservation of momentum states that: “The total momentum of an isolated system always remains constant”

OR

“The momentum of an isolated system, before and after collision remains conserved.”

DERIVATION:

Consider two spherical non-rotating bodies of masses $m_1$ and $m_2$ moving in a straight line with an initial velocity of $u_1$ and $u_2$ respectively in an isolated system. As shown in the figure. Since, the two bodies are moving with different velocities in a same line , so after some time interval $t$ they will collide with each other. After having an elastic collision, the velocities of the two bodies will be $v_1$ and $v_2$ respectively.

Total momentum of the system before collision = $m_1u_1+m_2u_2$

Total momentum of the system After collision = $m_1v_1+m_2v_2$

According to law of conservation of momentum:

Total momentum of system = Total momentum of system before collision after collision

$\boxed {m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2}$