# Conservation of Momentum

## Key Questions

• The Law of Conservation of Momentum states that for a closed system, the total momentum is constant.

[Closed system is one which does not exchange matter with external surroundings, and where no external force acts on the system.]

Considering a two particle system with particles of masses ${m}_{1}$ and ${m}_{2}$ moving with initial velocities (before colliding) ${u}_{1}$ and ${u}_{2}$ and final velocities ${v}_{1}$ and ${v}_{2}$ respectively.

Summarising it:

Masses -- Initial Velocities -- Final Velocities
${m}_{1} - - - - {u}_{1} - - - - {v}_{1}$
${m}_{2} - - - - {u}_{2} - - - - {v}_{2}$

Then, by law of conservation of momentum,
${m}_{1} {u}_{1} + {m}_{2} {u}_{2} = {m}_{1} {v}_{1} + {m}_{2} {v}_{2}$

This will hold true for a multiple particle system as well.

${m}_{1} {u}_{1} + {m}_{2} {u}_{2} = {m}_{1} {v}_{1} + {m}_{2} {v}_{2}$

#### Explanation:

if two elastic balls collide horizontally (no other forces affecting at that direction) then the momentum is conserved between them
so if one ball loses speed the other ball will gain speed so the above relation is applied

Example: as in this examples even though the first ball stopped, its momentum was transmitted to the other ball.

$\textcolor{g r e e n}{\text{Note:}}$ the above relation is direction dependant so you suppose one direction to be positive so velocities on that direction is positive while the velocities on the other direction is negative

I hope this helps.