Under what circumstances is momentum conserved?

The Law of conservation of momentum states that the total momentum of a system always remains constant before and after collisions or we can say that the initial momentum before the collision of a system is equal to the final momentum of the system after the collision

We have the equation for the momentum of an object of mass m moving with a velocity, v is given by$p=mv$

According to the law of conservation of momentum,$p=acons\tan t$

Or $mv=acons\tan t$

We know that mis a constant, so v must be a constant so that the above equation is valid.

That is$v=acons\tan t$

The velocity of an object is constant only when there is no force acting.

That is when F = 0,$v=acons\tan t$

We have Newton’s second law of motion in terms of momentum given by the equation,

$F_{net}=\frac{\Delta p}{\Delta t}$ ,

where F_netis the net external force acting on the system.

Substitute the value of$F_{net}=0N$in the above equation we get,

$\frac{\Delta p}{\Delta t}=0$

Or we can say that,$∆p=0$, or there is no change in momentum or momentum is a constant or momentum is conserved.

Hence, momentum will conserve only when there is no net external force acting on the system.