Question

Under what circumstances is momentum conserved?

Short answer

Momentum is conserved only in the absence of net external force (F_net) acting on the system.

Step-by-step solution

The statement of the law of conservation of momentum.

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

Proving that the momentum will conserve only in the absence of net external force.

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.