# Momentum Conservation during Collision

Is momentum really conserved when two bodies collide?

What about friction between the 2 bodies during collision and between the bodies and the ground?

Does friction become internal force here?

I just assumed that the time interval of collision is small so friction can be ignored during collision... am I correct?

But then when friction is impulsive, it is not ignored and momentum is not said to be conserved... so my small time interval assumption doesn't really work out here.

(Also,unrelated but when does friction become impulsive so that momentum won't be conserved?)

Edit: @dominecf

'Momentum is supposed to be conserved at all circumstances.'

Its most certainly is not conserved in this case right? Friction is said to be impulsive in this case and hence momentum is not conserved.

My doubt is when 2 bodies collide (straight on). Won't there be impulsive forces acting on them? And so how could momentum be conserved?

• Does friction become internal force here? What do you mean by 'internal force'?
– Gert
Dec 7, 2021 at 17:10
• en.wikipedia.org/wiki/Momentum#Conservation
– Gert
Dec 7, 2021 at 17:34
• After the edit: still the same. Balls hitting steps are described by off-axis collision of rotating bodies. Momentum stays always conserved. Maybe you have some deeper idea, but I am unable to grasp it from what you write. Dec 8, 2021 at 18:04

Momentum is always conserved. Any force is always matched by an equal and opposite force elsewhere as is described by Newton's third law.

In the case of collisions, the two objects colliding will feel the same force from the collision, but in opposite directions, so that the total momentum does not change, it's only transferred between the colliding objects. This is true for (approximately) instant momentum transfers, or slower momentum transfers: it's always the same for both objects, in opposite directions.

For friction, the breaking force felt by the moving object is matched by an opposite force on the material causing the friction. So a car slowing down due to friction from the road is applying a forward force on the ground.

Momentum is supposed to be conserved at all circumstances.

If internal force is one which is exerted by one body within the investigated system unto another, and if Earth becomes part of the physical problem - then yes, by definition, friction becomes internal force.

The shorter the collision, the larger the force is - so momentum is conserved. In the idealized limit, the forces appear like Dirac δ-functions, but this does not change the result.