# How does conservation of momentum actually work? [closed]

I just studied about Momentum. So I thought of an experiment. If a body is moving with a constant velocity, it has a constant momentum. But as soon as a force is applied on the body, it accelerates and hence, the momentum also changed. Is this experiment violating Law of Conservation of Momentum ? If not, please tell how.

• What is applying the force? Is it coming from another body? Is that body also accelerating? Jul 30, 2021 at 11:06
• If you just studied about momentum, you may have overlooked an esential item in the formulation of the Law of conservation of momentum. How is it formulated in the source that you use for your study?
– nasu
Jul 30, 2021 at 12:25
• Newton's 2nd law can also be formulated as $F=\frac{\Delta P}{\Delta t}$, meaning that by definition, a force causes a rate of change in momentum. Jul 30, 2021 at 18:15
• I personally don't think that this is a homework question. Aug 1, 2021 at 13:42

Newton's 3rd Law say that 'for every force there is an equal and opposite force'.

When the force is applied to the body an opposite force acts on a different body and gives it an equal change of momentum, but in the opposite direction.

When adding up the new total momentum it'll come to the same total as before, as one body has gained momentum, but the other body has lost some.

• Glad it helped, worth an upvote or tick!? Jul 31, 2021 at 9:41

Considering a single body, conservation of momentum is valid until there is no external force.

Momentum is given by $$p=mv$$. If you exert an external force, $$v$$ of the object increases (or decreases if it was an opposing force), according to $$F=ma$$, . So momentum changes.

But as a system, momentum is always conserved because there are only internal forces. The objects in the system can increase their momentum by internal forces while the opposite forces of that same internal forces (according to Newton's laws) decrease the the momentum of the other objects within the system.

For instance, think you and your friend are standing on a frictionless horizontal plane. You push the other, then he will gain some velocity. Therefore his momentum increases. According to the Newton's third law your friend exerts a same amount of force on you but in the opposite direction, increasing your momentum. But since momenta of you and your friend are along the opposite direction, they cancel out each other (because momentum is a vector), making the total change of momentum zero.