Question

When isn't momentum conserved?

Answer 1

When there are external forces involved...\[F= dp/dt\] so the change in momentum can only be 0 if F is 0

Answer 2

No, that effect of force is nullified by Newton's 3rd law - for every action, there is equal and opposite reaction. If some body loses momentum due to force, some other body will gain an equal amount. So, momentum will be conserved even when forces are acting.

Answer 3

gokuldas_tvm:
The forces you are talking about are internal forces... not external. Momentum is conserved when it doesn't change in time, right? - when \[p _{final} = p _{initial}\] which is the same as saying the time rate of change of momentum - dp/dt - is 0. It can only be zero when there are no EXTERNAL forces

Answer 4

Practically, the case is same for both internal and external. There is always some compensation for change in momentum. It just gets transferred.

If you are not convinced, do cite example of external forces acting. We will see how the momentum is transferred.

Answer 5

You are simply wrong about this. What does Newton'd 2nd law say:\[F = dp/dt\] If F is not 0, how can dp/dt be 0? If dp/dt is not 0, how can it be conserved? Conserved means it doesn't change in time

Answer 6

Did you ever consider the possibility that there may be a -dP1/dt for a +dP2/dt ?

Conservation of momentum is not a theory to be applied on an isolated body - it has to be applied on every body interacting in a force system.

DId you consider any example to support your claim before accusing that the statement is wrong? Can you cite just one example at the least?

Answer 7

If you do not allow the existance of an external force - by saying everything is part of the system - then we are both right, because then no force is ever external - my issue with this approach is that it omits a whole class of useful concepts - like impulse.

Answer 8

It really does not exclude impulse - since impulse is only change in momentum. Just like momentum, impulse also causes one body to accelerate and the other body to decelerate. My favourite example is the rocket. The rocket gets the impulse precisely because the jet exhaust gets their velocity reduced (or increased in the opposite direction).

The problem is that theory of conservation of momentum insists on momentum being conserved. If you are not willing to consider all the bodies involved in momentum exchange, the theory is pretty much meaningless. That in itself is not a premise to say that momentum is not conserved.

A good example is someone throwing a rock up. The rock gains momentum, but the person doesn't. Does this mean that the momentum is not conserved? Not really - it is just the wrong way of applying the theorem. When the rock gains momentum, an equal opposite momentum is gained by the person and the Earth together. This is the truth - however weird it may sound.

Answer 9

Your thrown rock example is not wierd - you are just defining the "system" differently. Personally I don't want to calculate the change in the momentum of the earth and man, so I say an external force was applied which accounts for the change in momentum. I don't know how you can say it doesn't exclude impulse - impulse is the change in momentum, but its also the average external force times the time it is applied. If you claim there are no external forces, how can there be a change in momentum. Can't have it both ways.

Answer 10

Thank you Stan and Goku your arguments define what I was looking for

Answer 11

@Shawn: Sure! Anytime!

@Stan: Let me simply put it this way - Impulse is the amount of momentum transferred from one body to the other. Conservation of momentum still holds.

Answer 12

I think there is a need to define my stance.

There is no problem in calculating changes in momentum of individual bodies. However, if you plan to use theorem of conservation of momentum, you MUST consider ALL bodies involved in momentum exchange. Not doing that and saying that the theorem is only conditionally true would be a complete misinterpretation of the theorem itself.

Answer 13

no one is arguing that if you define your system to include everytyhing then momentum is conserved - I pointed out from the first statement that it is not conserved when there are EXTERNAL forces... if you set up your system so that there can never be external forces then it is a no-brainer that dp/dt is 0. Most people don't do that in every circumstance. This is not worth arguing about any more - the way you approach a problem depends on the system definition. You allow no external forces - strange but fine.

Answer 14

@Stan: Please read my previous reply - I posted it while you were typing, without knowing it