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[Phys-l] force +- momentum flow



This has got little if anything to do with the causation thread ...
but it is interesting and important.


Bob LaMontagne wrote:


Where is the N#3 force coming from?

Oooh, that's a teachable moment. I get versions of that question
all the time: "Where does the force come from."

Asking where does xxx come from is a good habit, but AFAICT
the really big payoff only comes if xxx is a conserved quantity.

Now it turns out that force is not exactly the relevant
conserved quantity. In the context of Newton's third
law, _momentum_ is the relevant conserved quantity.
It is exceeeedingly useful to keep track of where the
momentum is coming from and where the momentum is going.

Every force problem can easily be rejiggered to be a momentum
problem. Sometimes (but not always) the momentum representation
is incomparably easier.

Example: In fluid dynamics, you can drive yourself crazy
trying to calculate "the" force at a particular place X
in the fluid. Do you mean the force that parcel A exerts
on parcel B, or vice versa, or what? I gave up on this a
long time ago.

______________
| | |
| A x B |
|______|______|

In contrast, it is easy to keep track of how much momentum
flows across the A/B boundary ... and that is quite sufficient
to tell you what you need to know.