# Linear momentum conservation puzzle

Discussion in 'Physics & Math' started by Q-reeus, Nov 13, 2016.

1. ### danshawenValued Senior Member

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A capacitor can be considered a kind of battery. It has a charged and a discharged state, just like a chemical or atomic battery would. In every important respect, this does not change the identity of the scenario.

I'm now going to stipulate that whatever it is you have in mind, it has nothing whatsoever to do with the Earth's or any other external magnetic field. This would violate the isolation of the system, for one thing.

There is something satisfying about the kind of mathematical rigor it takes to publish over 100 pages of math to derive the identity of unity, 1 = 1. Likewise, I find it satisfying that this problem has already beaten the whole issue of COM to a pulp, and in the process seems to have proven a number of theorems that would seem to be a precursor to understanding all of the concepts used in Newton's laws; that mass / inertia exists, that it is possible for it to move, thereby moving its center of mass, and that energy density can be increased or decreased at will to support moving the COM. Not to mention the intimate relationship between linear and angular (spin) momentum.

COM ideas were used to derive E=mc^2. It isn't like it is a trivial matter to consider in detail. Before 1905, no one knew that.

3. ### Q-reeusBannedValued Senior Member

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I don't resort to tricks and would have indicated anything like that in #1 if it was relevant.

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5. ### OceanBreezeRegistered Member

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I suspect we have all been over-thinking this thing. Is this just some fancy variation of Newton’s cradle? There must be some impulse sent along the shaft that is reflected back and cancels out, conserving linear momentum.

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7. ### The GodValued Senior Member

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Motor and generator are connected with batteries through conducting wires only. Discharging may cause some drop in voltage, thus reduction in motor speed, this will require some kind of braking.

Any change in battery health is not going to impact the shaft by any means other than through V and I.

For Q-reeus,

In place of discharging-battery, say I have a variable DC source (assume DC motor), everything else is unchanged. Now after sometime somehow without disturbing the isolated condition of the system I change the DC voltage (reduce it by 10%), will it create some axial impulse as sought by you?

8. ### danshawenValued Senior Member

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Good one. Most springs also impart torque as they compress/decompress, like a Wilberforce pendulum. Pretty sure that isn't the point, however.

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9. ### Q-reeusBannedValued Senior Member

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Sorry, you are on the wrong track there. No reflected waves or such involved.

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Yes.

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13. ### The GodValued Senior Member

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Reduction of voltage on motor, creates axial impulse in shaft under such condition, you agree.

So in your puzzle, the battery discharges, which reduces the voltage, thus an axial impulse is created.

14. ### Q-reeusBannedValued Senior Member

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There is an association between changes to your perennial V, I, in scenario of #1, and an axial impulse. But that was implicit from the outset - right there in #1.

15. ### The GodValued Senior Member

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So you want to know how V changes once battery starts discharging?!

16. ### Q-reeusBannedValued Senior Member

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No. What gives you that idea? Remember the task is for one or collectively all of you to both qualitatively and quantitatively identify where and how a COM preserving axial impulse arises. Given I way back let it out that such an impulse does in fact exist. Till that point even existence of such was in doubt.

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17. ### The GodValued Senior Member

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I have told you the cause of impulse if any long back; but you agree now that change in V would cause pulse.

It appears that you are just freaking out! I am tired and out of this thread, till you let know what's in your mind.

18. ### hansdaValued Senior Member

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Say initially, the shaft is spinning around its axis. Now, the shaft is twisted. So, a twisting force is applied on the spinning shaft. This will cause a precession to the spinning shaft. This precession will try to change its angular momentum. This can generate an axial impulse to the shaft.

19. ### Q-reeusBannedValued Senior Member

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Who is 'freaking out'? Let's get this clear. The lazy, careless, formal way to handle the case would have been to just invoke conservation of momentum as primary principle. No need to then care where or how any restorative impulse arises - it just must just because. I say not good enough. One must show that such actually exists and precisely where and how. Neither you nor anyone else here has succeeded. Not my problem if you keep aiming in wrong directions. All the clues have been laid out. A long list of failed attempts have greatly narrowed the options.
OK. A commitment. The answer will come before 2016 is done. Forum time. That still gives someone time to get it right

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20. ### Q-reeusBannedValued Senior Member

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Your reasoning can't be right but let's at least have a diagram so I know what you even mean by all that.

21. ### The GodValued Senior Member

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Thats ok. You can play with dP/dt term as mdv/dt + vdm/dt for both the batteries and try to freak out. The question here is axial impulse on the shaft, which, if at all, could only be created by change in V or I. I am fully convinced some useless or not-so-use-worthy stuff is up your sleeve.

PS : Thank God, you made some commitment.

22. ### Q-reeusBannedValued Senior Member

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No freaking out. Your focus has been all wrong. But still time to change. Or just sit back and wait if that's your choice.

23. ### OceanBreezeRegistered Member

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I have mixed feelings about the deadline; as much as I enjoy this thread, and all the interesting tangents it has spawned, it can overstay its welcome if people start to lose interest.

I have been looking, naively for a nice simple solution, apparently, there is none.

So, we really need to use special relativity, Lorentz transform and tensor analysis to solve this, eh? I have been trying my best to avoid that!

As I said earlier, I can’t figure out what to apply a transform to, and what velocity can act as a reference.
There are no mechanical parts that are moving at anything close to relativistic speeds, and you didn’t seem to think transforming the shifted mass sounds right.

About all I see left is the angular velocity of the shaft.

From experience, I know there is a damping force on shaft drives that amounts to a linear reaction force to angular shaft velocity. This mainly applies to pumps, but in this case a mass is being moved by the shaft, so in some respects it does resemble a pump.

Unfortunately, I don’t know much about the damping force, as I am not in the business of designing shaft drives, but I do know there is a sort of Lorentz transform that applies.
I won’t even bother to define the terms unless you tell me this is related to the problem, and if it isn’t, I Officially give up!

Oh, and I don't know if the latex will display correctly. It seems buggy to me:

$\frac { 1 }{ \sqrt { { \left[ 1-\frac { { \omega }^{ 2 } }{ { \omega }_{ c }^{ 2 } } \right] }^{ 2 }+\quad { \eta }^{ 2 } } }$