Angular momentum of Moebius strip?

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Discussion Overview

The discussion revolves around the angular momentum of a Moebius strip, particularly considering a scenario where the twist of the strip rotates while the mass remains stationary. Participants explore whether this configuration would possess angular momentum and the implications of symmetry in this context.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether a rotating twist in a stationary Moebius strip would have angular momentum, seeking clarity on the conditions and outcomes.
  • Another participant asserts that the strip would have angular momentum, but later claims it would be zero, suggesting symmetry leads to cancellation of angular momenta.
  • A further argument is presented that the total angular momentum can be calculated as r*dp integrated over the strip, emphasizing that symmetric conditions would result in zero angular momentum due to pairing of elements with equal and opposite momenta.
  • Another participant introduces a related but separate question about the effects of a magnetic field on a Moebius strip, speculating on the induced current and suggesting the presence of local eddy currents but questioning the existence of a global current.

Areas of Agreement / Disagreement

Participants express differing views on the angular momentum of the Moebius strip, with some asserting it is zero due to symmetry, while others support the idea that it possesses angular momentum. The discussion on the magnetic field introduces additional speculation without consensus.

Contextual Notes

The discussion includes assumptions about symmetry and the conditions under which angular momentum is evaluated. The implications of the magnetic field on the Moebius strip remain unresolved, with participants offering differing perspectives on induced currents.

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Here is something that keeps me up at night...Assume a Moebius strip with mass m and radius r. Let the twist rotate but not the mass of the strip in general. Would it have an angular momentum? If yes, what would it be?
 
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Would it have an angular momentum?
Yes.
If yes, what would it be?
Zero.
 
and the argument goes as follows...
 
The total angular momentum would be r*dp integrated over the strip.If the twist is symmetric & is turned evenly, we can pair up elements with equal & opposite angular momenta by symmetry. So, the answer would be zero if we have sufficient symmetric conditions.
 
Although it should be posted as a different question, I couldn't help but wonder what would happen if we turn a Moebius strip in a magnetic field.What would be the current induced in the strip?
 
Good argument. Symmetry is sufficent. Thanks.
Cool idea with the induction. I am tempted to bring out my hammer...
There would be a local eddy current in the twist for sure but I don't think there would be a global current. A gigant Moebius strip in sitting above the equator of Earth for example.
 

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