Angular momentum of Moebius strip?

AI Thread Summary
A Moebius strip with mass and radius can exhibit angular momentum if the twist rotates while the mass remains stationary. However, under symmetric conditions, the total angular momentum would be zero due to the pairing of elements with equal and opposite angular momenta. The discussion also raises the intriguing question of how a Moebius strip would behave in a magnetic field, particularly regarding induced currents. While local eddy currents may form in the twist, a global current is unlikely. The conversation highlights the complexities of angular momentum and electromagnetic induction in unique geometries.
Nemus
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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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I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
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