Angular momentum of Moebius strip?

[Nemus]

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?

 

[Bill_K]

Would it have an angular momentum?

Yes.

If yes, what would it be?

Zero.

 

[Nemus]

and the argument goes as follows...

 

[Eynstone]

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.

 

[Eynstone]

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?

 

[Nemus]

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.