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Well, elementary particles have no moment of inertia $I$. But what is the nearest possible answer to the question for a free, spinning electron?

In general, one has a relation with spin $J$ given by
$$ J = I \omega.$$ For an electron, the magnitude of spin is $J=\sqrt{3/4} \hbar$. But since $\omega$ is not defined, there is no way to speak about a moment of inertia.

Or can one say more?

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  • $\begingroup$ The classical picture of angular momentum doesn’t work for spin angular momentum. Electrons are not actually spinning like a ball. $\endgroup$ – G. Smith Jul 24 at 23:28
  • $\begingroup$ True! Indeed, I did not say that they were spinning like a ball - just that they are spinning. There are may other ways to spin... $\endgroup$ – Christian Jul 26 at 5:17
  • $\begingroup$ I’m not clear on whether you got my point or not. They’re not spinning like anything spins in classical mechanics. “Spin” in QM is essentially just a confusing and unfortunate historical misnomer. $\endgroup$ – G. Smith Jul 26 at 5:26
  • $\begingroup$ See motls.blogspot.com/2012/12/… for a different point of view. $\endgroup$ – Christian Jul 26 at 15:31
  • $\begingroup$ Lubos is a member of PSE, so perhaps he will answer and tell you what the electron’s moment of inertia is. $\endgroup$ – G. Smith Jul 26 at 16:29

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