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An electron has angular momentum. Shouldn't it also have angular velocity?

Ignoring the g-factor (just for the order of magnitude approximation) and the fact that an electron is not a sphere the electron's angular velocity should be around:

$$ \omega \approx \frac{\mu}{er^2} $$

or about 0.01 to 10^17 rad/s depending on whether the radius is the classical radius, the compton wavelength, or the planck length.

Is there some "average" angular velocity that can be assigned to the electron?

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You can't generate spin 1/2 from motion in space, so no, there is no way to assign an angular velocity to the electron. Orbital angular momentum only comes in integer multiples of h-bar.

This situation actually doesn't change very much even if we do discover substructure to the electron. Google "preon" and "confinement problem." You're still going to need a preon with half-integer spin, and that spin still can't come from orbital angular momentum.

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the spin is assumed to be an intrinsic property unrelated to rotation, as it is assumed usually that the electron is truly elementary and does not have any size. The same happens with the expansion of space into... the nothingness, not necessarily into another spatial dimension. If you can accept that you are a long way into understanding physics.

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    $\begingroup$ The reason why we don't assign a spatial scale to the electron is because we haven't seen any on experiments and that's not for lack of trying. The hardest step to the understanding of physics for many seems to be that it's completely driven by observations and experiments. $\endgroup$ – CuriousOne Jun 15 '16 at 5:20

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