I am curious though how you come to the linear speed of a point on the surface of the sphere at 1 million times c, that’s 3 x 1014 m/s. I back calculated, that means rotation speed would be 1030 rpm and a centripetal acceleration of around 1047 m/s2! Lol!
Take an angular speed ω around the z axis. A point located at a distance r from the center (in spherical coordinate) lies at a distance r sin θ from the z axis. It will therefore rotate with a velocity ω r sin θ.
Let us now calculate the angular momentum. We need to integrate over a sphere of radius R and constant density ρ the quantity ω ρ r2 sin2 θ dV. This gives
L = 2/5 m v R
where m is the electron mass and v=ω R.
Now, for having this being associated with a spin of 1/2, we must also have
L = 1/2 hbar.
The rest is easy and you get v = 5/4 hbar / (m R) = 1.45 1014 m/s.
Yet, these physical representations are really practical to understand and predict things. But they do have limits
This is what is important. We need to keep in mind the limits of the representations. I hope we will meet at Virgo in September :)
Thank you @leMouth, it made me revise my moments of Inertia :-).
I would love to come to Virgo in September! Yet, It will corresponds to the second week of the scholar year, a time where my agenda is a just a big mess... not the best period to plan things ahead. Still, I am reflecting if I could manage it as it could be quite something!
Fingers are crossed! :D