What is the formula for calculating rotation speed?

[zincshow]

In wiki under spin it says:

"Electrons are spin-1⁄2 particles. These have only two possible spin angular momentum values, called spin-up and spin-down. The exact value in the z direction is +ħ/2 or −ħ/2. If this value arises as a result of the particles rotating the way a planet rotates, then the individual particles would have to be spinning impossibly fast. Even if the electron radius were as large as 14 nm (classical electron radius) then it would have to be rotating at 2.3×10^11 m/s. The speed of rotation would be in excess of the speed of light, 2.998×10^8 m/s, and is thus impossible.[2] Thus, the spin angular momentum has nothing to do with rotation and is a purely quantum mechanical phenomenon."

This quote implies a calculation to relate the radius and speed, what is the formula that is used in this calculation to get the rotation speed? TIA

 

[Spinnor]

If you can get this article,

What is spin? by Hans C. Ohanian

American Journal of Physics -- June 1986 -- Volume 54, Issue 6, pp. 500-505
Issue Date: June 1986

from the abstract:

According to the prevailing belief, the spin of the electron or of some other particle is a mysterious internal angular momentum for which no concrete physical picture is available, and for which there is no classical analog. However, on the basis of an old calculation by Belinfante [Physica 6, 887 (1939)], it can be shown that the spin may be regarded as an angular momentum generated by a circulating flow of energy in the wave field of the electron. Likewise, the magnetic moment may be regarded as generated by a circulating flow of charge in the wave field. This provides an intuitively appealing picture and establishes that neither the spin nor the magnetic moment are ``internal''—they are not associated with the internal structure of the electron, but rather with the structure of its wave field. Furthermore, a comparison between calculations of angular momentum in the Dirac and electromagnetic fields shows that the spin of the electron is entirely analogous to the angular momentum carried by a classical circularly polarized wave.

©1986 American Association of Physics Teachers

 

[ytuab]

In wiki under spin it says:

"Electrons are spin-1⁄2 particles. These have only two possible spin angular momentum values, called spin-up and spin-down. The exact value in the z direction is +ħ/2 or −ħ/2. If this value arises as a result of the particles rotating the way a planet rotates, then the individual particles would have to be spinning impossibly fast. Even if the electron radius were as large as 14 nm (classical electron radius) then it would have to be rotating at 2.3×10^11 m/s. The speed of rotation would be in excess of the speed of light, 2.998×10^8 m/s, and is thus impossible.[2] Thus, the spin angular momentum has nothing to do with rotation and is a purely quantum mechanical phenomenon."

This quote implies a calculation to relate the radius and speed, what is the formula that is used in this calculation to get the rotation speed? TIA

The classical electron radius is not 14nm. (nm --> fm is correct?). nm is too big. For example, the proton size is 10^-15 m.
If the electron is a sphere, the (spinning) angular momentum is 2/5 Me r^2 w. (Me: electron mass, r: sphere radius, w: angular frequency).
This value is equal to the spin angular momentum, 1/2 hbar.
If the r is the classical electron radius (2.8 x 10^-15 m), the sphere speed rw becomes more than 100 times the speed of light.

If you can get this article,

What is spin? by Hans C. Ohanian

American Journal of Physics -- June 1986 -- Volume 54, Issue 6, pp. 500-505
Issue Date: June 1986

from the abstract:

According to the prevailing belief, the spin of the electron or of some other particle is a mysterious internal angular momentum for which no concrete physical picture is available, and for which there is no classical analog. However, on the basis of an old calculation by Belinfante [Physica 6, 887 (1939)], it can be shown that the spin may be regarded as an angular momentum generated by a circulating flow of energy in the wave field of the electron. Likewise, the magnetic moment may be regarded as generated by a circulating flow of charge in the wave field. This provides an intuitively appealing picture and establishes that neither the spin nor the magnetic moment are ``internal''—they are not associated with the internal structure of the electron, but rather with the structure of its wave field. Furthermore, a comparison between calculations of angular momentum in the Dirac and electromagnetic fields shows that the spin of the electron is entirely analogous to the angular momentum carried by a classical circularly polarized wave.

©1986 American Association of Physics Teachers

This is interesting. But the electron has the mass and charge. And the electron is known to be too small. You say the mass and charge of one electron is actually spreading over much larger space? If so, the electron size will be much bigger by the scattering experiment?
And you say the electron spin is caused by the actual circulating frow?
But the spinning electrons go back to their original forms when they are rotated by an angle of 4 pi (not 2 pi).
I think that it is difficult to explain the electron spin using the actual circulating flow model.

 

[alxm]

This quote implies a calculation to relate the radius and speed, what is the formula that is used in this calculation to get the rotation speed? TIA

Uh, try the definition of http://en.wikipedia.org/wiki/Angular_momentum" .