applet-magic.com Thayer Watkins Silicon Valley & Tornado Alley USA

String Theory and String Rotation

Strings

An elaborate theory has been developed that elemental particles such as quarks and leptons are
very small strings, which may be open or closed.

Do they rotate? Do they ever!

From the work of Aage* Bohr and Dan Mottelson we have that at the nuclear level the angular momentum of a structure
is quantized according to the formula

Jω = h(I(I+1))^{½}

where J is the moment of inertia of the structure, ω is its rate of rotation, h is Planck's constant divided by
2π and I is a positive integer.

The moment of inertia of a circular closed ring of radius r and mass m rotating like a wheel is mr². The moment of inertia for a closed
ring rotating like a flipping coin is same as that of the ring rotating as a wheel.

The masses of the up and down quarks are estimated to 1/470 and 1/296 of the mass of a proton, respectively

m_{up} = 1.673×10^{-27}/470 = 3.56×10^{-30} kg
r = 2×10^{-16}
J_{up} = 3.56×10^{-30}(2×10^{-16})² = 1.4242×10^{-61} kg m²

Therefore the minimum rate of rotation is given by

ω = h(2)^{½}/J_{up} = (1.05457×10^{-34})√2/1.4242×10^{-61} = 1.05×10^{28} per second

A ring rotating this fast through spinning and flipping motion would have the appearance and effect of a spherical shell.

The Danish name Aage is properly pronounce like the English word owe with a slight eh at the end. This
is because the proper spelling of this name in Danish is Åge. The letter å has the sound oh.