## FANDOM

138 Pages

Some baryons families exhibit a relation between the spin and mass, where the spin scales as the mass squared $J \propto M^2$. In what follow we present a mechanical system that exhibits a similar relation between its mass and angular momentum. Let us consider rigid rod rotating in such a way that its ends are moving at the speed of light $c$. Suppose that this rod has mass density per unit length $\mu$ and length $l$, so its mass is $m = l \mu$. The angular velocity is given by $\omega = c/l$. The energy of the string, even when its spinning, is proportional to the mass $e \approx m c^2$. The angular momentum is given by

$J \propto m \omega^2 l \approx \frac{m^2 c}{\mu} \propto m^2$

Similar ideas are used in string theory to represent particles as modes in a vibrating string.