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.