In the late 1970s A.O.Barut put forth an alternative theory for the inner constitution of baryons and mesons, in which the basic pieces would be the stable particles, namely the proton, the electron, and the neutrino, rather than quarks with fractionary charges. At the same time Barut proposed also that the short range strong interactions between such internal constituents would be magnetic in nature. Quite recently, in vixra 1511.0005, we developed a phenomenological model based upon the concept that the magnetodynamic energy of zitterbewegung intrinsic motion is the source for the rest energies, and therefore, the source of mass in particles. In the present paper we show that our recently proposed model can be applied to leptons and to the full baryon octet with almost perfect accuracy, in a way consistent with Barut´s proposal. It is shown that mass for all these particles depends on two quantities, namely, the number of magnetic flux quanta trapped in an intrinsic vibrational motion, and the magnetic moment of the particle.