In this work, we calculate the moment of inertia of the pulsar of the binary system J0737-3039A in the framework of Einstein's gravitational theory combined with a relativistic field theoretical approach for nuclear matter in the slow rotating regime, taking into account that the star's frequency is much smaller than Kepler's frequency. In the description of the EoS for nuclear matter, we consider a generalized class of relativistic multi-baryon Lagrangian density mean field approach which contains adjustable nonlinear couplings of the meson fields with the baryon fields. Upon adjusting the model parameters to describe bulk static properties of ordinary nuclear matter, we determine the EoS of the pulsars. By analyzing the results, dynamical constraints for neutron star models are identified.