In the present paper, we introduced a general model of the equations of the formulation in the context of Lord-Shulman theory which includes one thermal relaxation time and Green-Lindsay theory with two thermal relaxation times as well as the classical dynamical coupled theory to study the effect of the rotation and the magnetic field on the total deformation of a micropolar thermoelastic medium with an internal heat source that is moving with a constant speed. The analytical method used to obtain the formula of the physical quantities is the normal mode analysis. Comparisons made with the results of the three theories in the presence and absence of the magnetic field as well as an internal, heat source. A comparison is also made with the results of the three theories for different values of the rotation. (C) 2017 Elsevier Ltd. All rights reserved.