One proves that the Newtonian force acting on the particle, if it is derivable from the corresponding Mayer's potential, has, in the most general case, the form of the Lorentz force. The necessary and sufficient conditions providing the existence of the mentioned Mayer's potential, obtained in the case of the holonomie rheonomic dynamical system by the authors in [2], reduce, in the case of the system consisting of a free particle, which is considered in this paper, to the equations having the form of the Maxwell's equations. One further proves that the Coriolis force, which can be considered as the Newtonian force in the dynamics of relative motion, is derivable from the corresponding Mayer's potential, which one determines, only in the case of a constant angular velocity of the moving frame. F'inally, the obtained result is illustrated by an example.