We investigate the director relaxation of a nematic liquid crystal cell by considering the molecular moment of inertia, surface viscosity and anchoring energies at the boundaries. The problem solved here corresponds to a more complete description of the nematic director reorientation, since it incorporates ingredients that are usually neglected due to the mathematical difficulty raised by the moment of inertia and surface viscosity. In order to face this problem, we apply the half space approximation for the sample with the surfaces characterized by a time dependent easy direction, which can be mechanically or optically induced in the system. The results show that both, the molecular moment of inertia and the surface viscosity, have influence on the relaxation process of the director. In particular, the presence of the molecular moment of inertia introduces a finite phase velocity and, consequently, leads to a non-instantaneous response time for the distortion propagation in a liquid crystal cell.