The orientational diffusion of a rodlike particle embedded in a glassy polymeric matrix is considered; the underlying kinetics is that of local rearrangements. A defining parameter of the theory is the length of the particle. The timing of steps of the random walk in orientation space is determined by rearrangements. We discuss the physical properties of the glass state in connection with the rearrangement kinetics. The orientational diffusion is influenced by the local disorder; this influence is different for dipoles of different length. For a short dipole, the resulting diffusion is of generalized Debye type. Nonexponential relaxation of physical quantities may then be caused by the distribution of rearrangement barriers. For longer dipoles and if the orientation is uniquely determined by the configuration of the embedding duster, the motion is a random walk on a given random map on a sphere. An ensemble of random mappings is considered. For even longer dipoles, hierarchical (multiscale) relaxation is expected. We discuss the relation of the theory to the shea time depoling kinetics in a system of dipoles having different length, such as are found in relaxation of electrically poled polymer materials.