A detailed derivation of the density of states function for both the iso-propyl radical and the propene molecule is given. Classical kinetic energy coupling between internal and external rotors is treated exactly for rigid-frame models having attached symmetric tops. Formulae for both free and hindered internal rotation are presented. A free rotor treatment which includes kinetic energy coupling yields a density of states which differs from that obtained by assuming independent internal rotation. A hindered rotor treatment has an additional, and temperature dependent, effect on the density of states. Inclusion of kinetic energy coupling and hindering potential affect the values of physical parameters extracted from fits to kinetic data for the title reaction.