Experimental studies of intramolecular vibrational energy redistribution (IVR) point repeatedly to the involvement of rotation-vibration coupling. We consider the full rotation-vibration Hamiltonian with a view to examining the mechanisms through which vibrations and rotations couple in polyatomic molecules. Two mechanisms are identified, namely, Coriolis coupling and centrifugal coupling, and estimates are arrived at for the relative contribution of each of these coupling mechanisms to vibrational-state mixing. The estimates suggest that for low J states Coriolis coupling will be the dominant mechanism; however, because of the different J dependence of these two terms, for sufficiently high J they can become comparable. The actual point at which they become comparable will depend upon the particular vibrational modes coupled and will vary from mode to mode within a molecule and from molecule to molecule. The estimates show that Coriolis coupling cannot always be assumed to be the dominant mechanism responsible for rotation-induced coupling unless the rotational population is confined to very low J, as, for example, in a molecular beam. In general our estimates suggest that high J states (J > 100) are almost certain to be coupled as strongly by a centrifugal pathway as by a Coriolis pathway. Since high J states attain a significant population in molecues with large moments of inertia, the role of centrifugal coupling in room-temperature IVR experiments will increase with molecular size. The ranking of terms in the Hamiltonian used to compare Coriolis and centrifugal coupling is further used to ascertain coupling pathways and the fraction of available states that will contribute to time dynamical measurements of IVR. In general, the coupling matrix elements decrease with increasing difference in vibrational quanta, Δν and only couplings involving small Δν changes are likely to be strong enough to cause sufficient mixing to influence the time dynamics. We show using a specific example that in the threshold region of IVR state mixing, only a subset of the isoenergetic states with the correct symmetry will normally play an effective role in intramolecular vibrational redistribution.