The effects of the degrees of rotational freedom, as defined by the Hayes factor n, on the physical properties of polymers were studied. The applicability of the Hayes relationship was extended to include polymers with aromatic entities in the backbone chain and also the various units within a polymer repeat unit that are capable of independent motion. A rule of constant specific heat at Tg, ΔCp, dependent upon rotational motion was established. This rule was subsequently used to derive an inverse relationship between n and the characteristic ratio o. A strict linear dependence was found to exist between these two variables within a specific polymer grouping, but, in turn, is dependent upon structural complexity and the free volume present. The rule was employed to interpret the type of rotational motion present at and below Tg, the result being that torsional oscillation or hindered rotation around single bonds is the best description. An interpretation of Wunderlich's rule of constant ΔCp is presented within this framework.