Molecular dynamics simulations are employed to study the phenyl-ring flip in polystyrene, thought to be the molecular origin of the gamma-relaxation. The results show that upon cooling the system toward the glass transition the motion of the phenyl ring becomes more heterogeneous, which seems to result from a distribution of local energy barriers in combination with slower transitions between states with these local energy barriers. The growing of the heterogeneity affects the determination of the effective energy barrier. In particular, the "static" energy barrier (as determined from the distribution of the orientation of the phenyl ring with respect to the backbone) is found to be different from the "dynamic" energy barrier, as determined from the temperature dependence of some relaxation time (i.e., the activation energy). However, below the glass transition temperature it appears that the two methods render the same value for the height of the energy barrier, although the time scales differ approximately by a constant factor. It is shown that another relaxation time can be determined to characterize the ring-flip process, which seems not to be affected by the growth of heterogeneity and which closely follows the "static" energy barrier. The effective barrier as determined in this way by the simulations is in fair agreement with experimental values for the gamma-relaxation.