Phenyl ring flip motion in polystyrene involves a cooperative movement of the phenyl ring and the chain backbone. In previous work, we described this cooperative rotation in single chains of polystyrene by defining the conformational transition in terms of a multidimensional reaction path and calculating torsion angle and energy profiles along this path. In this paper, we have extended our approach to study phenyl ring rotation in model structures of atactic polystyrene glasses. Reaction paths, energy profiles, free energy barriers, and rate constants were calculated for the rotation of 10 different phenyl rings in the same local backbone conformation. The results show that local intrachain steric interactions, that dominate rotation in single chains, do so in the polymer glass as well. In addition, the free energy barriers cover a wide range of values corresponding to a distribution of characteristic times for ring rotation that spans 21 decades. This distribution is also bimodal. The results are compared with observations from NMR experiments and previous molecular mechanics calculations.