We have investigated the dynamics of phenylene rings in glassy bisphenol-A (BPA) polycarbonate (PC) by means of quasielastic neutron scattering. Taking advantage of selective deuteration of the samples, we have studied the incoherent scattering of hydrogens in phenylene rings on the one hand, and on the other hand the coherent quasielastic scattering of all the atoms in the sample. Two different types of neutron spectrometers, time of flight and backscattering, were used in order to cover a wide dynamic range, which extends from microscopic (approximately 10(-13) s) to mesoscopic (approximately 10(-9) s) times. Moreover, neutron-diffraction experiments with polarization analysis were carried out in order to characterize the structural features, and the relative coherent and incoherent contributions of the samples investigated. In contrast with previous studies of phenylene ring dynamics in BPA polysulfone performed by us also by neutron scattering, phenylene rings in BPA PC exhibit an "extra" motion in addition to those found for BPA polysulfone's phenylene rings. This extra motion of the rings in PC perfectly correlates with the main carbonate group motion followed by dielectric spectroscopy and allows us to (i) consistently interpret the PC's gamma relaxation in terms of two different motions; and (ii) experimentally confirm the relation between the motion of phenylene rings and carbonate groups within BPA PC formerly predicted by computational methods.