The local dynamics of syndiotactic poly(methyl methacrylate) (PMMA) are investigated by explicit atom molecular dynamics (MD) simulations and quasielastic neutron scattering at temperatures well above the glass transition temperature. Using MD, we are able to isolate specific local motions well above T-g. These include rotations of the alpha-methyl and ester methyl, rotations of the entire ester side group and segmental motion of the chain backbone. This capacity is unique to simulation as proton motion at high temperatures necessarily involves multiple motions. The force field used is validated by direct comparison to structural and dynamic neutron scattering measurements, and by comparison via temperature extrapolation of activation energies and rotational times for methyl group rotations. We find that the rotation of the ester side group is consistent with the beta-relaxation at low temperatures: the activation energy closely matches that assigned from dielectric spectroscopy (DS), and relaxation times are also consistent with these measurements. Although the ester protons rotate continuously with no preferred spatial orientation, the rotation of the ester oxygen around the C-1-C bond [O-C-C-1-C-3] does appear to be a 2-fold jump as observed in NMR experiments. The alpha-relaxation is associated with the motion of the main chain. Relaxation times for these protons are not Arrhenius, but rather begin to diverge as the temperature is lowered. Rotation of the slower alpha-CH3 group occurs with rates similar to the alpha- and beta-relaxations in the temperature range we investigate. Both this rotation and that of the ester side group are more prominent at smaller scales and explain why neutron scattering measurements on PMMA reveal the alpha-relaxation as the spatial scale is increased.