The dynamics of atactic polypropylene has been explored with quasielastic neutron scattering (QENS) measurements in the temperature range 4-460 K and momentum transfer range q = 0.2-2.25 Angstrom(-1). In parallel, molecular dynamics simulations of the same polymer have been conducted in the temperature range 260-600 K, using both a fully atomistic model and a model with united-atom methyl groups. In conjunction with the second model, a computational procedure for introducing the motion of methyl hydrogens a posteriori is proposed and tested against the fully atomistic simulation results. Simulated intermediate incoherent scattering functions I(q,t) reveal an initial exponentially decaying regime of duration ca. 1 ps, which is dominated by bond angle bending vibrations and torsional oscillations, as well as features attributable to torsional transitions of the methyl groups and to correlated conformational transitions of the backbone bonds at longer times. The time decay of I(q,t) beyond 1 ps is well-described by stretched exponential functions, the stretching exponent being around 0.5 at 600 K and decreasing with decreasing temperature. Analysis of the atomistic simulation trajectories yields distributions of relaxation times with a distinct log-Gaussian peak characteristic of methyl motion, from which a Gaussian distribution of activation energies for methyl torsional transitions with mean around 15 kJ/mol and standard deviation around 3 kJ/mol is extracted, in excellent agreement with QENS estimates. Torsional transitions of different methyls occur essentially independently of each other. QENS experiments reveal a nondecaying elastic contribution to the scattering over the time window of the measurement, which is not seen in the simulations. Apart from this, computed I(q,t) and incoherent dynamic structure factor S(q,w) curves are in very favorable agreement with the measured QENS spectra and with earlier NMR, data on atactic polypropylene.