Free radical decay in gamma-irradiated atactic poly(propylene) (a-PP) and microscopic chain dynamics in the same polymer have been studied by electron spin resonance and quasi-elastic neutron scattering simultaneously. It was found that an acceleration of the decay at the first acceleration temperature T-acc,T-1 = 190 K in the sub-T-g region correlates not only with the literary values of the Vogel temperature T-o for alpha-segmental dynamics, but also with the onset temperature of the so-called fast motion at Ti. The other acceleration temperature T-acc,T-2 = 250 K agrees not only with the macroscopic glass transition temperature T, from DSC measurement, but also with the course of conformational transitions as evidenced by the recent two-dimensional C-13 NMR study on the same sample. The relationships between T-acc,T-1, T-f and T-o both for a-PP as a typical polymer with the simple chemical structure and for the more complex polymers studied previously, where T-acc-T-o correlation is present but T-acc-T-f correlation absent, are discussed.