Energetic atoms influence the composition, the thermal structure and the evolution of the upper atmosphere. We investigate the slowing of energetic O(³ P) atoms by elastic and inelastic collisions with N₂. Results of quantum mechanical and semiclassical calculations of energy and angle-resolved cross sections are presented for elastic and inelastic collision of O(³ P) with N₂. A general analytical expression is developed for the kernel of the Boltzmann equation for the energy distribution function which is valid for elastic and inelastic collisions and incorporates both the angle and the energy dependence of the cross sections. The Boltzmann kernel for the energy relaxation of fast O(³ P) atoms is evaluated using the computed cross sections. We report values of the collision frequency, the average energy loss in elastic and inelastic collisions with N₂, and the mean time and the number of collisions required to thermalize initially energetic O(³ P) atoms. We compare the efficiencies of elastic and inelastic collisions in slowing down fast O(³ P) atoms. These data are basic to the development of a reliable model of the atmospheric effects of the hot oxygen atoms produced by dissociative recombination, collisional quenching, photodissociation and photoelectron impact dissociation.