Crossed-beam and beam-gas experiments on the reaction Ba+HI-->BaI+H have been performed, in which the most probable collision energy ranges from 3 to 17 kcal/mol. The results, combined with previous experimental studies on this reaction system, show a remarkable collision energy dependence. Between low and high collision energies, a transition occurs in the intensity, width, and peak location of the product vibrational and rotational population distributions. The onset of this transition is estimated to occur at approximately 5 kcal/mol. For collision energies smaller than 5 kca/mol, the product vibrational distribution is bell shaped and peaks at v=12. For collision energies larger than 5 kcal/mol, a second maximum appears at v=0 in the vibrational distribution. The rotational distributions of the crossed-beam experiments are extremely narrow but broaden at lower collision energies. As the collision energy is increased above 5 kcal/mol, the BaI rotational excitation is very near the energetic limit, and the maximum for the BaI(v=0) rotational population distribution moves from J=415.5 to 5=538.5. In contrast, below the transition onset, the maximum remains unchanged around J=420.5. Moreover, the peaks of the BaI(v=1) and BaI(v=2) rotational distributions appear at successively lower J values, as expected from energy conservation arguments. The nature of the kinematic constraints for this reaction allows the determination of the opacity functions for the production of the BaI product in a specific vibrational level v. Detailed analysis of the collision energy dependence of the specific opacity functions offers insight into the role of conservation of energy and angular momentum in influencing this reaction. At low collision energies, the maximum reactive impact parameter, b(max), is determined by an angular momentum (centrifugal) barrier. At collision energies larger than 5 kcal/mol, conservation of energy dictates the value of b(max). These two processes are identified as the mechanisms that control the Ba+HI reaction cross section. The transition between the two mechanisms provides an interpretation for the bimodal character of the BaI product internal-state distribution.