Zeeman quantum beat spectroscopy has been used to determine the thermal (300 K) rate constants for electronic quenching, rotational energy transfer, and collisional depolarization of OH(A(2)Σ(+)) by H2. Cross sections for both the collisional disorientation and collisional disalignment of the angular momentum in the OH(A(2)Σ(+)) radical are reported. The experimental results for OH(A(2)Σ(+)) + H2 are compared to previous work on the OH(A(2)Σ(+)) + He and Ar systems. Further comparisons are also made to the OH(A(2)Σ(+)) + Kr system, which has been shown to display significant non-adiabatic dynamics. The OH(A(2)Σ(+)) + H2 experimental data reveal that collisions that survive the electronic quenching process are highly depolarizing, reflecting the deep potential energy wells that exist on the excited electronic state surface.