We perform a detailed analysis of the dynamics of the dissociative adsorption of H-2 molecules on a Pd(111) surface using ab initio data for the molecule-surface interaction and classical trajectory methods. We show that the reaction probability is completely determined by the molecule-surface interaction in the approach toward the surface before it reaches a critical distance of 1.5 Angstrom. The corresponding dynamics can be reduced to a 2D one, involving only the translational and rotational degrees of freedom, except in the lower energy range where an important role is played by dynamic trapping. We establish the relation between the dissociation probability and the shape of 2D cuts of the potential energy surface using a simple model of the evolution of orientational forces as the molecule approaches the surface. Whereas above 1.5 Angstrom the molecule evolves "as a whole," below 1.5 Angstrom the dynamics has the character of independent atom-surface interactions which explains why it dissociates with a probability close to one once it has reached the critical distance of 1.5 Angstrom.