For nearly a decade, N-body simulations have revealed a nearly universal dark matter density profile. This density profile appears to be robust to changes in the overall density of the universe and the underlying power spectrum. Despite its universality, however, the physical origin of this profile has not yet been well understood. Semi-analytic models have suggested that scale lengths in dark matter halos may be determined by the onset of the radial orbit instability. We have tested this theory using N-body simulations of collapsing dark matter halos. The resulting halo structures are prolate in shape, due to the mild aspect of the instability. We find that the radial orbit instability sets a scale length at which the velocity dispersion changes rapidly from isotropic to radially anisotropic. Preliminary analysis suggests that this scale length is proportional to the radius at which the density profile changes shape, as is the case in the semi-analytic models; however, the coefficient of proportionality is different by a factor of ~2. We conclude that the radial orbit instability may be a key physical mechanism responsible for the nearly universal profiles of simulated dark matter halos.