Recently has been proved in the Newtonian N-body problem that,given a minimal central configuration a and an arbitrary configuration x,there is a completely parabolic orbit starting on x and asymptotic to the homothetic parabolic motion of a, furthermore such an orbit is a free time minimizer of the action functional. In this paper we extend this result in abundancy of completely parabolic motions by proving that under the same hypothesis it is possible to get that the completely parabolic motion starting at x has null angular momentum, we achieve this by rotating conveniently the choosen minimal central configuration and by characterizing the rotation invariant weak KAM solutions of the Hamilton-Jacobi equation asociated to the problem as those defining a lamination of the configuration space by free time minimizers with null angular momentum. ; Comment: 9 pages