A well-characterized Ag(111) surface in an ultrahigh vacuum system is bombarded with supersonically cooled N2 and the scattered molecules are detected near the specular angle using 2+2 resonance enhanced multiphoton ionization. The first three even spatial moments of the angular momentum distribution have been measured. The zeroth moment is the population of a given rotational level, while the second and fourth moments describe the quadrupole and hexadecapole alignment of the J vector with respect to the surface normal. The relative population distribution shows an excess at high J characteristic of rotational rainbow scattering. For J>7, the second and fourth moments closely approach their limiting values expected when the J vector lies in the plane of the surface. It is concluded that the N2/Ag(111) system closely approaches the ideal of a rigid rotor colliding with a flat surface.