Quadrupolar spectroscopy of weakly polar nematic liquid crystals shows temperature-dependent Debye relaxation at low megahertz frequencies. The quadrupolar technique, which is similar to dielectric spectroscopy but which probes the motions of electric quadrupoles, reveals details of the single-particle reorientation potential which complement information from dielectric studies. In particular, the results are consistent with a nematic potential which, unlike the simplest mean-field theory of the nematic state, includes higher-order terms and a strong density dependence.