The properties of a neutron star are determined by the equation of state (EOS), which provides a link between microphysics and macrophysical observables such as mass and radius of the star. Although neutron star properties depend sensitively on the EOS, approximately universal relations exist between certain dimensionless quantities. During the last years, nearly EOS-independent relations were found between the moment of inertia and the stellar compactness as well as between the moment of inertia, the quadrupole moment and the tidal Love number. These relations can be used to constrain stellar properties which are difficult to access experimentally, such as the neutron star radius. However, the approximate universality is only preserved within certain boundaries, for instance in the limit of slow rotation. In this talk, a new fit for the normalized moment of inertia as a function of compactness is presented and the impact of rapid uniform rotation on this relation is investigated.