Projected angular momentum dispersion σ_Lz profiles for King models with different velocity anisotropy profiles (panel a) and their respective velocity anisotropy profiles (panel b). As the King models become more radially anisotropic (smaller values of r_a/r_h), the projected angular momentum dispersion decreases. The insets on panel a show the distribution of the projected angular momentum at r ~ 2R_h for the models with the most and the least radial anisotropy. The grey area in panel a shows the range of radial distances of stars used to calculate the histograms in the panel. We normalised σ_Lz by the half-mass angular momentum L_h, corresponding to the angular momentum of a circular orbit of an equivalent point-mass potential (see Sect. 3).