Rotational dynamics of three structurally similar coumarins; coumarin 6, coumarin 7, and coumarin 30 has been studied using a steady-state fluorescence depolarization technique. The idea is to understand how the friction experienced by a polar solute in a polar solvent depends on its dipole moment. Ab initio molecular orbital methods have been used to calculate the ground and excited state dipole moments. Although these coumarins are structurally similar their excited state dipole moments are quite different. Because of their similarity in shape and size they experience almost identical friction in alkanes, which is purely mechanical. However, in alcohols, the observed reorientation times do not follow the trend predicted by the dielectric friction theories of Nee-Zwanzig and van der Zwan-Hynes, based on their dipole moment values. Plausible reasons for the observed trend are discussed.