The rotational motion of aromatic groups which constitute a thermotropic copolyester, vectra was investigated in terms of the quasielastic neutron scattering (QENS) originating from incoherent scattering of hydrogen. Vectra which is a random copolyester of p-hydroxybenzoic acid (HBA) and 2-hydroxy-6-naphthoic acid (HNA) with a faction of 73/27 (mol/mol), gives rise to the nematic phase transition at T-m=558 K from semicrystalline phase, i.e., a mixture of crystalline and amorphous phases (T-g=393 K). In the region above T-m, the elastic incoherent scattering cross section due to hydrogen, obtained for optical geometry in which q vector is normal to the molecular axis of vectra, was successfully decomposed into (i) the Debye-Waller factor due to vibrational hydrogen, (ii) the elastic incoherent structure factor (EISF) for the rotational aromatic groups with hydrogen and (iii) the QENS for the rotational aromatic groups with hydrogen. The QENS spectra and EISF thus obtained were well reproduced by a free rotational model for the aromatic groups, in which residing sites for hydrogen on the rotational circle is infinite. On the other hand, in the solid (semicrystalline) phase below T-m, the QENS spectra and EISF became less q dependent with decreasing temperature; these observations agree qualitatively with a more restricted motion, e.g., a jump rotation having finite residing sites for hydrogen.