Abstract We report on molecular dynamics simulations of an isolated cylindrical grain in copper shrinking under capillary forces. At low temperatures, the coupling between grain boundary (GB) migration and grain translation induces rotation of the grain towards higher or lower misorientation angles, depending on the initial misorientation. The dynamics of the GB motion and grain rotation are studied as functions of the initial misorientation angle and temperature. The effects of imposed constraints blocking the grain rotation or exerting a cyclic torque are examined. The simulation results verify several predictions of the model proposed by Cahn and Taylor [Acta Mater 52, 4887 (2004)]. They also indicate that the GB motion is never perfectly coupled but instead involves at least some amount of sliding. This, in turn, requires continual changes (annihilation or nucleation) in the GB dislocation content. Dislocation mechanisms that can be responsible for the motion of curved GBs and dislocation annihilation in them are proposed.