In conditions of ideal axisymmetry, for a magnetized plasma in a generic bounded domain, necessarily toroidal, the uniform absorption of external energy (e.g. rf or isotropic alpha heating) clearly cannot give rise to net forces or torques. A rather common experimental observation on contemporary tokamaks is that the near central absorption of auxiliary heating power (often ICH, ECH, and LHCD) and current drive in presence of non axisymmetric magnetic perturbations, including tearing modes, drives a bulk plasma rotation in the co â Ip direction. Also growing tearing modes provide a nonlinear magnetic braking that tends to flatten the rotation profile and clamp it at the q-rational surfaces. The physical origin of the torque associated with Paux absorption could be due the effects of asymmetry in deposition or in the equilibrium configuration, but here we consider also the effect of the response of the so called neoclassical offset velocity to the power dependent heat flow increment. The neoclassical toroidal viscosity (NTV), due to error fields, internal magnetic kink or tearing modes tends to relax the plasma rotation to this asymptotic speed, which in absence of auxiliary heating is of the order of the ion diamagnetic velocity. It can be shown by a kinetic calculation, this offset velocity is a function of the absorbed heat and therefore of the injected auxiliary power, thereby forcing the plasma rotation in a direction opposite to the initial, to large values. The problem is discussed in the frame of the theoretical models of neoclassical toroidal viscosity.