In this work, the friction anisotropy of hexagonal MoS2 (a well-known lamellar compound) was theoretically investigated A molecular dynamics method was adopted to study the dynamical friction of two-layered MoS2 sheets at atomistic level Rotational disorder was depicted by rotating one layer and was changed from 0 degrees to 6 degrees in 5 degrees intervals The superimposed structures with misfit angle of 0 degrees and 6 degrees are commensurate and others are incommensurate Friction dynamics was simulated by applying an external pressure and a sliding speed to the model During friction simulation the incommensurate structures showed extremely low friction due to cancellation of the atomic force in the sliding direction, leading to smooth motion On the other hand in commensurate situations all the atoms in the sliding part were overcoming the atoms in counterpart at the same time while the atomic forces were acted in the same direction, leading to 100 times larger friction than incommensurate situation Thus, lubrication by MoS2 strongly depended on its interlayer contacts in the atomic scale According to part I of this paper [Onodera T et al J Phys Chem B 2009 113 16526-16536] interlayer sliding was source of friction reduction by MoS2 and was originally derived by its material property (interlayer Coulombic interaction) In addition to this interlayer sliding the rotational disorder was also important to achieve low friction state