  We investigate dynamical stability of a single propeller-like shaped
molecular cogwheel modelled as the fixed-axis rigid rotator. In the realistic
situations, rotation of the finite-size cogwheel is subject of the envi-
ronmentally-induced Brownian-motion effect that we describe by utilizing the
quantum Caldeira-Leggett master equation, in the weak-coupling limit. Assuming
the initially narrow (classical-like) standard deviations for the an- gle and
the angular momentum of the rotator, we investigate dynamics of the first and
second moments depending on the size, i.e., on the number of blades of both the
free rotator as well as of the rotator in the external har- monic field. The
larger the standard deviations, the less stable (i.e. less pre- dictable)
rotation. We detect the absence of the simple and straightforward rules for
utilizing the rotator's stability. Instead, a number of the size-related
criteria appear whose combinations may provide the optimal rules for the ro-
tator dynamical stability and possibly control. In the realistic situations,
the quantum-mechanical corrections, albeit individually small, may effectively
prove non-negligible, and also revealing subtlety of the transition from the
quantum to the classical dynamics of the rotator. As to the latter, we detect a
strong size-dependence of the transition to the classical dynamics beyond the
quantum decoherence process.
