[en] Contrary to what is stated in the Newtonian dynamics, rotation of a reference frame is not sufficient for the occurrence of the centrifugal force. Instead, the necessary and sufficient condition is a motion along a path different from that of a photon trajectory in space. This calls for a rather fundamental change in understanding of the very nature of the centrifugal force. It also has important practical physical consequences: in a strong gravitational field, where light trajectories are substantially curved, centrifugal force is much weaker than the Newtonian theory predicts. In addition, when there are closed (circular) photon trajectories in space, the centrifugal force may reverse its direction - it attracts towards the rotation axis!. The weakening of the centrifugal force in strong gravitational fields and the reversal of its direction in the neighbourhood of close photon trajectories in space fully and clearly explain puzzling examples of counter intuitive behaviour of dynamical effects of rotation found previously by several authors: e.g. reversal of the ellipticity behaviour of the relativistic Maclaurin spheroids (Chandrasekhar and Miller, 1974), reversal of the viscous torque action (Anderson and Lemos, 1988), or the fact that rotation increases internal pressure of a sufficiently compact star (Abramowicz and Wagoner, 1974). Weakening of the centrifugal force implies that rotating neutron stars are less oblate (and probably more stable) than the Newtonian theory predicts. This is important for the recently discussed question of how fast can pulsars spin. (author). 23 refs, 3 figs