Abstract: A passive dynamic inertial rotor balance system including a plurality of balancing members fitted onto a rotor shaft at locations of predicted maximum shaft modal deflection. Each of the balancing members has at least one chamber and located within the at least one chamber is a plurality of movable weights and a viscous fluid. As the shaft accelerates toward an unbalance point, the weights move within the at least one chamber to a location which is opposite from the unbalance point. The viscous fluid provides damping for the movable weights to prevent excess movement within the chamber and to provide lubrication thereof. A system for self-correcting an unbalance of a turbomachinery rotor during rotation of the rotor and a method for balancing a rotor in a turbomachinery is also provided.