A rotational speed control device maintains a shaft rotation speed. The device includes a housing containing a viscous fluid and a shaft disposed in the housing and rotatable relative to the housing. A rotor is coupled with the shaft for rotation in the viscous fluid. In one arrangement, the rotor is axially displaceable along the shaft between a low-shear position and a high-shear position. A spring mechanism is disposed in the housing and biases the rotor toward the low-shear position. In another arrangement, the rotor may be designed to cooperate with the housing or other nonrotating features within the housing to vary a shear gap according to radially expanding components of the rotor. The rotor, housing and spring mechanism can be designed to cooperate to create large changes in braking torque in response to small changes in shaft rotational speed. This allows the rotation speed to be controlled within a relatively narrow range.