A rotor for a rotary wing aircraft having a single blade with a longitudinal pitch axis and that is hinge mounted on the rotary shaft for rotating the rotor, the hinge being about an axis that is transversal relative to the rotary shaft, said rotary wing describing a cone when its pitch angle is not zero, the rotor possessing a balancing flyweight device for balancing the resultant of the horizontal component of the lift force and of the rotary drag force of the blade, the device being mounted to rotate with the rotary wing about its rotary shaft and, under the effect of the centrifugal force to which it is subjected while the rotary wing is rotating, generating a horizontal force that is applied to the rotary shaft of the motor and that opposes the above-mentioned resultant with a magnitude of that is a function of the position of the flyweight(s) of the balancing device relative to the rotary shaft of the rotor.