The general field of the invention is that of passive resonator gyros comprising an injection laser emitting an initial optical beam at a first frequency and a fibre optic cavity. The gyro according to the invention operates with three optical beams at three different optical frequencies. A first beam is injected in a first direction of rotation, the second and the third beam are injected in the contrary direction. The gyro includes three slaving devices maintaining each optical frequency at a specific mode of resonance of the cavity. The gyro includes means for measuring the frequency differences existing between the different frequencies. Combined together, these differences are representative of the length of the cavity and the angular rotational velocity of the cavity along an axis perpendicular to its plane.