(color online) (a) Schematics of the gyroscope containing the three-mode optomechanical system. A 2D mechanical oscillator (without mechanical drive) is placed on a platform rotating with angular velocity Ω (Ω is parallel to the z axis). The two mechanical modes are coupled by the Coriolis effect due to the absolute rotation. The mechanical motion in the x direction is coupled to an optical cavity by radiation pressure. (b) Schematics of the balanced homodyne measurement. The output field from the cavity is mixed with a much stronger classical reference laser at the input of a 50:50 beam splitter. The output from the beam splitter is fed to two photo-detectors D₁ and D₂. The difference in the photodetector readings gives the phase of the output field from the cavity.