A ground-state cooling strategy for the mechanical oscillator is proposed to suppress the thermal noise excited by the external thermal environment. For this purpose, the quantitative relationship between the rotation angular velocity and the amplitude of the output light field signal is determined. Then, the influence of the radiation pressure-induced fluctuation spectrum on the number of phonons in the mechanical oscillator is discussed. Finally, the cooling rate and the number of steady-state phonons are investigated to optimize the system parameters and thereby cool the mechanical oscillator to its ground state, that is, to the extent that the number of steady-state phonons is less than 1. Theoretical analysis and simulation results show that the peak value of the radiation pressure-induced fluctuation spectrum can be leveraged to strengthen the cooling process, and its valley value can be utilized to suppress the heating process. The proposed dual-cavity quantum gyroscope model can cool the mechanical oscillator by reducing the number of steady-state phonons to 0.19 and ultimately reduce the thermal noise in the system.