A single-channel control system is a common control method for a rotating aircraft. In order to improve the flying dynamic quality of the aircraft, the control system adds a damping loop, of which a gyro is one of the key components. The gyro is used to sense the attitude motion of the rotating carrier, and feeds back the transverse input angular velocity of the rotating carrier to the control end of the system to adjust the damping of the aircraft. In this paper, a solving method of the transverse input angular velocity has been proposed based on a new type of Si micromechanical gyro. Firstly, we introduce the structure and working mechanism of the Si micromechanical gyro driven by a rotating carrier in detail. Utilizing Euler’s dynamics equation, the motion equation of the gyro and its solution were obtained. Next, the output voltage signal of the gyro was attained by a sensing circuit. Then, we analyzed the signal in detail. The analyses have shown that the gyro output signal is an amplitude-modulated (AM) signal. Its envelope is proportional to the transverse input angular velocity of the rotating carrier, and the carrier frequency can automatically tune the spin frequency of the rotating carrier. Finally, an algorithm was proposed by using Hilbert transform for solving the transverse input angular velocity of the rotating carrier. The algorithm was validated through different experiments under three working conditions. The theoretical analyses and experimental results have demonstrated that the method can effectively realize the solving of the transverse input angular velocity of the gyro.