Micro-gyroscopes based on the Coriolis principle are widely employed in inertial navigation, motion control, and vibration analysis applications. This paper presents our main contributions which include a novel dual-frame optomechanical gyroscope, a unique photonic crystal cavity design, and advanced numerical simulation and optimization methods. The proposed design utilizes an optical cavity formed between dual oscillating frames, whereby input rotation induces a measurable phase shift via optomechanical coupling. Actuation of the frames is achieved electrostatically via an interdigitated comb-drive design. Through theoretical modeling based on cavity optomechanics and finite element simulation, the operating principle and performance parameters are evaluated in detail. Results indicate an expected angular rate sensitivity of 22.8 mV/°/s and angle random walk of 7.1×10-5 °/h1/2, representing superior precision than to existing micro-electromechanical systems gyroscopes of comparable scale. Detailed analysis of the optomechanical transduction mechanism suggests this dual-frame approach could enable angular vibration detection with resolution exceeding state-of-the-art solutions.