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In this paper, we report, for the first time to the best of our knowledge, the detailed modeling and design of a guided-wave optical angular-velocity sensor based on Raman amplification in a silicon-on-insulator resonant cavity. Theoretical results for continuous-wave Raman laser emission are compared with experiments in the literature, demonstrating very good agreement. The model includes the influence of a number of physical effects on the propagation of both counterpropagating pumps and Stokes waves, such as stimulated Raman scattering, two- photon absorption, free-carrier dispersion, self- and cross-phase- modulation induced by the Kerr effect, and the lock-in effect. Investigation of optical dithering features by intracavity phase modulation is also presented. Performance is derived to optimize the device sensitivity for both medical, robotics, automotive, and entertainment gyro applications.