From ControlTheoryPro.com

Contents
1 Introduction to Vibratory MEMS Gyroscopes
See Also 

All MEMS gyroscopes currently use vibrating proof masses. Those masses typically vibrate at a high frequency. As the sensor housing rotates in inertial space a Coriolis force is induced on the proof mass. The Coriolis force causes a vibration in an orthogonal plane and the amplitude of the orthogonal motion can be measured.
2 Operating Principle of MEMS vibratory gyros^{[1]}
A simplified model of vibratory gyros is shown in Figure 1. The system has 2 orthogonal vibration modes; one mode corresponds to the vibration of the mass in the xdirection, the other the ydirection. The vibration frequency of the xaxis is ω_{x} and the equivalent for the yaxis is ω_{y}. Typically ω_{x} is almost equal to ω_{y}.
When powered on, the mass is driven in the xdirection with a driving frequency ω_{d} which is close to ω_{y}. When the entire MEMS gyro is rotated about the zaxis (out of the plane of the screen), an alternating force in the ydirection is caused by the Coriolis force. The amplitude of this vibration in the ydirection is used as a measure of the angular rate.
All MEMS gyroscopes use the Coriolis effect.
where:
 is the force of the proof mass,
 is the proof mass,
 is the velocity of the mass, and
 is the angular velocity of the reference frame (or sensor housing).
2.1 The role of mechanical resonance in vibratory gyros
The Coriolis force is typically weak. As a result mechanical resonance is used to amplify the motion and thus keep the signal to noise ratio high over the desired bandwidth. The driving frequency, ω_{d}, and the 2 resonance frequencies, ω_{x} and ω_{y}, must be designed carefully.
3 Types of Resonating MEMS Gyroscopes^{[2]}
All MEMS gyros require a resonating mass. The most common types of resonating MEMS gyros are
 Tuning Fork Gyros (TFG)
 Hemispherical Resonating Gryo (HRG) or Wine Glass Resonator Gyro
 VibratingWheel Gyros
 Foucault Pendulum Gyros
4 Resources
 SensorMag site on the basics of MEMS sensors
 Mohite, S., Patil, N., Pratap, R., "Design, modeling and simulation of vibratory micromachined gyroscopes.", Journal of Physics: Conference Series 34 (2006), pp. 757763.
 Thermoelastic Damping and Engineering for High Q MEMS Resonators
 Boa, M. 2004 Micro Mechanical Transducers. 2nd. Elsevier. ISBN 044450558X
 Gaura, E., and Newman, R 2006 Smart MEMS and Sensor Systems. 1st. Imperial College Press. ISBN 1860944930