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A simple rate gyro, which may be used to measure angular speeds, is shown in Figure P6.32. The angular speed of spin is ω and is kept constant at a known value. The
angle of the rotation of the gyro about the gimbal axis (or the angle of twist of the torsional spring) is θ and is measured using a displacement sensor. The angular
speed of the gyro about the axis that is orthogonal to both gimbal axis and spin axis is Ω. This is the angular speed of the supporting structure (vehicle), which
needs to be measured. Obtain a relationship between Ω and θ in terms of parameters such as the following:
J is the moment of inertia of the spinning wheel
k is the torsional stiffness of the spring restraint at the gimbal bearings
b is the damping constant of rotational motion about the gimbal axis and the spinning speed
Figure P6.32

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