The sensitivity to angular rotation of the top class Sagnac gyroscope GINGERINO is carefully investigated with standard statistical means, using 103 days of continuous operation and the available geodesic measurements of the Earth angular rotation rate. All features of the Earth rotation rate are correctly reproduced. The sensitivity of fractions of frad/s is attained for long term runs. This excellent sensitivity and stability put Sagnac gyroscopes at the forefront for fundamental physics, in particular for tests of general relativity and Lorentz violation, where the sensitivity plays the key role to provide reliable data for deeper theoretical investigations. The achieved sensitivity overcomes the conventionally expected one for Sagnac ring laser gyroscopes.
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