A mechanical gyroscope is a device consisting of a wheel or disc mounted so that it can spin rapidly about an axis, which is itself free to alter in direction. The orientation of the axis is not affected by the rotation of the platform it rests upon. The surface beneath it can rotate while the gyroscope remains static in space.
In these discussions the mechanical gyroscope is used as evidence that the Earth is not rotating, since the gyroscope will maintain the same position in space for long periods of time. The typical response to these experiments is to dismissively suggest that the gyroscope must not be sensitive enough, or to claim that too much weight is being put on the bearings as to prevent free rotation. However, the same gyroscopes are seen to rotate when placed on a slowly rotating platform with a 24 hour period, contradicting the assertions of faulty equipment.
John Savage of Savage Plane has conducted a number of different types of gyroscope tests, showing that the gyroscope is stationary when sitting on the Earth's surface, and also appears unaffected by the underlying rotation when sitting on a platform rotating with a 24 hour period.
Rob Durham has provided content suggesting that the mechanical gyroscope stays static in space.
Flat Earth and the Gyro REVISITED - "A follow up to my gyro video series showing more tests that would seem to suggest that science has lied to us about gyroscopes."