I’ve read many places (such as the FAA’s Instrument Flying Handbook) that a turn coordinator can sense both roll rate and turn rate due to the gyro being tilted 30 degrees.
However, why does tilting it do this, vs a turn and bank indicator without the tilt? I’m looking for an explanation of the applied physics and how the mechanisms inside the instrument turn that into a useful indication.
I do understand the principles of rigidity and precession, or at least how they apply to the attitude indicator and directional gyro, so no need to rehash those unless my question indicates I don’t actually understand them as well as I think.