What happens to a MEMS gyro's null point if it starts up while actively rotating? Does the internal hardware make any assumption about the initial motion of the sensor when it starts up?

Say the gyro is sitting on a 50 deg/s spinning turntable when it is initially energized. Does the gyro stabilize to 50 deg/s +/- the normal initial null instability, or does it report an initial rate of ~zero even though it is actually spinning?

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It might, but I would have to consult the datasheet for the specific device you have. I believe (I'm not referencing anything here, just going off my memory) that there are 2 ways to make a MEMS gyro, the first implements a very small beam with sensors on both sides that measures the deflection of the beam due to rotation, and the other kind heats up very small bubbles of fluid and when they are rotated their temperature changes, something to that effect. I'm pretty sure that both kinds deal with some very small physical object that applies force to a transducer, so I would think that powering the device with a force already applied would calibrate it to that accordingly. Someone correct me.
That is my guess as well, but I am hoping for a report of the form "using vendor x's gyro model y, I actually observed z".

On the other hand, the fact is that the ADXRS 610 startup behavior is widely temperature dependent. The slope of that dependency varies from one sample to the next, which leads me to think that it isn't performing a self-calibration on startup. Alas, I do not own such a sample at this time, and am hoping to lean on the material assets of the community a bit :)
I believe he asked about MEMS gyros, not laser ring gyros.

A MEMS gyroscope is a vibrating structure gyroscope. It can be implemented as the tuning fork resonator, vibrating wheel or (planar) wine glass resonator. You might find the Watson report, "Improved Vibratory Gyro Pick-off and Driver Geometry" useful in understanding the technology. It also goes into the physical characteristics of said devices, thus possibly aiding in deducing their behavior relative to the rotation question.

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