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In this video, we see a little toy vehicle with two wheels that is unstable by itself. However, when an attached gyroscope is running (a rotating mass) it stabilizes itself.

When the mass starts to rotate and accelerates, at some point, see here, the vehicle suddenly starts to lift itself from lying on the table to an upright position. I am wondering, where does the torque/force came from to lift the vehicle?

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See my 2012 answer for an explanation of gyroscopic precession, and the forces involved.

This exposition of the physics of gyroscopic precession is not in terms of the angular momentum vector. Instead this exposition capitalizes on symmetry; a wheel is very symmetric.


Specific to the device demonstrated in that video:

The suspension of the gyro wheel of that device is such that an actuator is set up to change the orientation of the gyro wheel with respect to the device.

The camera angle of the video is unfortunate: the actuator is to a large extend obscured. Whoever made that video did a poor job; the crucial bit is obscured.

The actuation movement can be seen at 1:30 into the video. You see the actuator changing the angle of the gyro wheel with respect to the device as a whole.

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  • $\begingroup$ If I got it right: The wheel in the video is spinning from right to left (in the perspective shown in the video) around the yaw axis when the vehicle lies on the table. Hence the angular momentum vector points down. So, to lift it up, the wheel must turn from the front to the back (torque vector pointing to the left) around the pitch axis. The effect would be a spin from left to right around the roll axis, which results in the uplift. So, this is the explanation, right? I guess I can see this spinning in the pitch direction when the vehicle lifts itself. $\endgroup$
    – StefanH
    Nov 12 '21 at 22:36
  • $\begingroup$ @StefanH Well, to try and understand gyroscopic precession in terms of angular momentum vector being affected by torque is to introduce unnecessary complexity. The angular momentum vector is a highly abstract concept, unnecessarily abstract for understanding gyroscopic precession. I added a paragraph to my answer, specifying that the explanation in my 2012 answer does not use the angular momentum vector. $\endgroup$
    – Cleonis
    Nov 12 '21 at 23:05
  • $\begingroup$ I see, the rotation "transports" the impulse, so to say, resulting in this "shifted/rotated new rotation". Nice explanation btw! $\endgroup$
    – StefanH
    Nov 12 '21 at 23:26
  • $\begingroup$ @StefanH I think of it as response to being set in motion. Let the gyro wheel be spinning: let's call the spin axis the x-axis. Introduce another rotation, let's call the axis of that the y-axis. Then in response the gyro wheel will turn around the z-axis. The response motion is at 90 degrees angle to the input motion because of quadrant symmetry. (Some authors offer the suggestion that the response of the gyro wheel is a delayed response, responding 90 degrees later than receiving the input. That suggestion could not be more wrong; there is zero delay: the response is instantaneous) $\endgroup$
    – Cleonis
    Nov 13 '21 at 0:07

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