Why do gyroscopes not fall down?

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A.T. said:
Laithwaites misconceptions ...
I think there are a couple in that video. I only posted the video because of the large gyros. Near the start of the video, he demonstrates that apparent static friction is less for the smaller objects on a tilted surface, without a clear explanation (which is probably related to surface area versus mass, since the smaller objects are thinner vertically (I seem to recall something about a type of bonding that occurs between solid objects that adds to static friction effects)). Next he doesn't understand how transformers work with a pair of coils with the driving one on the bottom and the driven on placed on top.

As for the large gyro on the stand with the spring, the spring supported mount does not move upwards despite his claim that it does so when he speeds up the the rotation of the pole. However, the center of mass of the system does have an effect. When the center of mass is accelerated vertically, the spring supported mount will react accordingly. Also when he's grabbing the pole, he could be exerting a vertical force in addition to the horizontal force.

Near the end of the video, he demonstrates a "gyro" made up of a bunch of masses at the end of spokes. This demonstrates the 90 degree delay from torque to peak position lateral position of the masses (which is why the cyclic control on a helicopter is advanced by 90 degrees).
 
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A.T. said:
An alternative is the explanation in the video below, which uses linear dynamics to explain it (e.g. force couple instead of torque):



If you like the above explanation, but want more detail on the internal transmission of the forces in the spinning rigid body, I recommend the below animation:

 
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