Let's consider the classical example, the wheel hung by one side of the axle:

bicycle wheel¹

When the wheel is not spinning, it will tilt down the free end of the axle first.

When the wheel is spinning, it will rotate around the suspension point due to precession. I do understand how it comes to be—the acceleration at the top/bottom points change the direction of the part passing through that point so that the plane of rotation rotates around the vertical axis. When the rotation is “fast enough”, it's obvious.

But what happens in between? What if the wheel is spinning extremely slow. One turn per minute? One turn per hour? One turn per millenium? In fact in practice you won't ever achieve exactly zero angular momentum as it will inherit some from the Earth.

So how does the transition between the two kinds of behaviour look?

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    $\begingroup$ There is a fine discussion of this problem in the article "'It has to go down a little in order to go around'—Revisting Feynman on the Gyroscope" which appeared in The Physics Teacher vol 49 in 2011. The Discussion by Feynman referenced in the title is in The Feynman Lectures on Physics which are now available in their entirety on-line. Both are worth reading. In anycase, the key vocabulary word that would help with searching for material on the subject is nutation. $\endgroup$ – dmckee --- ex-moderator kitten Aug 3 '18 at 2:52
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    $\begingroup$ The article is available on Arxiv: 'It has to go down a little in order to go around' Feynman's discussion is in section 20-3, 'gyroscopes', part of chapter 20 Rotation in space $\endgroup$ – Cleonis Aug 3 '18 at 8:29

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