I’ve seen plenty of videos explaining how gyroscopes work, but almost non of them why they are constrained to work in such way. From seeing only angular momentum vectors, how could one predict precession?
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About the angular momentum vector:
While efficient, the concept of angular momentum vector is itself already a mathematical abstraction.
In order to grasp gyroscopic precession we need to see how it relates to $F=ma$, and the concept of angular momentum vector being itself an abstraction actually makes that harder.
(See also my answer to the question: why is angular momentum a vector?)
There is a 2012 answer by me with an explanation of gyroscopic precession in which the concept of angular momentum vector is not used. The explanation given there does not lend itself to being expressed in terms of angular momentum vector.
Cleonis
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