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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$\begingroup$ Related VSauce "Laws and Causes" youtu.be/_WHRWLnVm_M $\endgroup$– naturallyInconsistentCommented Jul 18 at 4:13
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2 Answers
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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.
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$\begingroup$ Thanks for recommendation. However, what confuses me is not the basic idea of angular momentum, but the way these vectors add. Their direction indicates total opposite of what happens, even if I carefully try to visualize it $\endgroup$ Commented Jul 18 at 2:57
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$\begingroup$ By using addition of vectors, we may conclude that the total angular momentum $\vec{L} = \vec{L_0} + \vec{\tau} dt$ where $L_0$ is the angular momentum gyroscope has gained by let’s say initial spinning. Adding these two vectors we obtain vector $\vec{L}$ . The vector should, I suppose, have direction of new axis. However, the vector is tangent to the circular path system will follow? $\endgroup$ Commented Jul 18 at 2:50
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$\begingroup$ The change in angular momentum vector $\Delta L$, is in the same direction of the torque, and perpendicular to the total angular momentum of the object, so its effects is to change the direction of L, not the magnitude. That happens for every little $\Delta t$, that is what the diagram is showing. Not too different than circular motion, where the force is perpendicular to the velocity and so is the $\Delta v$, resulting in circular motion at constant speed. $\endgroup$ Commented Jul 18 at 2:59
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$\begingroup$ There is an interesting idea I found on YouTube: angular momentum vector of gyroscope will rotate as if it wants to come closer to torque (exerted by gravity) vector, but torque actually keeps going away from it, as if angular momentum was trying to catch the torque but it’s running away. However, it feels to me like memorization instead of understanding it in some general sense. What is strange to me is behavior of resultant angular momentum vector $\endgroup$ Commented Jul 18 at 3:12
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$\begingroup$ An answer cannot be a single picture. You should add some words of explanation and be aware that a picture without a textual description is useless for people with visual impairment using a screen reader. $\endgroup$ Commented Jul 18 at 5:41
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$\begingroup$ @GiorgioP-DoomsdayClockIsAt-90 you made me feel bad about people visually impaired. But, thinking about it more, I am sure there is software that can describe images as well as reading text. I am curious, how do visually impaired people read/listen to equations? $\endgroup$ Commented Jul 18 at 5:49