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In many demonstrations of analysis of gyroscopic precession, the analysis goes on by choosing two axes, one about which angular momentum is calculated, another about which torque of gravity is considered.

For example: consider a precessing supported on a block. Angular momentum about the rod connecting the block and the centre of the wheel is in radial direction, however the torque of gravity in this axis is 0, as it passes through centre of mass. If the line perpendicular to block and through point of attachment to block is taken as axis, torque of gravity is constant, but angular momentum is variable.

Reference:enter image description here Note that the author takes angular momentum about the axis, but torque about the point $O$. The torque about the axis is $0$

How do we correctly choose the axes then?

Eisenstein
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  • Can you provide the diagram ? As of now, it is not clear what you are trying to say – khaxan Sep 23 '23 at 16:19
  • @khaxan Added a picture for better clarity. – Eisenstein Sep 23 '23 at 16:31
  • You can refer to this answer for intuition: direction of gyroscopic precession – khaxan Sep 23 '23 at 16:38
  • @khaxan I have no problem understanding that. My question was regarding how does different choices of axis maintain the physics of the system? – Eisenstein Sep 23 '23 at 16:40
  • Initially(without letting go of the wheel), the wheel had angular velocity along the horizontal rod. Now when you let go of the wheel, a torque develops but is in 90 degs with the angular velocity. So angular velocity keeps changing direction but HOW? By moving the axis of rotation of the wheel (along the rod). Linear analogue: what happens if force is 90degs to the velocity vector? – khaxan Sep 23 '23 at 16:44
  • @khaxan Yes I also got that. But why is choosing clearly different points and axes to calculate torque and angular momentum allowed? – Eisenstein Sep 23 '23 at 16:47

1 Answers1

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About the onset of gyroscopic precession:

There is a 2012 answer by me about gyroscopic precession In that answer I discuss the mechanism of onset of gyroscopic precession and the nature of sustained gyroscopic precession.


In addition:
2010 article by Svilen Kostov and Daniel Hammer:
It has to go down a little, in order to go around

Kostov and Hammer describe a tabletop experiment that they have performed for the purpose of corroborating a remark by Richard Feynman in the Feynman lectures.

Feynman points out: the precessing gyro wheel has an angular momentum around the axis of precession, where does that angular momentum come from?

Feynman points out that momentum considerations alone are sufficient for the conclusion that as the precessing motion commences the center of mass must drop a little. Hence the statement: 'It has to go down a little, in order to go around'.

Feynman's discussion is in Volume I, section 20
In section 20-3 (following figure 20-5) Feynman's discussion is along the following lines: let's say that before the gyro wheel is released the spin angular momentum of the gyro wheel is pointing in adirection in the horizontal plane. We have that when the gyro wheel is released the gyro wheel initially drops a little. That corresponds to a direction of the spin angular momentum (of the gyro wheel) in a slightly downward direction. The difference between those two angular momentum vectors is a vector in the vertical direction. That corresponds to the angular momentum of the precessing motion of the gyro wheel.

As we know: the faster a gyro wheel is spinning, the slower the corresponding rate of precession.

Kostov and Hammer test a gyro wheel at 5 different rates of spin. The higher the rate of spin, the smaller the amount that the center of mass drops. Kostov and Hammer report that in their tabletop experiment the amount that the center of mass drops is in accordance with what is to be expected on the basis of momentum considerations.


General discussion

Considerations of angular momentum are not suitable for intuitive understanding of what is going on. The concept of angular momentum vector is a highly abstract concept, and in cases such as gyroscopic precession it is far from transparent.

In my 2012 answer I capitalize on symmetry. I divide the gyro wheel in 4 quadrants. There are horizontal and vertical mirror symmetries. We have that the response of the gyro wheel to an applied torque is at a 90 degrees angle. The quadrants approach allows transparent explanation of that 90 degrees angle.

Cleonis
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