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Let's consider a wheel extended with its axle on both sides. Tie a string at both ends of axle. Note that we should keep the wheel vertical. Upon leaving one string the wheel will tilt. Now keeping the wheel vertical, put the wheel in rotation around the axle and now leave one string. One notices that wheel doesn't fall down as earlier but also rotates and revolves around the axis.

The reason to why the wheel is both rotating around axle and around axis is somehow related to angular momentum and torque but i was wondering how? enter image description here

RAHUL
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  • There is a answer, submitted by me in 2012, with discussion of the phenomenon that you ask about: gyroscopic precession In that discussion I give a 'seat of the pants' understanding (rather than only presenting abstract mathematical expressions.) (The reasoning presented can be stated mathematically, I've done that, elsewhere.) – Cleonis Apr 03 '22 at 19:05
  • Many basics physics texts point out that torque (from gravity here) is a change in angular momentum, and if there is large initial angular momentum (wheel spinning) the torque vector adds to the initial angular momentum vector and the wheel precesses and does not fall. While true, to me this is not a very satisfactory explanation. The discussion by @Cleonis (referenced in the comment above) is very good. There are many false "explanations" on the internet. A complete mathematical treatment is complicated and involves Lagrange's equations and Euler's angles. – John Darby Apr 03 '22 at 19:58
  • @JohnDarby On the question what is necessary for complete mathematical treatment. In my 2012 answer I discussed only the simplest case: all angles 90 degrees angles. When all angles are 90 degrees angles the configuration is highly symmetric; my discussion capitalizes on that. However, I believe that the same strategy can be extended to cover the total space of all angles. The key to the strategy in the 2012 answer is to not use the angular momentum vector. It is the concept of angular momentum vector that skyrockets the complexity. – Cleonis Apr 03 '22 at 20:28
  • @John Darby, Would you please post the mathematics behind it that you were talking about? – RAHUL Apr 04 '22 at 08:56
  • @Cleonis, As you mentioned the case you posted was for only 90 degrees. And I was wondering how that can be extended to higher cases? – RAHUL Apr 04 '22 at 08:57
  • The mathematics are too involved to present and discuss here. See an intermediate/advanced physics mechanics test, such as Classical Mechanics by Goldstein or Mechanics by Symon. Entire books have been written on this; e.g,. Theorie Des Kriesels by Klein and Sommerfeld (1918). The detailed motion is not simple to develop. – John Darby Apr 04 '22 at 12:49

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