= Spinning-wheel precession experiment
https://www.physics.purdue.edu/demos/display_page.php?item=1Q-30[Purdue's Bicycle Wheel Gyroscope demonstration] uses a bicycle wheel on a long axle, with a ball at one end seated in a freely rotating socket on a heavy stand. Spin the wheel by hand or with the supplied motor, seat the ball, and release the nearly horizontal axle. The readout is the axle sweeping around the vertical while the wheel continues spinning. Compare with the stopped wheel, which falls when one end is released; reverse the spin with the same support and the <precession> reverses. These are the page's documented apparatus, presentation, and reversal checks. <Bicycle Wheel Gyroscope by Purdue University, Department of Physics and Astronomy>[1Q-30, apparatus paragraph, Directions, and Suggestions for Presentation; page updated 30 November 2023]{ref}
An alternative in https://sprott.physics.wisc.edu/demobook/CHAPTER1.HTM[Physics Demonstrations by Julien Clinton Sprott] (section 1.3, Materials and Procedure) suspends one axle end by stainless steel wire and a fishing-line swivel. The swivel allows <precession> without winding up the suspension. Sprott describes the axle bobbing as <nutation> and <precession> becoming faster as spin decreases. A suspended support can move, whereas the calculation here assumes a fixed $O$; use the socket version for the closest realization. <Physics Demonstrations: A Sourcebook for Teachers of Physics (1996 online manuscript) by Julien Clinton Sprott/Bicycle Wheel Gyroscope (section 1.3)>[section 1.3, Bicycle Wheel Gyroscope: Materials, Procedure, and Discussion]{ref}
A proposed quantitative extension is to record an overhead view of an axle marker against a fixed <angle> scale, together with a side view for $\theta(t)$. Time successive overhead passages to estimate $\Omega=2\pi/T$; count passages of a rim mark to estimate $|\omega_3|=2\pi f$. Record the spin sense too. Measure $M$ and the <centre of mass> offset $d$ of the whole moving assembly, and determine its axial <moment of inertia> $I_3$ independently. Wheel, axle, support, release <angle>, and observation interval should stay the same between spin trials. Measuring both $\Omega$ and $\theta(t)$ distinguishes azimuthal <precession> from <nutation>; an overhead movie alone can miss the latter. These camera readouts and parameter checks are proposed here, not reported measurements from the demonstration pages.
For slow <precession>, compare $\Omega I_3\omega_3$ with $Mgd$, and test whether reversing $\omega_3$ reverses $\Omega$ with nearly unchanged magnitude. A brief interval minimizes spin loss from <friction>; repeat at several starting spin rates rather than interpreting an entire slowing run as one steady state. A suspension restoring <torque> governed by its <torsion constant>, socket <friction>, support motion, a misplaced <centre of mass>, and a push at release can all supply extra <torque> or change the initial conditions. The swivel reduces the twist that activates the suspension's <torsion constant>; it does not demonstrate zero <torque>.
Steady <precession> keeps $\theta$ constant; <nutation> changes $\theta$ while the axle may also precess. Sudden release generally excites both. A small initial drop is consistent with <conservation of energy> and conserved vertical <angular momentum>: some <gravitational potential energy> supplies the motion around the vertical, and the axial contribution to vertical <angular momentum> adjusts. Bearing <friction> may damp the bobbing, but an ideal undamped <heavy symmetric top> need not settle into steady <precession>. <The Feynman Lectures on Physics, Volume I by Richard Feynman and others/Chapter 20: Rotation in space> explicitly distinguishes uniform <precession> from release transients and <nutation> (section 20-3, paragraphs following equation 20.15).<The Feynman Lectures on Physics, Volume I by Richard Feynman and others/Chapter 20: Rotation in space>[section 20-3: sudden release, nutation, and the small drop needed for precessional angular momentum]{ref}
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