Precession: A picture using only forces

[greypilgrim]

Hi,

If the axis of a spinning top isn't vertical, it starts to precess. I'm perfectly familiar with the explanation using torque, angular velocity and momentum vectors, then the direction of the precession comes out just by taking a vector product.

However, to me it's absolutely not intuitive without that math, especially the direction of the precession. I'm trying to use a "microscopic" picture with the top modeled as a ring consisting of many small masses on which only act forces (and no torque). So far I haven't been successful with this picture to produce a net force pointing in the direction of precession.

I'm not quite sure what forces I need to consider. There is gravity of course and a centripetal force to keep the masses on the ring. The sum of the centripetal forces on all the particles on the ring cancels. However there are also forces that keep the center of the ring at the same distance from the tip and the plane of the ring perpendicular to the line from the center to the tip, but I don't know how to deal with those forces.

Any ideas?

 

[robphy]

http://scitation.aip.org/content/aapt/journal/tpt/52/1/10.1119/1.4849150

"Gyroscopic Motion: Show Me the Forces!"
Harvey Kaplan and Andrew Hirsch
Phys. Teach. 52, 30 (2014); http://dx.doi.org/10.1119/1.4849150

 

[brainpushups]

Another resource which you may find interesting is a sort of 'walkthrough' of how to analyze Feynman's famous wobbling plate from the point of view of forces. However, this problem involves free precession (not torque induced precession) and so is not exactly what you asked about.