Rotational stability and Fosbury Flop questions

[John3022]

TL;DR Summary

Why are rotations more stable the faster they rotate and what is the consequence of the fosbury flop?

What is the consequence of the center of gravity passing below the rod in the high jump? Fosbury flop.
Which equation is responsible for a bike being more stable the faster it's driven? and in rotating things in general being more stable the faster they're rotating.

 

[Lnewqban]

Welcome, John!

Please, see:
https://www.pbs.org/newshour/science/the-not-so-hidden-physics-of-your-favorite-olympic-event

 

[jbriggs444]

Which equation is responsible for a bike being more stable the faster it's driven? and in rotating things in general being more stable the faster they're rotating.

Bicycles are complicated. There is more than one thing going on. You should not expect to find a single equation with a single unknown called "stability". Instead, you will find a collection of inter-related equations with a plethora of parameters.

Gyroscopic precession in particular is a bit simpler. You are probably concerned with torque-induced precession: https://en.wikipedia.org/wiki/Precession#Classical_(Newtonian)

The faster something is spinning, the less precession rate you get for a fixed input torque.
The faster a bike is moving, the more centripetal force you get for a fixed yaw rate.

 

[berkeman]

Welcome to PF.

Which equation is responsible for a bike being more stable the faster it's driven?

Which kind of stability? Stability when everything is mellow and changing slowly, or the loss of stability called a "tank slapper" at speed? (Full disclosure -- I saved my one and only life threatening tank slapper merging onto a freeway at high speed in an early morning commute, and installed a steering damper on my CBR600F4 the next week).