The gyroscope: an amazing toy, for children...

...and for physicists!

This page is dedicated to the counterintuitive proprieties of gyroscopes. The treatement at present is elementary (will become "Lagrangian" in the future), and the page contents have not been updated since June 1997.

If you possess the basics, the starred (*) sections will be sufficient to understand gyros (though they were not written to be independent!).

Index of contents:

1. Introduction

2. Basic Rotational Physics Notions

2.1 Torque

2.2 Angular Momentum

2.3 The equation of rotational motion *

3. Rigid bodies

3.1 Spinning rigid bodies and symmetry exploitation *

4. Steady precession! *

4.1 Working out W *

References

1. Introduction

You may be asking yorself "what in the world is a gyroscope?". A gyroscope is a smart word to describe a flywheel spinning rapidly about its axis. The latter is pivoted upon a structure which: allows handling of the gyro' if it's a "toy" gyroscope (Fig.1) or allows the gyroscope freedom to swing in any direction whatsoever in the case of a "scientific" (Fig.2) gyroscopes. The amazing thing about gyroscopes (and you need to have seen one, in order to appreciate what I'm trying to put in words, but I'm sure you've seen a spinning top, and it's analogous) is that they make fun of our pysical intuition and,just apparently, seem to do what they want, rather than what you think they should do. For example if you put a gyroscope (spinning with a sufficiently big speed) on the floor you think "it's obviously going to fall down" (a torque due to Gravity and the reaction force [see next heading for definitions] of the floor is applied to it). But NO(!), our little crazy gyro(or top) does not seem to obey gravity and, instead, starts (after initially giving in to gravitation very slightly) going around in circles about an axis perpendicular to the point where it touches the ground (this is what we call "precession", which is another smart word for a simple phenomenon). Another amazing feature of the gyro (and this is something you can't experience with a top) is that when you hold it in your hands and turn it one way it actually reisists you and pushes in a direction at right angles with that in which you were trying to push him. This is sometimes known as gyrocopic inertia, but there really is non need for all these technical words, because, as I will attempt to illustrate later, the misterious behaviour of gyroscopes can be accounted for as a consequence of one, very useful(!), phyisical quantity, (which some of you may recall if you've ever encountered phyisics [or listened to a Bad Religion record!]): Angular momentum (which I will soon define).

2. Basic Rotational Physics Notions

Index