The Physics behind the classic Gyroscope

Have you ever wondered what a Gyroscope was, and what, if anything, are their practical uses? Well the earliest known gyroscope was made by Johann Bohnenberger in 1817, although he called it simply the 'Machine.' Gyroscopes move in peculiar ways and in some cases, even seem to defy gravity. These special properties make gyroscopes useful in everything from toys to navigation systems on ships and even the space shuttle.

The spinning gyroscope in the picture here is displaying an effect called precession. Basically, the gyroscope is trying to rotate about an axis perpendicular to the force axis (in this case the spin axis) and the string is lifting the machine (opposite this force). Sounds simple, right? Read on...

The "simple" physics of a gyroscope would include a study of precession, nutation, angular velocity, and angular momentum. Plus a handful of other force vectors and scalars. A scalar is a simple number with a magnitude but no direction-- i.e., 12 rpm. A vector is a unit with both a magnitude and a direction-- i.e., a car traveling 50 mph due east would have a velocity vector. The following simple equation summarizes the variables of a spinning gyroscope...

where the bold symbols (tau, lambda, omega and alpha) represent vectors. Tau is the torque, lambda (the capital L) is angular momentum, omega (looks like a lower-case w) is the angular velocity, and alpha is angular acceleration. The capital I is its moment of inertia (a scalar). So to figure out the torque vector, one just has to take the first derivative of the angular momentum with respect to time. Okay, so maybe it's not that simple for anyone without a PhD in physics or math.

But in a nutshell, a gyroscope works because of the principle of conservation of angular momentum. If a gyroscope is spinning, its torque will be a force vector pointing from the center and perpendicular to its angular momentum. If it's spinning fast enough, this force will be great enough to make the gyroscope "stand up" and apparently defy gravity.

You can easily try this experiment yourself. A spinning gyroscope with its spin axis oriented vertically will stand perpendicular on the tip of a pencil or even balance on a string as you can see in the picture here. A spinning gyroscope with its spin axis oriented horizontally will balance on its side (as seen in the top picture).

References:

U.S. Department of Energy's Newton BBS, "Ask a Scientist" feature at www.newton.dep.anl.gov. Richard A. Gerber.

Brain, Marshall. ‘How Gyroscopes Work’, howstuffworks.com