Intuition and the Magic of the Gyroscope – Reloaded

I am baffled by the fact that my article The Spinning Gyroscope and Intuition in Physics is the top article on this blog so far.

So I believe I owe you, dear readers, an update.

In the previous article I have summarized the textbook explanation, some more intuitive comments in Feynman’s Physics Lectures, and a new paper by Eugene Butikov.

But there is an explanation of the gyroscope’s motion that might become my new favorite:

Gyroscope Physics by Cleon Teunissen

It is not an accident that Cleon is also the main author of the Wikipedia article on the Coriolis flow meter, as his ingenious take on explaining the gyroscope’s precession is closely related to his explanation of the flow meter.

The Coriolis force is a so-called pseudo-force you “feel” in a rotating frame of reference: Imagine yourself walking across a rotating disk, or rolling a ball soaked in white color rolling across a black disk and watch its trace. In the center of the rotating disk, there is no centrifugal force. But you would still feel being dragged to the right if the disk is rotating counter-clockwise (viewed from the top).

This force dragging you to the right or making the path of the ball bend even in the center – this is the Coriolis force. It also makes tubes bend in the following way when a liquid flows through them and allows for determining the flow velocity from the extent of bending:

Vibration pattern of the tubes during mass flow. Credits: Cleon Teunissen.

Vibration pattern of the tubes during mass flow. Credits: Cleon Teunissen – Coriolis flow meter

The “loop” formed by the tubes rotates about an axis which is parallel to the direction of the flow whose speed should be measured (though not the full 360°). Now the Coriolis force always drags a moving particle “to the right” – same with the volume elements in the liquid. Note that the force is always directed perpendicular to the axis of rotation and perpendicular to the velocity of the flowing volume element (mind the example of the rolling ball).

In the flow meter, the liquid moves away from the axis in one arm, but to the axis in the other arm. Thus the forces acting on each arm are antiparallel to each other and a torque is exerted on the “loop” that consists of the two arms. The loop is flexible and thus bent by the torque in the way shown in the figure above.

Now imagine a gyroscope:

Gyroscope with Coriolis force per quadrant indicated. Credits: Cleon Teunissen.

Gyroscope with Coriolis force per quadrant indicated. Credits: Cleon Teunissen – Gyroscope Physics

Gravity (acting on the weight mounted on the gyroscope’s axis) tries to make the gyroscope pitch. Cleon now shows why precession results in an “upward pitch” that compensates for that downward pitch and thus finally keeps the gyroscope stable.

The clue is to consider the 4 quadrants the gyroscope wheel consist of separately – in a way similar to evaluating the Coriolis force acting on each of the arms of the flow meter:

The tangential velocity associated with the rotation about the symmetry axis of the gyroscope (“roll”, spinning of the wheel) is equivalent to the velocity of the flowing liquid. In each quadrant, mass is moving – “flowing” – away from or to the “swivel axis” – the axis of precession (indicated in black, parallel to gravity).

The per-quadrant Coriolis force is again perpendicular to the swivel axis and perpendicular to the “flow velocity”. Imaging yourself sitting on the blue wheel and looking into the direction of the tangential velocity: Again you are “dragged to the right” if precession in counter-clockwise. As right is defined in relation to the tangential velocity, the direction of the force is reversed in the two lower quadrants.

A torque tries to pitch the wheel “upward”.

.

If you want to play with gyroscopes yourself: I have stumped upon a nice shop selling gyroscopes – incl. a steampunk version, miniature Stirling engines, combustion engines (… and strange materials such as ferrofluids).

This is a gyroscope that is subject to precession – due to the counter weight:

Gyroscope gimbals kit with counter weight. Credits: www.gyroscope.com

4 thoughts on “Intuition and the Magic of the Gyroscope – Reloaded

  1. Pingback: The Twisted Garden Hose and the Myth of the Toilet Flush | Theory and Practice of Trying to Combine Just Anything

    • Thanks, Bert! Yes, I can relate! The very first gyroscopes I played with as a child were tooth wheels (with rather long axes) from old clocks I had dismantled – they could spin for quite a while… precessing and nutating beautifully!

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