Foucault Pendulum

UAA's Foucault Pendulum [pdf]

UAA Physics Professor James Pantaleone

Foucault Pendulum

Wikipedia

The Foucault Pendulum is named for the French physicist Jean Foucault (pronounced "Foo-koh"), who first used it in 1851 to demonstrate the rotation of the earth. It was the first satisfactory demonstration of the earth's rotation using laboratory apparatus rather than astronomical observations.

If you start a Foucault Pendulum swinging in one direction, after a few hours you will notice that it is swinging in a quite different direction. How does this happen?

Imagine you are in a museum located at the north pole and that the museum has a Foucault Pendulum suspended from the ceiling at a point exactly over the pole. When you set the pendulum swinging it will continue to swing in the same direction unless it is pushed or pulled in some other direction. (This is due to a basic law of nature called Newton's First Law.) The earth, on the other hand, will rotate once every 24 hours underneath the pendulum. Thus if you stood watching the pendulum, after a quarter of an hour or so, you would be likely to notice that the line of the pendulum's swing has changed to a different direction. This would be especially clear if one marked the position of the line of swing in the morning and had the pendulum knocking down pegs arranged in a ring at the center.

However, if you are standing on the floor of a building housing a pendulum (which is connected to the earth), you will naturally think that the floor is stable and the pendulum is moving. This is because we naturally assume that the base on which we stand is stable unless our eyes or sense of balance tells us otherwise. If our base moves slowly or accelerates smoothly, we are easily fooled into thinking that another object we see is moving. You have probably experienced this in a car, a train, or an airplane, that begins to move very slowly and smoothly, and for a split second you think that a nearby car, train, or even a building, seems to move. Thus, after thinking for a while about the total situation you might be willing to agree that what you are seeing is a real demonstration that the earth is rotating under the pendulum and that the line of swing of the pendulum just appears to rotate.

At the north pole the apparent rotation would be a full circle of 360 degrees each 24-hour day, or about 15 degrees per hour. This case is fairly simple, because here the earth and the pendulum are not exerting much influence on each other. As you move off the north pole down to a more southerly point like Washington, for example, the earth not only rotates under the pendulum, but it carries Washington, the building, and the pendulum, in a great circle about its axis. That is, the motion of the earth is now mixed in a complicated way with the motion of the pendulum. As you can prove if you watch the pendulum for a while, the effect of this is to slow down the apparent rotation of the swing. Instead of seeming to rotate 15 degrees (about 1/24 of a full circle) in one hour, it only changes by about 9 degrees (about 1/40 of a full circle). The further south you go, the slower the apparent rotation gets, and at the equator there is no rotation at all. Below the equator the apparent rotation begins again, but in the opposite direction.

Any pendulum consists of a cable or wire or string and a bob. For a pendulum to easily demonstrate the Foucault effect, it should have as long a cable as possible (this one is 52 feet) and a heavy symmetrical bob (this one is hollow brass, weighing about 240 pounds). Like all pendulums this one loses a bit of energy with each swing due to friction from air currents and vibrations in the cable and other factors. Thus, left to itself the pendulum would swing in shorter and shorter arcs until after a few hours it will decrease almost to zero. To keep the Foucault Pendulum going, one must replace the energy lost with each swing. This can be done by giving the pendulum a little "kick" with each swing.

To do this, two iron collars are attached to the cable near the top. There is a doughnut-shaped electromagnet built into the ceiling, and the iron collar swings back and forth inside the hole of the doughnut. When the pendulum cable reaches a particular point in its swing, it is detected by an electronic device and the magnet is turned on at just the right time to give the collar (and thus the cable and the bob) a little "kick" in the exact direction of its natural swing. This restores the energy lost during the swing and keeps the pendulum from stopping. It has no effect on the direction of the swing, and thus does not interfere with the demonstration that the earth is rotating.

Some people have built their own pendulums; you don't need a ceiling 50 feet high. If you are interested in building your own, you might like to go to your library and read two articles from Scientific American magazine: pages 115-124 of the June 1958 issue and pages 136-139 of the February 1964 issue. You may also wish to contact the California Academy of Science in San Francisco, California.