Foucault Pendulum Background

What is a Pendulum?

A pendulum is any mass that is suspended by a rigid arm or flexible string. You can swing the mass and the mass will continually move back and forth (oscillation) until it stops from friction. Examples of pendulums are in grandfather clocks and a child’s swing.

Jean Bernard Léon Foucault’s Pendulum

Jean Bernard Léon Foucault was a French physicist. He found that if he took a flexible metal rod, clamped it at one end in a lathe, and made it vibrate, he would see a strange effect. As the lathe spun, the vibrating rod would tend to stay in the same plane. Foucault realized that this would apply to any oscillating mass. If you had a pendulum swinging, you could rotate the pendulum and its stand and still have the swing tend to stay in the same plane. He also realized that if you had a big enough pendulum and could keep it going long enough, that it too would tend to stay in the same plane with relation to the rest of the universe. But to the people watching this on earth, the direction of the swing would seem to be changing, because the Earth is rotating.

Foucault’s Pendulum was the first non-astronomical instrument to show that the earth rotates. His original pendulum was 220 ft (67 m) tall and had a bob that weighed 62 lbs (28 kg). The bob was connected to the ceiling by a wire. When the bob was pulled back and let go, the pendulum swung back and forth. The pendulum continued to swing for many hours because it was very massive and the angle it moved through at the top was very small. Over time, the direction of the swing turned or rotated, just as Foucault predicted. There are only two explanations for this phenomenon – one, that the universe is turning around the Earth, or two, that the Earth is rotating. Considering how far away the stars and galaxies are, for the former explanation to be true, they would have to be moving extremely fast (faster than the speed of light) to be rotating around the earth. Since there is no indication that they either are moving that fast or even can move that fast, the second explanation, that the Earth is rotating, must be true. Occam's Razor states, “Given two equally predictive theories, choose the simpler.” So it’s much simpler to believe that the Earth is rotating than that everything else in the universe is rotating around the Earth.

In 1851 Foucault built his pendulum and exhibited it at the Panthéon in Paris. He received the Copley medal for his work on this pendulum and a similarly behaving gyroscope. The Copley medal was the highest award granted by the Royal Society of London. His pendulum was soon on public display and was all the rage in Paris. This amazing demonstration has been on public display ever since then.

 

Present Day Foucault Pendulums

Ever since Foucault demonstrated his first pendulum, the big, but relatively simple device has been duplicated not only by science museums the world over, but by other institutions that want the singularly impressive device in their atriums. There are at least one hundred of the big Foucault Pendulums all over the world. Most large science museums have one, but they are also found in such diverse places as the UN headquarters in New York and a science station at the South Pole.

The reason that there aren’t more Foucault Pendulums installed is because they are expensive to buy and a large building is needed in which to house them. With the advent of our new small Foucault Pendulum, this situation will change and these devices will be much more accessible to everyone.

Prof. Dooley’s Experiments and Other Foucault Pendulums

The long parametrically driven pendulum was created by Sir Brian Pippard of Cavendish Laboratory in Cambridge, England in 1988. Prof. John Dooley of Millersville University in Millersville, Pennsylvania and his students pioneered the use of the short parametrically driven pendulum. Their second pioneering innovation was the use of a light bob. Previous small pendulums used a heavy bob, usually made of lead. This product is an extension and refinement of the work done by both Prof. Dooley and Sir Pippard.

For an overview of the small Foucault Pendulum go to Prof. John Dooley’s web site: http://muweb.millersville.edu/~physics/exp.of.the.month/35/index.html

Most Foucault Pendulums use an electromagnet located in the base or on the wire near the top to keep the pendulum moving. Most driven Foucault Pendulums also use a Charron ring. This is a ring that is placed at the top of the pendulum wire to keep the pendulum movement confined to a circular path. We frown and scoff (scoff, scoff, scoff) at both these mechanisms. The use of a magnet to pull or push to wire or bob seems like cheating, even if it technically isn’t. It certainly looks like the magnet is not only driving the bob, but could be turning the path of the swing. The Charron ring is another gimmick that is ideally supposed to dampen transverse motions and limit the amplitude of the swing without affecting the path.

But how do we know it was installed that way? Is it possible for the ring to actually cause the swing direction to change? We don’t know if any particular Foucault Pendulum out there is being “helped” by a improperly installed Charron ring. We just know that they keep adjusting the ring until the pendulum works properly. But this begs the question, “Is it turning because the ring is not adding to the turning motion or because it is?”

The Foucault Pendulum’s Energy Pump

The Science Design Foucault Pendulum uses only a vertical driving motion. If it isn’t vertical, the pendulum’s swing won’t turn as well and the pendulum might find a preferred direction.

A pendulum is constantly converting potential energy to kinetic energy and back again. At the end of the swing, the motion of the pendulum is zero, but the pendulum is at its highest point and highest maximum potential energy. The pendulum then falls from this highest point to the middle. It then has zero potential energy but maximum kinetic energy (maximum velocity). The equation that shows the potential energy is:

E = gmh

The equation that shows the kinetic energy is:

E = ½mv²

Since energy is mostly conserved between the top and bottom parts of the swing. We can equate the two equations.

gmh = ½mv²

This can be simplified to:

h≈20v²

This equation shows that the greater the height of the bob, the faster it will swing at the bottom. The faster the bob moves, the higher the end of the swing will be. We can add energy either by making the bob move faster at the bottom, by raising the bob higher at the top of the swing, or by increasing the mass of the bob. This pendulum adds energy by increasing height (h) at the top of the swing.

The vertical motion of the bob and wire is adding energy at the ends of each swing. The bob is being dropped at the ends of the swing and the bob is being raised in the middle of the swing. This has the effect of increasing the (h) in the equation for every swing. Grabbing the bob at the end of the swing and raising it higher would give the same effect. Since the bob has farther to fall it gains energy. Raising the bob in the middle does not take kinetic energy from the swing.