Sci: The torsion pendulum

The torsion pendulum was a toy that used to fascinate my students when I taught a very hands-on sort of physics. Come to think of it, I enjoyed playing with it as well, but it was always much more than a toy. All the same, it's a great playwith.

Charles Coulomb used a torsion pendulum to measure tiny electrical forces and establish Coulomb’s Law in France, at about the same time, but from Cavendish’s notes, we know Michell thought of the idea first. The torsion pendulum was one of those ideas that physicists all knew, back then.

When you start a simple pendulum swinging, it keeps going because it either has a restoring force acting on it, or it has momentum. Ignore the momentum, and concentrate on the restoring force, the force that pulls somebody on a swing down from the high point, and which slows them as they approach the next high point. By a stroke of luck for physicists, the restoring force is proportional to the distance away from the lowest point, a distance called the displacement.

If the bar of a torsion pendulum is very heavy, it swings very slowly, but the restoring force will still always be proportional to the displacement, the distance from rest. Now turn that on its head: we can say just as truly that the displacement will always be proportional to the restoring force. John Michell reached this point before he died, and luckily, he had enough time to construct an apparatus which was later passed on to the immensely clever but slightly odd Henry Cavendish.

When you start any pendulum swinging, it keeps going because it either has a restoring force acting on it, or it has momentum. Ignore the momentum, and concentrate on the restoring force, which pulls my granddaughters on a swing down from the high point, and slows them as they approach the next high point. At the lowest point, there is no restoring force, but at the top, the restoring force is at a maximum.

Tto make one, take a short length of solid wood and tie a string around it, so the beam dangles horizontally. Hang it from a hook in a doorway, and nudge it so it starts to turn. You have just made a torsion pendulum, which will turn one way until all the motion energy is stored in the twisted string. Ever so gently, the beam comes to a halt, and then it unwinds as the stored energy is returned to the wood.

Back and forth, like a swinging pendulum, it repeats this over and over, controlled by a restoring force which varies over time. The force is proportional to its displacement, the beam’s distance from the rest point. Now because physicists are cunning, they can use this type of pendulum to weigh the world, and to measure the tiny forces of attraction and repulsion experienced by magnets and small electrical charges.

This is because the same restoring-force rule applies to a torsion pendulum: double the displacement and you double the restoring force. If the beam is very heavy, it will swing very slowly, but the restoring force will always be proportional to the displacement. If you use magnets or an electric charge to repel or attract a pendulum away from its rest point by 200 mm, you can calculate how big the force is.

Making your own

You will need some wire, two tables or chairs, a length of 3” x 2” timber (that is, 75 x 50 mm), about two metres long, and a metre length of 2” x 1” (41 x 19 mm DAR) dressed timber. You will also need a drill and drill bit, pliers or wire cutters, and a couple of heavy weights.

Piano wire is the best, and hardware stores sometimes sell piano wire but it might be hard to get. I have sometimes used bicycle wheel spokes for short lengths. You can even get fencing wire or baling wire to work, so long as the pendulum does not swing too far from side to side. You may want a couple of clamps to hold the whole rig on the tables: be sure to use scrap timber (and/or cloth) to protect the tables or chairs from the jaws of the clamps, or somebody will get angry!

Drill two holes close together (look at the picture below) through the larger piece of timber, and cut off about 800 mm of the wire. Push some of the wire through one hole, use pliers to bend a right angle in it, and then another, so that you can ram the short end into the second hole (the idea is to have the wire attached to the beam in such a way that the wire can’t slip.)

A torsion pendulum.

The torsion pendulum has a constant period, regardless of the starting displacement. Try varying things, and see how long the period is. (The period of a pendulum is defined as one full cycle from stop, through turn to stop, through turn back to stop again).

Extra reading for the enthusiast

Do your own digging, but three names stand out. Charles-Augustin de Coulomb developed the theory so he could carry out experiments on electrical charge in the 1820s. Some time earlier, John Michell planned to use the torsion pendulum in an experiment that would weigh the earth, but he died in 1793 and in the end, his experiment was done by Henry Cavendish.

Cavendish's torsion pendulum.

Here is how Cavendish described his pendulum:

The apparatus is very simple; it consists of a wooden arm, 6 feet long, made so as to unite great strength with little weight. This arm is suspended in an horizontal position, by a slender wire 40 inches long, and to each extremity is hung a leaden ball, about 2 inches in diameter; and the whole is inclosed in a narrow wooden case, to defend it from the wind.

Coulomb explained that a very thin wire, which delivers a very weak restoring force, would allow even small forces to be measured. And he said the beautiful part is that you can use simple mathematics to calculate the very tiny restoring force associated with a deflection of just a few degrees.

And for older readers: when you read Brave New World, you will understand what image I had in my mind as I wrote this. Yes, even STEM people read literature, which is why we now call it STEAM! Here is a quote that lacks context, quite deliberately...

Slowly, very slowly, like two unhurried compass needles, the feet turned towards the right; north, north-east, east, south-east, south, south-south-west; then paused, and after a few seconds, turned as unhurriedly back towards the left.
—Aldous Huxley, Brave New World.

Note 1: when you get a quotation as long as either the Cavendish one or the Huxley one, a web search on any ten words of it will usually get you the whole context. I just found Cabendish's quote with “to each extremity is hung a leaden ball, about 2 inches in diameter”.

Note 2: In the late 1990s, a torsion pendulum was used to prove the existence of something called the Casimir effect. You will have to hunt this one up for yourself. There will always be enough terms to help readers do an intelligent search.

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