I was listening to a fairly recent podcast discussing the well known School demo of a whirling tennis ball.

The setup is to have a smooth plastic tube (say 1.5cm diameter), long enough to hold in your hand, A piece of string passes through the tube and one end is attached to a tennis ball and the other to a mass of, say 1kg.

You whirl the ball around your head and the 1kg mass hangs down, providing tension in the string (10N of force). When you get the speed right. you get an equilibrium condition - easy with a bit of skill - and, if the tube and string are smooth enough, this will last for a few seconds.

If you try to whirl a bit faster, the ball will move outwards and, of course, the 1kg mass will rise - to allow the extra string in the horizontal section. When you reach another equilibrium condition, the mass will stop rising and there will be EXACTLY THE SAME tension in the string as before (10N) - the tension can't have increased, or the mass would be pulled right up to the top and hit the tube.

I have heard other teachers state (and read in descriptions of the experiment) that the tension actually increases. This was also, sort of implied on the podcast . Also the problem has confused many teachers and students, to my knowledge because the real point is not pushed enough. It's one of those experiments which no one really gets right and they tend to rewrite the history of what they saw to fit the statement. So I put on my nitpicking hat and rushed to the computer and to protect all TNS readers.

What the experiment demonstrates is that, for circular motion, the central force (i.e. tension in the string) the radius and speed of the ball are related.

Force = mass X speed^{2}/radius is the formula.

Or

radius = mass X speed^{2}/ Force

This means that, if you have a fixed tension in the string (as in the experiment), the radius is proportional to the speed squared. It does not show the tension increases because it is constant (in this experiment), once it has settled down. Of course, you need same extra tension in the string whilst you are whirling your arm around up but that is just transitional.

If you wanted to show that the tension increases as you increase the speed you would need a spring balance in place of the 1kg mass - then the string would stay the same length and the tension would increase as you whirled faster.

The reason for the LHC needing a huge radius is shown exactly by the demo (and **this** point was properly made on the prog, as you'd expect from a Physicist) Your available deflection force is limited so you need to increase your radius. Unfortunately, to double the speed, you need to quadruple the diameter - 100+km! (Then there are relativistic effects. . . .)