Broom Handle

According to the laws of physics, is it possible to balance a broom on the handle end?

I was just watching a film and there was a scene in which a lecturer was teaching a physics class and commented that according to the laws of physics it was impossible to balance a broom on its handle end. He then went onto introduce the the concept of ‘feedback’ and demonstrated its value in defying physics (in a sense!) by balancing the broom on his hand.

For something to balance it has to be in a stable position, with the centre of mass over the area of contact. For simplicity, let’s assume that the broom is to be balanced on a perfectly horizontal surface. If the broom handle has a flat end, then the area of contact is the thickness of the handle – not much room for error. The broom head would need to be very symmetrical, the handle would need to be straight, and the handle-end would need to be cut exactly at right angles, otherwise it would be almost certain that the centre of mass would be outside the area of contact, and the broom would fall over. If the handle has a round end, you have the same problem but much worse – now the area of contact is a point, and it needs to be exactly under the centre of mass.

Now even this is not actually a stable state – it’s a meta-stable state, because the slightest perturbation (a bump, or even a draught) is very likely to temporarily move the centre of mass outside the area of contact and knock the broom over.

However, what feedback does is that it allows you to make a correcting movement to push the centre of mass back over the area of contact. The time you have to react is quite small but perfectly manageable. The broom still isn’t really balanced, but it appears to be.

1896 German Broom Handle Mauser C96