Analysis: Pure twist – the couple

SPEAKER: Before we look at the experiment on pure twist, we’ll do an extra test with our disc rig. We left that rig with four washers on the left hand string. Now we will take two of the washers off the left hand string, and add them to the right hand string. The rotation, as much as before. But the translation has gone back, more or less, to the starting value. That shows there is no net force. We have generated a couple– two equal, opposite parallel forces with a separation between them. This is an important concept. We will come across this a lot. It’s something really quite elegant. It works like this. The two equal and opposite forces, F cancel out.

But because they are separated by a distance, a, they leave a pure twisting effect. And that’s what we call a couple. The moment due to a couple is a times F, whatever point you choose when you calculate it. Sometimes we call it a pure couple, uncontaminated by any net force. You could try taking moments about different points. Pause the video and calculate the total moment of the two forces at one, a point on the line of action of each force, and, two, a point halfway between them.

You should get a times F clockwise each time. Theory says that the effect of a pure couple on the equilibrium of a rigid object is independent of where it is applied. So you just add it in when you apply some of the moments equals nought. We’ll be doing that later. Now let’s look at the experiment on pure twist. We’ll follow the forces in the linkage and see how it works. Notice that the two small links are equalisers. They equalised the forces on each end of the link. Take moments about the centre of each one, if you are not convinced.

Starting with the lower right hand link, the string on the left hand end is connected directly to the large cardboard shape. The string on the right hand end of the link takes a longer path. It pulls down on the right end of the link above it. The other end of this upper link then pulls up on the string at that end. This string is connected to the large cardboard shape. Now we have the classic requirement for a pure twist on the large cardboard shape– two equal, opposite parallel forces with a distance between their lines of action. That’s enough for now. We’ll look at this experiment again when we have equilibrium with a rigid body under our belt.