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Analysis: The twisting effect of a force
Here you'll gain the words for describing twist, and the method for calculating it.
SPEAKER: In week 2, forces acted as a single point. Next, we look at forces that act at several points in a rigid body. For that, we need to know about twist. That’s our topic for week three. Here is a spanner being used to tighten a nut. Car maintenance manuals often list recommended tightening torques. Now “torque” is one word for twisting effect. It is also used to specify the twist that a motor can supply. Its units are Newton metres. Another word for twisting effect is “moment.” Here is a rigid body. It’s a circular disc. The disc is supported from a back plate by strips from an aluminium can. The strips are arranged to allow rotation only.
The back plate is supported from a fixed plate by four more strips of aluminium taken from a soft drink can. This time, they are arranged so that it can only translate horizontally. Just like the force transducers in weeks one and two, these spring assemblies can measure the twisting force and the translating forces we load up the disc. We load it up with weights that act through strings that go around pulleys. Maybe you’d like to make your own rig like this one. Now we’ll use this rig to demonstrate the twisting effect of a force. With only a lightweight hook on the string, you’ll note where the two pointers point. Now we’ll add two washers to the left string.
The disc has rotated anti-clockwise about half a division and translated to the left a whole division. Now we’ll add two more washers. The disc has rotated more and translated more, too. It’s about double the amount. So double the load has given roughly double the deflections. Although it isn’t demonstrated here, doubling the diameter of the disc would double the twist without affecting the translation. Now we will see how to calculate the twist due to a force. We call it the moment due to a force. This is how it’s done– the moment due to force F about axis A is given by the magnitude of the force times the perpendicular distance from the axis to the line of action of the force.
In our model, the moment arm is always the same, so double the force should give double the moment, as we found. It’s not always that simple. For example, with this configuration, you have to use basic trigonometry to find the moment arm. In two dimensions, an axis viewed end-on looks like a point, and we often say moment about a point. But moment about an axis is more precise. The moment has a direction, too. In two dimensions, the direction is either clockwise or anti-clockwise. If you specify a sign convention, this becomes either positive or negative. With our model the force is trying to rotate the body anti-clockwise around the axis, so it is a counter-clockwise moment.
And it will be positive if we specify counter-clockwise as positive. Of course it will be negative if we specify clockwise as positive. That’s the basic idea. Now we’ll use it to check out the experiment on balancing. Remember, we suspended the card about the axis when axis was a pin. It looks like a point end-on. The moment of one of the weights about a suspension point is one way, and the moment of the other weight is the other way. One is positive and the other is negative. And if the card is in equilibrium, these moments must add to 0. We will take a moment to check that our result agrees with this.
You should draw an FBD when doing these sorts of calculations, even if it’s a simple one. Here’s what the FBD for this looks like. All the information you need is on the drawing, the forces and the dimensions. We’ve included the weight and the reaction at the pivot as well. Now theoretically, there could be a horizontal component of the reaction force; but since all the other forces are vertical, there won’t be a horizontal component in our case. And this is how you use the FBD. We’ll take moments about o. This way, the forces at o don’t come into the equation, because there is no moment arm. In the analysis, we use the sigma sign to indicate adding.
Let’s check with our experiment on balancing. We got these values– F1 was 8 washers, F2 was 4 washers, D1 was 20 millimetres, and D2 was 40 millimetres. Put this into the equation on the left hand side of the equation, which is the sum of the moments is 0. And all is well. In the next video, we will look at pure twist, the couple.
Here you’ll gain the words for describing twist, and the method for calculating it.
The general public has some idea of forces, but for them twist (or the related words moment or couple or torque) is a mystery.
It’s not really a difficult concept to grasp, but it does have wide-ranging implications. Once you’ve grasped it you’ll have expanded your understanding of the world. And you’ll have gained a vital part of ‘engineers’ eyes’.
Feel free to use the data we’ve supplied in the Downloads section below.
Talking points
- Where have you come across any of the terms for twist that were mentioned in the video (moment, torque), or the special twist called a ‘couple’ (which we’ll introduce later)?
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Through Engineers' Eyes - Introducing the Vision: Engineering Mechanics by Experiment, Analysis and Design
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Through Engineers' Eyes - Introducing the Vision: Engineering Mechanics by Experiment, Analysis and Design
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