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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.
In week two, we considered forces that acted as a single point. Now we’ll consider rigid bodies where forces act at several points. One difference between forces acting a point and acting on a rigid body is it introduces the effect of twist. Here is a spanner being used to tighten a nut. Perhaps you’ve looked at a car maintenance manual and noticed the recommended tightening torques. Torque is one word for twisting effect. It is often used when specifying a twist to the spanner, or the twist of a motor. Its units are Newton metres. Another word for twisting effect is the moment. Here’s a rigid body with a force acting on it.
The moment about axis A due to the force is the magnitude of the force times the perpendicular distance from the axis to the line and action of the force. We call that 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 the sign convention, this becomes either positive or negative. In the case of this diagram, the force is trying to rotate the body clockwise around the axis.
So it is a clockwise moment, and it would be positive if we specify clockwise as positive. It would be negative if we specify counter-clockwise as positive. You can see this from the experiment on balancing. The card is suspended about an axis, the pin. It looks like a point end-on. The moment of one of the weights about the suspension point is one way, and the moment of the other weight is the opposite way. So one is positive, and the other is negative. And if the card is in equilibrium, they must add to zero. We’ll take a moment (the pun is intended) 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. Notice that all the information you need is on the drawing– the forces and the dimensions. We’ve included the weight and the reaction of the pivot, as well. There could theoretically be a horizontal component of the reaction force, but since all the other forces are vertical, it won’t have 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. We use the sigma sign to indicate adding.
Let’s check with our experiment on balancing. We got these values. F1 was eight washers. F2 was four 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 try something more complicated.
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)?
This article is from the online course:
Through Engineers' Eyes: Engineering Mechanics by Experiment, Analysis and Design
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Through Engineers' Eyes: Engineering Mechanics by Experiment, Analysis and Design
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