Name: couple moment work in rotation
Uploaded: 2023-09-22T11:49:20.000Z
Duration: 1 min 12 s
Channel: JoVE

Consider a rigid body with two equal and opposite forces acting at two points separated by a distance.
This couple produces a moment equal to force times the distance between them. As a result, the rigid body undergoes translation as well as rotation to reach the final position.
During the translation, the work of one force is equal and opposite to the work of another force. So, the net work done by the two forces during translation is zero.
However, during rotation, angular displacement due to one of the forces gives an equivalent linear displacement which results in work.
Expressing the work in terms of angular displacement and using the expression for the magnitude of the moment of the couple gives the final amount of work done, which depends on the couple moment and the angle of rotation.
If the couple moment and the angle of rotation have the same sense, the work done by the couple moment is positive.
In contrast, if they have the opposite sense, the work done is negative.

work of a couple moment

Mechanical engineering involves the study of motion, energy, and force, and is concerned with designing, manufacturing, and maintaining mechanical systems. One important concept in this field is the couple moment, produced by two equal and opposite forces acting at two points in a rigid body separated by a certain distance.
When the rigid body undergoes a differential displacement due to a couple, its motion can be divided into two parts: equal translation of the two points to their final positions and rotation about one of them. During the translation, the two forces undergo the same amount of displacement, but in opposite directions. Therefore, the work done by the forces, being opposite in sign but equal in magnitude, results in zero work.
However, during the rotation, the force causes an angular displacement, which leads to non-zero work. The work done during rotation can be calculated as the product of the magnitude of the couple moment and the angle of rotation.
If the couple moment and angle of rotation have the same sense, the work done by the couple moment is positive. Conversely, if the couple moment and rotation angle have opposite senses, the work done will be negative.
The work done by a couple moment is an essential factor to consider in designing mechanical systems. Engineers take into account the amount of work that will be done during rotation, as well as the magnitude and direction of the couple moment, to ensure that the system will function properly.

Work of a Couple Moment

Mechanical engineering involves the study of motion, energy, and force, and is concerned with designing, manufacturing, and maintaining mechanical ...

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Mechanical Engineering

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Virtual Work

KEY TERMS AND CONCEPTS

couple moment work in rotation

Mechanical engineering studies motion, energy, and force, and it uses the idea of a couple moment to describe how two equal and opposite forces act on a rigid body. A couple moment is created when those forces act at two points on the body that are separated by a distance.

When a rigid body moves because of a couple, its displacement can be split into two parts. First, the two points move by the same amount to their final positions. Then the body rotates about one of those points.

During the translation part, each force moves the same distance but in the opposite direction. Because the forces are equal in magnitude and opposite in sign, the work done in this step is zero.

The rotation part is different. Here, the force produces an angular displacement, so the work is not zero. The work done by the couple moment equals the magnitude of the couple moment times the angle of rotation.

The sign of the work depends on direction. If the couple moment and the rotation angle have the same sense, the work is positive. If they have opposite senses, the work is negative. Engineers use this idea when they design mechanical systems, since the amount of work during rotation matters, along with the size and direction of the couple moment.

Couple Moment Work in Rotation

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Mechanical engineering studies motion, energy, and force, and it uses the idea of a couple moment to describe how two equal and opposite forces act on a rigid body. A couple moment is created when those forces act at two points on the body that are separated by a distance. When a rigid body moves because of a couple, its displacement can be split into two parts. First, the two points move by the same amount to their final positions. Then the body rotates about one of those points. During the...

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key terms and concepts

Learn how a couple moment does zero work during translation but non-zero work during rotation, and how sign depends on the direction of rotation.

Couple Moment Work in Rotation | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

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Couple Moment Work in Rotation

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