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

Considérons un corps rigide avec deux forces égales et opposées agissant en deux points séparés par une distance.
Ce couple produit un moment égal à la force multiplié par la distance qui les sépare. En conséquence, le corps rigide subit une translation ainsi qu’une rotation pour atteindre la position finale.
Au cours de la translation, le travail d’une force est égal et opposé au travail d’une autre force. Ainsi, le travail réseau effectué par les deux forces pendant la translation est nul.
Cependant, pendant la rotation, le déplacement angulaire dû à l’une des forces donne un déplacement linéaire équivalent qui entraîne un travail.
En exprimant le travail en termes de déplacement angulaire et en utilisant l’expression de l’intensité du moment du couple, on obtient la quantité finale de travail effectué, qui dépend du moment du couple et de l’angle de rotation.
Si le moment de couple et l’angle de rotation ont le même sens, le travail effectué par le moment de couple est positif.
En revanche, s’ils ont le sens opposé, le travail effectué est négatif.

<ol>
	<li>Hibbeler, R.C. (2016). Mécanique du génie : Statique. Quatorzième édition, New Jersey : Pearson. Section 11.1, p. 582.</li>
	<li>Meriam, J.L., Kraige, L.G. et Bolton, J.N. (2016). Mécanique de l’ingénierie : statique et dynamique. Huitième édition, Singapour : John Wiley & Sons. P. 393 et 394.</li>
	<li>Beer, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. et Self, B.P. (2016). Mécanique vectorielle pour les ingénieurs. Onzième édition, New York : McGraw-Hill Education. Section 10.1A, p. 577</li>
</ol>

travail d'un couple moment

Work of a Couple Moment

L'ingénierie mécanique implique l'étude du mouvement, de l'énergie et de la force, et est concernée par la conception, la fabrication et la maintenance des systèmes mécaniques. Un concept important dans ce domaine est le moment de couple, produit par deux forces égales et opposées agissant sur deux points d'un corps rigide séparés par une certaine distance. Lorsque le corps rigide subit un déplacement différentiel dû à un couple, son mouvement peut être divisé en deux parties : une translation égale des deux points vers leurs positions finales et une rotation autour de l'un d'eux. Pendant la translation, les deux forces subissent la même quantité de déplacement, mais dans des directions opposées. Par conséquent, le travail effectué par les forces, étant opposé en signe mais égal en magnitude, donne un travail nul. Cependant, pendant la rotation, la force provoque un déplacement angulaire, ce qui entraîne un travail non nul. Le travail effectué pendant la rotation peut être calculé comme le produit de la magnitude du moment de couple et de l'angle de rotation. Si le moment de couple et l'angle de rotation ont le même sens, le travail effectué par le moment de couple est positif. En revanche, si le moment de couple et l'angle de rotation ont des sens opposés, le travail effectué sera négatif. Le travail effectué par un moment de couple est un facteur essentiel à prendre en compte dans la conception de systèmes mécaniques. Les ingénieurs tiennent compte de la quantité de travail qui sera effectuée pendant la rotation, ainsi que de la magnitude et de la direction du moment de couple, pour s'assurer que le système fonctionnera correctement.

Travail d'un couple Moment

Le génie mécanique implique l’étude du mouvement, de l’énergie et de la force, et s’intéresse à la conception, à la fabrication et à l’entretien ...

Education

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Mechanical Engineering

Génie mécanique

Unit 1

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Virtual Work

Travail virtuel

KEY TERMS AND CONCEPTS

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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

work

Work in Force and Motion

Work connects force, motion, and energy in mechanics. It happens when a force acts on an object and the object moves along the line of action of that force. Work can also be described as energy transfer caused by applying a force, which leads to a change in the object’s motion or position. Work is calculated as the force multiplied by the part of the displacement in the same direction as the force. It can also be written as the dot product of the applied force and the object’s displacement. In...

work of a couple moment

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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Virtual work is a mechanics principle used to check equilibrium with imaginary motion. If a body is in static or dynamic equilibrium, the total virtual work from external forces and couple moments must be zero for any virtual displacement. A virtual displacement is an imagined small movement. It can be a shift or a rotation. The virtual work done by a force equals the force dotted with the virtual displacement in the force’s direction. For a couple moment, virtual rotational work is found by...

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Finding Forces with Virtual Work in Linked Bodies

Virtual work helps find forces in a system of connected rigid bodies. It is a useful method when several links move together and the system is in equilibrium. In that case, the total virtual work is zero. To analyze the system, start with a free-body diagram. Use one independent coordinate to describe the link configuration. Then mark the deflected position that comes from a positive virtual displacement. This makes the small change in position clear before any calculations begin. Next,...

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Mechanical efficiency shows how well a machine turns input work into output work. It is calculated as the ratio of output work to input work. An ideal machine has an efficiency of one, which means the input work equals the output work. Real machines are never perfectly ideal because some energy is lost. Friction is one of the main causes of that loss. In a toggle vise used to compress wooden blocks, the sliding block rubs against the horizontal plane and creates friction. To find the...

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Conservative Forces and Path-Independent Work

Conservative forces are forces whose work depends only on an object’s starting and ending positions. The path between those positions does not change the amount of work done. This idea is important in mechanical engineering because it helps describe how energy moves through a system. A conservative force also conserves energy in the sense that its work is path independent. Gravity is one example. Electrostatic forces and springs modeled by Hooke’s law are also examples. A ball rolling down a...

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Gravitational and Elastic Energy Stored

Gravitational and elastic potential energy are forms of stored energy from conservative forces. A conservative force, such as gravity or an elastic force, gives a body the capacity to do work. This capacity is measured as potential energy and depends on the body’s position relative to a fixed reference point, or datum. For gravitational potential energy, the datum is the level where the energy is taken as zero. If a body is above this reference plane, its weight has positive gravitational...

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Potential energy helps determine when a mechanical system is stable at equilibrium. When a system is acted on by gravitational and elastic forces, its total potential function is the algebraic sum of gravitational potential energy and elastic potential energy. If the system is already in equilibrium and is given a small displacement, the work done on the system equals the negative of the change in potential energy between the starting and ending positions. For a virtual displacement, which is...

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Types of Equilibrium in Mechanical Systems

Types of equilibrium in mechanical systems are stable, neutral, and unstable. These three cases help explain how a structure or object responds when it is pushed slightly away from balance. They are important for predicting whether a system will return to its original position, stay where it is, or move farther away. Stable equilibrium occurs when a system returns toward its original position after a small displacement. In this case, the potential energy is at a minimum. A cantilever beam...

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A one-degree-of-freedom system uses a single independent variable to describe its state and behavior. In mechanical engineering, this kind of model helps explain how parts in a larger system respond to force. It also gives engineers a way to predict motion before a design is built in real life. A simple harmonic oscillator is one example of a one-degree-of-freedom system. A mass attached to a spring moves along one axis, and that position determines the system’s state. The spring force makes...

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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.

mechanical engineering

Couple Moment Work in Rotation

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