Name: couple moment in force systems
Uploaded: 2023-09-22T11:49:21.000Z
Duration: 1 min 29 s
Channel: JoVE

Un couple est une paire de forces parallèles ayant des amplitudes égales mais agissant dans des directions opposées, séparées par une distance perpendiculaire.
Le couple provoque une force de rotation qui fait tourner le corps autour d’un axe perpendiculaire au plan des forces, et le moment résultant est connu sous le nom de moment de couple.
Envisagez de serrer un boulon avec une clé à molette. Un couple de forces se forme lorsque deux forces égales et opposées sont appliquées sur la clé aux points A et B, séparés par une distance perpendiculaire.
Les vecteurs de position rA et rB sont dirigés de l’origine d’un système de coordonnées vers des points d’application.
Le couple moment autour de l’origine est la somme du produit vectoriel des vecteurs position et des forces.
La différence entre les vecteurs position rA et rB est le vecteur position r, qui est la distance entre les deux forces opposées.
Le moment de couple ne dépend que du vecteur de position r entre les forces et non des vecteurs de position rA et rB. Il est donc considéré comme un vecteur libre.

<ol>
	<li>Hibbeler, R.C. (2016). Génie mécanique \u2012 Statique et dynamique. Hoboken, New Jersey : Pearson Prentice Hall. page 154</li>
	<li>Bière, F.P. ; Johnston, E.R. ; Mazurek, D.F ; Cromwell, P.J. et Self, B.P. (2019). Mécanique vectorielle pour les ingénieurs \u2012 Statique et dynamique. New York : McGraw-Hill. pp – 120.</li>
</ol>

couple

Un couple est une paire de forces parallèles de même intensité mais de directions opposées. Les forces sont séparées par une distance perpendiculaire, connue sous le nom de bras du couple. Le couple provoque une force de rotation ou un moment qui fait tourner le corps autour d'un axe perpendiculaire au plan des forces. Le moment résultant est appelé moment du couple. L'unité internationale d'un moment de couple est le Newton-mètre (N-m). Un exemple typique pour comprendre ce concept est le serrage d'un boulon avec une clé à écrou. Un couple de forces est formé lorsque deux forces égales et opposées sont appliquées sur la clé aux points A et B, séparés par une distance perpendiculaire. Les vecteurs position respectifs sont dirigés depuis l'origine d'un système de coordonnées vers le point d'application. Le moment du couple par rapport à l'origine est la somme du produit vectoriel des vecteurs position et des forces. La différence entre les vecteurs position des deux forces opposées donne le vecteur position r, qui est la distance entre les forces opposées. Il est intéressant de noter que le moment du couple dépend uniquement du vecteur position r entre les forces, et non des vecteurs position individuelles des deux forces. Le vecteur position r est indépendant de l'origine. Cela signifie que calculer les moments des mêmes forces autour d'un point différent donnerait le même résultat. Le moment du couple est un vecteur libre. Contrairement au moment d'une force, le moment d'un couple dépend de la position à laquelle il est mesuré. Si deux couples produisent un moment de même intensité et de même direction, alors ces deux couples sont équivalents. Les couples équivalents ont un effet de couple ou de rotation égal, indépendamment de leur position, de leur direction ou de leur intensité. Calculer le moment du couple et comprendre ses effets est crucial dans la conception de systèmes stables et robustes capables de résister aux forces externes.

Couple

Un couple est une paire de forces parallèles d’intensité égale mais dans des directions opposées. Les forces sont séparées par une distance perpendiculaire, connue sous le nom de ...

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couple moment in force systems

A couple is a pair of parallel forces that are equal in magnitude and opposite in direction. The two forces are separated by a perpendicular distance called the couple arm. Together, they create a turning effect on a body instead of a net push.

This turning effect is called the couple moment. It rotates the body about an axis that is perpendicular to the plane of the forces. The SI unit for a couple moment is the Newton-meter (N-m).

A common example is tightening a bolt with a lug wrench. In that case, two equal and opposite forces act at points A and B on the wrench. These points are separated by a perpendicular distance, so they form a force couple.

The couple moment about the origin is found by adding the cross products of the position vectors and the forces. The position vector between the two opposing forces is r, which is the distance between them. The couple moment depends only on this vector r, not on the separate position vectors of the forces.

Because r does not depend on the origin, the same couple moment is obtained even if the moments are taken about a different point. This is why a couple moment is a free vector. A moment of a single force is different because it depends on where it is measured.

If two couples create moments with the same magnitude and direction, they are equivalent couples. Equivalent couples have the same torque, or turning effect, even if their positions, directions, or magnitudes differ. Understanding couple moments helps in designing stable systems that can resist external forces.

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key terms and concepts

Learn how a couple creates rotation, why couple moment depends on the distance between forces, and how equivalent couples are identified in force systems.

Couple Moment in Force Systems | JoVE K12

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Couple Moment in Force Systems

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