Name: net moment sign convention in 2d forces
Uploaded: 2023-09-22T11:49:20.000Z
Duration: 1 min 31 s
Channel: JoVE

Considérons une poutre en porte-à-faux sur laquelle des forces de 1000 N, 600 N, 750 N et 500 N agissent en différents points B, C, D et E, respectivement. Le moment généré au point A par une force particulière est le produit de l’une ou l’autre des forces ayant la distance perpendiculaire correspondante entre le point d’application de la force et le point fixe A.
Ici, les forces F1, F2 et F3 génèrent un moment dans le sens des aiguilles d’une montre, qui est conventionnellement considéré comme négatif, tandis que le moment produit par la force F4 est positif dans le sens inverse des aiguilles d’une montre.
Le moment résultant dû aux quatre forces est calculé comme la somme algébrique de tous les moments générés par chaque force dans le système.
Ici, puisque l’intensité du moment résultant est négative, il agit dans le sens des aiguilles d’une montre.
Supposons maintenant que la direction de la force F3 soit inversée. Le moment résultant sera positif, indiquant un moment dans le sens inverse des aiguilles d’une montre autour du point A.

<ol>
	<li>Hibbeler, R.C. (2016). Génie mécanique \u2012 Statique et dynamique. Hoboken, New Jersey : Pearson Prentice Hall. Pages 122.</li>
</ol>

moment résultant : formulation scalaire

Resultant Moment: Scalar Formulation

Lorsque plusieurs forces agissent sur un objet dans un espace bidimensionnel, le concept du moment net peut être utilisé pour comprendre la tendance de ces forces à induire un mouvement de rotation autour d'un point fixe. La formulation scalaire du moment résultant est un outil utile pour analyser l'équilibre des structures soumises à plusieurs forces. Pour déterminer le moment résultant, les moments causés par toutes les forces dans un système dans le plan x-y sont pris en compte. Les moments positifs sont généralement dans le sens inverse des aiguilles d'une montre, car ils sont dirigés le long de l'axe des z positifs, tandis que les moments négatifs sont dans le sens des aiguilles d'une montre. Chaque moment est signé en fonction de son sens de direction. Pour calculer le moment résultant dû à toutes les forces, une somme algébrique des produits de chaque force et de sa distance perpendiculaire respective par rapport à un point donné A est effectuée. <img alt="Equation 1" src="/files/ftp_upload/14252/14252_Equation_1v3.svg" style="text-align: center; height: 15px;"> Conventions de signe pour les moments sont utilisées dans le calcul. Après avoir substitué les valeurs de toutes les forces et de leurs distances perpendiculaires dans l'équation ci-dessus, si le résultat numérique de cette équation est un scalaire positif, le moment résultant sera dans le sens inverse des aiguilles d'une montre. De même, le moment résultant sera dans le sens des aiguilles d'une montre si le résultat est négatif.

Moment Résultant : Formulation scalaire

Lorsque plusieurs forces agissent sur un objet dans un espace bidimensionnel, le concept de moment net peut être utilisé pour comprendre la tendance de ces forces à ...

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net moment sign convention in 2d forces

Net moment in two-dimensional force systems shows how multiple forces can cause rotation about a fixed point. The scalar formulation helps analyze equilibrium in structures that are acted on by several forces. It focuses on the x-y plane and uses a simple sign rule to describe the direction of rotation.

To find the resultant moment, the moments from all forces in the system are considered about a chosen point A. Each moment is assigned a sign based on its sense of rotation. Positive moments are usually counterclockwise and point along the positive z-axis. Negative moments are clockwise.

The calculation uses the algebraic sum of each force multiplied by its perpendicular distance from point A. This sign convention makes it possible to combine the effects of all the forces into one scalar value. If the final result is positive, the resultant moment is counterclockwise. If the result is negative, the resultant moment is clockwise.

Net Moment Sign Convention in 2D Forces

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key terms and concepts

Learn how to use the scalar form of net moment in 2D force systems. See how sign convention, perpendicular distance, and rotation direction determine the result.

Net Moment Sign Convention in 2D Forces | JoVE K12

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Net Moment Sign Convention in 2D Forces

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