Name: torque about an axis in 3d systems
Uploaded: 2023-09-22T11:49:21.000Z
Duration: 1 min 30 s
Channel: JoVE

Considérons un poteau placé dans un système en 3 dimensions avec un câble attaché. Lorsque la tension de 15 kN est appliquée au câble, déterminez le moment autour de l’axe z passant par la base.
Le moment peut être déterminé à l’aide de deux méthodes.
Dans la première méthode, calculez la projection de la force le long du vecteur unité et multipliez-la par l'intensité de la force pour obtenir le vecteur force.
Le moment par rapport à l’origine est le produit vectoriel du vecteur position et de la force. Le moment le long de l’axe z peut être obtenu par le produit scalaire du moment par rapport à l’origine et le vecteur unitaire le long de l’axe z.
Vous pouvez également résoudre le vecteur de force en ses composantes. Les composants le long de l’axe y et de l’axe z n’exercent aucun moment lors de leur passage et sont parallèles à l’axe z, respectivement.
La tension dans la direction x peut être obtenue en multipliant la tension par le cosinus de direction par rapport à l’axe x.
Rappelez-vous l’équation du moment de force, et en substituant les termes, le moment autour de l’axe z peut être déterminé.

<ol>
	<li>Hibbeler, R.C. (2016). Génie mécanique \u2012 Statique et dynamique. Hoboken, New Jersey : Pearson Prentice Hall. pp 133 à 138</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. pages 96 à 99</li>
	<li>Meriam, J.L. ; Kraige, L.G. et Bolton, J.N. (2020). Génie mécanique \u2012 Statique. Hoboken, New Jersey : John Wiley. pages 78 et 79</li>
</ol>

principe des moments : résolution de problèmes

Le principe des moments est un concept fondamental en physique et en ingénierie. Il fait référence à l'équilibre des forces et des moments autour d'un point ou d'un axe, également connu sous le nom de pivot. Ce principe est utilisé dans de nombreux scénarios de la vie réelle, notamment la construction, les sports et les activités quotidiennes telles que l'ouverture des portes et la poussée des objets. Un tel scénario implique un poteau placé dans un système tridimensionnel avec un câble attaché. Lorsqu'une tension est appliquée au câble, il est nécessaire de déterminer le moment autour de l'axe z passant par la base. Il existe deux méthodes pour aborder ce problème. La première méthode consiste à calculer la projection de la force le long du vecteur unitaire et à la multiplier par la magnitude de la force pour obtenir le vecteur de force. Le moment par rapport à l'origine peut être calculé en prenant le produit vectoriel du vecteur de position et du vecteur de force. Une fois que le vecteur de moment est déterminé, le moment le long de l'axe z peut être évalué en prenant le produit scalaire du moment par rapport à l'origine et du vecteur unitaire le long de l'axe z. Sinon, décomposez le vecteur de force en ses composantes. Les composantes le long de l'axe y et de l'axe z n'exercent aucun moment car elles passent respectivement à travers et parallèlement à l'axe z. La tension dans la direction x peut être calculée en multipliant la tension par le cosinus de la direction par rapport à l'axe x. Ensuite, utilisez l'équation du moment de force et remplacez les termes appropriés pour déterminer le moment par rapport à l'axe z. Il est important de noter que le principe des moments est crucial pour comprendre le comportement des structures et des machines. Les ingénieurs et les concepteurs l'utilisent largement pour s'assurer que leurs créations sont stables, sécuritaires et efficaces. En équilibrant les forces et les moments autour d'un point de pivot, ils peuvent calculer les contraintes et les déformations auxquelles une structure ou une machine sera soumise et identifier des points de défaillance potentiels. En fin de compte, le principe des moments est un outil puissant qui permet de résoudre des problèmes liés aux forces, aux moments de torsion et aux mouvements. Que ce soit pour construire des ponts, analyser des techniques sportives ou simplement ouvrir une porte, on peut se fier à ce principe pour s'assurer que les choses sont faites correctement et efficacement.

Principe des moments : résolution de problèmes

Le principe des moments est un concept fondamental en physique et en ingénierie. Il s’agit de l’équilibrage des forces et des moments autour d’un point ou d’un axe, ...

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Principle of Moments: Problem Solving

torque about an axis in 3d systems

The principle of moments helps solve torque problems in physics and engineering. It describes how forces and moments balance around a pivot point or axis. It is used in many real-life cases, including construction, sports, and everyday actions like opening doors and pushing objects.

The problem here uses a pole in a three-dimensional system with a cable attached. When tension acts in the cable, the goal is to find the moment about the z-axis through the base. One method is to project the force along a unit vector to build the force vector. The moment about the origin is then found with the cross product of the position vector and the force vector. After that, the moment along the z-axis is found by taking the dot product of the moment vector with the z-axis unit vector.

A second method is to split the force into components. The y-axis and z-axis components create no moment in this setup. The y-axis component passes through the axis, and the z-axis component is parallel to it. The x-direction tension is found by multiplying the cable tension by the direction cosine with respect to the x-axis. Then the moment of force equation is used to determine the moment about the z-axis.

This kind of analysis is important in structures and machines. Engineers and designers use the principle of moments to check stability, safety, and performance. It helps them estimate the stresses and strains a structure or machine may face and spot possible failure points. The same idea also appears in bridges, sports technique, and simple tasks like opening a door.

Torque About an Axis in 3D Systems

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Resultant moment describes the total turning effect of multiple forces acting on an object. It shows how several forces can combine to make a body rotate about a point. In physics, moment is the tendency of a force to cause rotation. The resultant moment of a force system is a vector quantity. That means it can be added and subtracted like other vectors. For a system with two forces, F1 and F2, acting on a pole at points A and B, the resultant moment is written as MR = (rA x F1) + (rB x F2).

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principle of moments: problem solving

The principle of moments helps solve torque problems in physics and engineering. It describes how forces and moments balance around a pivot point or axis. It is used in many real-life cases, including construction, sports, and everyday actions like opening doors and pushing objects. The problem here uses a pole in a three-dimensional system with a cable attached. When tension acts in the cable, the goal is to find the moment about the z-axis through the base. One method is to project the force...

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key terms and concepts

Learn how the principle of moments is used to find torque about the z-axis in a 3D cable-and-pole setup using cross products and force components.

Torque About an Axis in 3D Systems | JoVE K12

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Torque About an Axis in 3D Systems

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