Name: torque from a couple: solving forces
Uploaded: 2023-09-22T11:49:21.000Z
Duration: 1 min 30 s
Channel: JoVE

Considérons un tuyau attaché à un accouplement au point O sur l’axe des x dans un système de coordonnées tridimensionnel.
Deux clés de longueur 0,12 mètre appliquent une force égale et opposée de 120 newtons le long de l’axe z. Les clés se trouvent à une distance de 0,5 mètre et à 0,7 mètre du point O le long de l’axe des x.
Déterminez le moment de couple du système.
Le moment de couple autour du point O est déterminé comme la somme des produits vectoriels des vecteurs position et des forces appliquées.
rA et rB représentent les vecteurs position provenant du point O aux points A et B, respectivement.
La différence entre les vecteurs position rA et rB est le vecteur r, qui est la distance entre les forces opposées.
Le moment de couple peut être exprimé sous la forme déterminante comme le produit vectoriel des vecteurs position et force.
L’intensité du moment de couple est déterminée en prenant la racine carrée de la somme des carrés des composantes du vecteur résultant.

<ol>
	<li>Hibbeler, R.C. (2016). Génie mécanique \u2012 Statique et dynamique. Hoboken, New Jersey : Pearson Prentice Hall. p. 154 à 156 et 165.</li>
</ol>

moment d'un couple : résolution de problèmes

Le moment d'un couple est un concept essentiel en physique et en ingénierie, utilisé pour calculer la force de rotation, ou le couple, qui est créé lorsque deux forces égales et opposées agissent sur un objet. Le moment d'un couple est trouvé en multipliant l'amplitude de l'une des forces par la distance perpendiculaire entre la ligne d'action des deux forces. Cela crée une force de torsion, qui peut être utilisée pour faire tourner un objet. Le moment d'un couple est utilisé pour résoudre des problèmes impliquant des forces équilibrées et non équilibrées. Le processus de résolution de problèmes du moment d'un couple implique plusieurs étapes clés. Tout d'abord, les forces pertinentes agissant sur l'objet doivent être identifiées et dessinées dans un diagramme clair et simple. Cela peut aider à visualiser le problème et le rendre plus facile à comprendre. Ensuite, trouvez le vecteur associé à la distance perpendiculaire entre les lignes d'action des deux forces. Le produit vectoriel du vecteur de force et du vecteur perpendiculaire nous donnera le moment du couple. La direction du moment peut être déterminée en utilisant la règle de la main droite, qui indique que la direction du couple est perpendiculaire à la fois à la force et au vecteur de distance. Enfin, le moment peut être utilisé pour résoudre le problème en question. Cela peut impliquer le calcul du couple global sur un objet, la détermination de la vitesse angulaire ou de l'accélération d'un objet en rotation, ou le calcul du travail effectué par le couple.

Moment d'un Couple : Résolution de Problèmes

Le moment du couple est un concept essentiel en physique et en ingénierie, utilisé pour calculer la force de rotation, ou couple, qui est créée lorsqu’un couple ...

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Moment of a Couple: Problem Solving

torque from a couple: solving forces

The moment of a couple is a key physics and engineering idea for finding torque, or rotational force. A couple is made of two equal and opposite forces that act on an object. When those forces work together, they create a twisting effect that can rotate the object.

The moment of a couple is calculated by multiplying the size of one force by the perpendicular distance between the two lines of action. That distance is the shortest straight-line distance between the force directions. This gives the moment needed to describe how strongly the couple turns the object.

Problem solving with a couple starts by identifying the forces on the object and drawing them in a clear, simple diagram. The next step is to find the vector for the perpendicular distance between the force lines. Then the cross product of the force vector and the perpendicular vector gives the moment of the couple.

The direction of the moment is found with the right-hand rule. This rule shows that the torque direction is perpendicular to both the force and the distance vector. Once the direction and size are known, the moment can help solve balanced and unbalanced force problems, find overall torque, determine angular velocity or angular acceleration, and calculate the work done by the couple.

Torque from a Couple: Solving Forces

moment of a force: scalar formulation

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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...

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Calculating moment with Cartesian vectors shows how position and force vectors work together. The moment of force is the cross product of these vectors, so it is a vector quantity. In Cartesian form, unit vectors help write the vectors in component form. The cross product can be arranged in determinant form. That determinant is then expanded to find the Cartesian vector form of the moment of force. This method gives a clear way to work through the calculation step by step. A revolving door...

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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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Torque About an Axis in 3D Systems

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The moment of a force about an axis describes how a force can make an object turn around a fixed line. In scalar analysis, the moment is found from the perpendicular distance between the axis of rotation and the line of action of the force. That distance is called the moment arm. A bicycle gives a clear example of this idea. When the cyclist pushes on the pedal, the chain applies a force to the wheel’s axle and makes it rotate. The axis of rotation passes through the axle, and the moment arm...

moment of a force about an axis: vector

Torque on a Bicycle Wheel: Vector Method

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couple

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...

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Couple moments describe the turning effect of two parallel forces that are equal in magnitude and opposite in sense. This force pair creates rotation instead of straight-line motion. A common example is a ship’s steering wheel, where a small turn can guide the ship through the ocean. A couple moment can rotate clockwise or anticlockwise. The right-hand rule helps identify its direction. To use it, curl the fingers of your right hand in the direction of rotation. Your thumb points in the...

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moment of a couple: problem solving

The moment of a couple is a key physics and engineering idea for finding torque, or rotational force. A couple is made of two equal and opposite forces that act on an object. When those forces work together, they create a twisting effect that can rotate the object. The moment of a couple is calculated by multiplying the size of one force by the perpendicular distance between the two lines of action. That distance is the shortest straight-line distance between the force directions. This gives...

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Structural systems often experience several forces and couple moments at the same time. Engineers simplify these loading cases by replacing them with an equivalent force and moment system at a chosen point O. This makes the analysis easier while keeping the same external effects on the member. A key idea in this process is the principle of transmissibility. A force is a sliding vector, which means it can be moved anywhere along its line of action without changing how the body behaves...

simplification of a force and couple system i

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Resultant Forces in Force and Couple Systems

Force and couple systems can be reduced to a simpler equivalent system. This makes rigid body analysis easier because the external effect of the forces is captured with fewer elements. When the resultant force and resultant couple moment have perpendicular lines of action, the system may be reduced further to a single resultant force along a new line of action. Three common force systems can be simplified this way: concurrent, coplanar, and parallel. A concurrent force system has lines of...

simplification of a force and couple system: ii

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Resultant Force and Wrench Motion

Resultant force and resultant couple moment describe how several forces and moments act together on a rigid body in three dimensions. When many forces act on an object, they can be replaced by one equivalent force. The moments from those forces can also be combined into one equivalent couple moment. In some cases, the resultant force and the resultant couple moment are not mutually perpendicular. That means the angle between them is not 90 degrees. To study this situation, the couple moment is...

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Load Distribution on Shelves and Dams

Load distribution helps engineers describe how force spreads across a surface or structure. A distributed load is a continuous force per unit area, rather than a single point force. It is a common idea in many practical situations. A bookshelf full of stacked books is one simple example. The weight of the books is spread along the shelf, so the pressure changes across the surface. This pressure is measured in Newtons per square meter, or Pascals. A hydroelectric dam gives another clear...

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distributed loads: problem solving

Equivalent Resultant Loads on Beams

Equivalent resultant loads on beams can be found by breaking a distributed load into smaller regions. This makes the beam easier to analyze. Each region can then be handled on its own before the results are combined. The magnitude of the equivalent resultant load for each region comes from the area of that region. In this setting, area represents the force applied by the distributed load over that part of the beam. After finding the force for each region, the position of each resultant load...

key terms and concepts

Learn how a couple creates torque, how to find its moment using force and distance, and how the right-hand rule helps solve rotation problems.

Torque from a Couple: Solving Forces | JoVE K12

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Torque from a Couple: Solving Forces

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