Name: torque on a bicycle wheel: vector method
Uploaded: 2023-09-22T11:49:21.000Z
Duration: 1 min 29 s
Channel: JoVE

Prenons l’exemple d’un cycliste qui pédale sur un vélo. Lorsqu’une force est exercée sur la pédale, le vilebrequin tourne de telle sorte que la chaîne attachée au vilebrequin exerce une force sur les pignons de la roue.
Lors de l’établissement d’un système de coordonnées, la force tangentielle sur les engrenages est le long de l’axe des x, tandis que le rayon des engrenages est le bras de moment exprimé en termes de vecteur de position.
Ici, le moment de force par rapport au point O est le long de la direction y perpendiculaire à la fois au vecteur force et au vecteur position et est exprimé comme le produit vectoriel des vecteurs position et force.
Le produit vectoriel peut être résolu en exprimant le coefficient des composantes de la force et du vecteur position sous la forme d’un déterminant.
En développant le déterminant, la composante du moment le long de l'axe x est exprimée en fonction des composantes y et z du vecteur force et position.
De même, en exprimant ses deux autres composantes en termes de composantes vectorielles de force et de position, le moment d’une force peut être exprimé sous forme vectorielle cartésienne.

<ol>
	<li>Hibbeler, R.C. (2016). Génie mécanique \u2012 Statique et dynamique. Hoboken, New Jersey : Pearson Prentice Hall. page 146</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 107 à 109</li>
</ol>

moment d'une force autour d'un axe : vecteur

Lorsqu'une force est exercée sur un objet, elle peut provoquer la rotation de cet objet autour d'un axe. Le moment d'une force, également connu sous le nom de couple, mesure la capacité de la force à provoquer cette rotation. Dans le cas d'un cycliste qui pédale sur un vélo, la force exercée sur la pédale provoque la rotation du vilebrequin, ce qui à son tour fait tourner la roue. Le moment de la force exercée sur la pédale entraîne la rotation de la roue. Tout d'abord, établissez un système de coordonnées pour comprendre comment fonctionne le moment d'une force. Prenons l'exemple du vélo. Établissez l'axe x comme tangentiel à la roue et l'axe y comme perpendiculaire à l'axe x et pointant vers le haut. L'axe z peut pointer vers l'extérieur de la roue. Lorsque le cycliste exerce une force sur la pédale, le vilebrequin tourne de telle sorte que la chaîne attachée au vilebrequin exerce une force sur l'essieu de la roue. La force exercée sur l'essieu se trouve alors le long de l'axe x. Le rayon de l'essieu est le bras de levier, qui peut être exprimé en termes de vecteur position. Le moment de force par rapport au point O se trouve le long de la direction z, perpendiculaire à la fois à la force et au vecteur position. Il est exprimé comme le produit vectoriel des vecteurs position et force. Le produit vectoriel peut être résolu en exprimant le coefficient des composantes de la force et du vecteur position sous forme de déterminant. Le déterminant peut être développé pour résoudre chaque composante du moment de force. Par exemple, la composante du moment le long de l'axe x est exprimée en termes des composantes y et z de la force et du vecteur position. De même, les deux autres composantes du moment peuvent être exprimées sous forme de vecteur cartésien. Comprendre le moment de force est important dans de nombreux domaines scientifiques et techniques. Cela peut nous aider à calculer les forces sur des objets tels que les engrenages, les poulies et les leviers, et peut contribuer à la conception de machines qui convertissent les forces en mouvement. Dans l'exemple du vélo, comprendre le moment de force peut nous aider à optimiser la conception du vilebrequin et de la chaîne afin de maximiser la force exercée sur la roue.

Moment d'une force autour d'un axe : vecteur

Lorsqu’une force est exercée sur un objet, elle peut faire pivoter cet objet autour d’un axe. Le moment d’une force, également connu sous le nom de couple, mesure le ...

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Moment of a Force About an Axis: Vector

torque on a bicycle wheel: vector method

Torque, or the moment of a force, explains how a force can make an object rotate about an axis. A bicycle is a clear example. When a cyclist presses on the pedal, the crankshaft turns and helps drive the wheel.

To analyze this motion, a coordinate system is set up first. The x-axis is tangential to the wheel, the y-axis is perpendicular to the x-axis and points upward, and the z-axis points outward from the wheel. In this setup, the force on the wheel axle lies along the x-axis.

The axle radius acts as the moment arm, and it can be written using the position vector. The moment of the force about point O points in the z-direction because it is perpendicular to both the force and the position vector. It is found using the cross product of the position and force vectors.

The cross product can be calculated by writing the force and position components in determinant form. Expanding the determinant gives the x-, y-, and z-components of the moment. The x-component, for example, depends on the y and z components of the force and position vectors.

Knowing how to find the moment of a force is useful in science and engineering. It helps with problems involving gears, pulleys, and levers. It also supports the design of machines that turn force into motion, including the bicycle crankshaft and chain system.

Torque on a Bicycle Wheel: Vector Method

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Torque, or the moment of a force, describes how a force can make an object turn about an axis. It is a vector quantity, so it has both size and direction. This idea is important in physics, mechanics, and engineering. A simple flywheel example shows how torque works. The flywheel rotates about point O when a force is applied to it. The moment arm is the perpendicular distance from point O to the line of action of the force. The moment, in newton-meter (N-m), is found by multiplying the force...

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Calculating force moments in problem solving helps students analyze rotation in mechanical systems. The scalar form of the moment of a force is used to work through these problems step by step. Start by drawing a free-body diagram, or FBD. An FBD is a sketch that shows every force acting on the system. Each force must be identified and included. Next, identify the axis or point about which the moment is calculated. In some problems, that axis or point is given. In other cases, you must choose...

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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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The moment of force describes the twisting effect a force can have on an object. It shows why a force may cause rotation instead of straight-line motion. The moment arm is the perpendicular distance from the force’s line of action to the axis of rotation. The moment of force is a vector quantity, not a scalar. Its vector form comes from the cross product of the position vector and the force vector. A cross product gives a vector that is perpendicular to both input vectors. The moment about a...

cartesian form for vector formulation

Calculating Moment with Cartesian Vectors

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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The principle of moments, also called Varignon's theorem, explains how a force creates rotation about a point. It is a key idea in physics and engineering. It also helps describe when a rigid body stays in equilibrium under external forces. The moment of a force is found by multiplying the force by the perpendicular distance from the point of application to the point being studied. A larger force or a larger distance gives a larger moment. This makes the idea useful for checking how strongly a...

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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...

moment of a force about an axis: scalar

Bicycle Torque and Moment About an Axis

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, or the moment of a force, explains how a force can make an object rotate about an axis. A bicycle is a clear example. When a cyclist presses on the pedal, the crankshaft turns and helps drive the wheel. To analyze this motion, a coordinate system is set up first. The x-axis is tangential to the wheel, the y-axis is perpendicular to the x-axis and points upward, and the z-axis points outward from the wheel. In this setup, the force on the wheel axle lies along the x-axis. The axle...

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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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key terms and concepts

Learn how torque, or the moment of a force, makes a bicycle wheel rotate. Follow the vector method, coordinate axes, and cross product step by step.

Torque on a Bicycle Wheel: Vector Method | JoVE K12

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Torque on a Bicycle Wheel: Vector Method

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