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

Considere um ciclista pedalando uma bicicleta. Quando uma força é exercida no pedal, o virabrequim gira de tal forma que a corrente presa ao virabrequim exerce uma força nas engrenagens da roda.
Ao estabelecer um sistema de coordenadas, a força tangencial nas engrenagens é ao longo do eixo x, enquanto o raio das engrenagens é o braço de momento expresso em termos do vetor de posição.
Aqui, o momento de força em torno do ponto O é ao longo da direção y perpendicular ao vetor de força e posição e é expresso como o produto vetorial dos vetores de posição e força.
O produto vetorial pode ser resolvido expressando o coeficiente de componentes de força e vetor de posição na forma de um determinante.
Expandindo o determinante, a componente do momento ao longo do eixo x é expressa em termos das componentes y e z do vetor força e posição.
Da mesma forma, expressando seus outros dois componentes em termos de componentes vetoriais de força e posição, o momento de uma força pode ser expresso na forma vetorial cartesiana.

<ol>
	<li>Hibbeler, R.C. (2016). Engenharia Mecânica \u2012 Estática e Dinâmica. Hoboken, Nova Jersey: Pearson Prentice Hall. pág. 146</li>
	<li>Cerveja, F.P.; Johnston, E.R.; Mazurek, D.F; Cromwell, PJ e Self, BP (2019). Mecânica vetorial para engenheiros \u2012 estática e dinâmica. Nova Iorque: McGraw-Hill. pág. 107 - 109</li>
</ol>

momento de uma força em relação a um eixo: vetor

Quando uma força é exercida sobre um objeto, ela pode fazer com que esse objeto gire em torno de um eixo. O momento de uma força, também conhecido como torque, mede a capacidade da força de causar essa rotação. No caso de um ciclista pedalando uma bicicleta, a força exercida no pedal faz com que o eixo do pedivela gire, o que por sua vez faz com que a roda gire. O momento da força exercida no pedal impulsiona a rotação da roda.

Primeiramente, estabeleça um sistema de coordenadas para entender como o momento de uma força funciona. Considere a bicicleta como exemplo. Estabeleça o eixo x tangencial à roda, e o eixo y perpendicular ao eixo x e apontando para cima. O eixo z pode estar apontando para fora da roda.

Quando o ciclista exerce uma força sobre o pedal, o eixo do pedivela gira de forma que a corrente presa ao pedivela exerça uma força no eixo da roda. A força exercida no eixo está ao longo do eixo x. O raio do eixo é o braço de momento, que pode ser expresso em termos do vetor posição.

O momento da força em relação ao ponto O está ao longo da direção z, perpendicular tanto à força quanto ao vetor posição. É expresso como o produto vetorial dos vetores posição e força.

O produto vetorial pode ser resolvido expressando o coeficiente dos componentes da força e do vetor posição na forma de um determinante. O determinante pode ser expandido para resolver cada componente do momento da força.

Por exemplo, o componente do momento ao longo do eixo x é expresso em termos dos componentes y e z da força e do vetor posição. Da mesma forma, os outros dois componentes do momento podem ser expressos na forma de vetor cartesiano.

Entender o momento da força é importante em muitas áreas da ciência e engenharia. Ele pode nos ajudar a calcular as forças em objetos como engrenagens, polias e alavancas, e pode auxiliar no projeto de máquinas que convertem forças em movimento. No exemplo da bicicleta, entender o momento da força pode nos ajudar a otimizar o design do pedivela e da corrente para maximizar a força exercida na roda.

Momento de uma força em relação a um eixo: Vetor

Quando uma força é exercida sobre um objeto, ela pode fazer com que esse objeto gire em torno de um eixo. O momento de uma força, também conhecido como torque, mede o ...

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JoVE Core

Mechanical Engineering

Engenharia Mecânica

Unit 1

Unidade 1

Force System Resultants

Resultantes de Sistemas de Forças

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

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

moment of a force: scalar formulation

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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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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

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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...

resultant moment: vector formulation

Calculating Torque from Multiple Forces

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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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...

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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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