Name: resolving forces in moment calculations
Uploaded: 2023-09-22T11:49:21.000Z
Duration: 1 min 20 s
Channel: JoVE

O princípio dos momentos, ou teorema de Varignon, descreve o equilíbrio de um corpo rígido sob a ação de forças.
Ele afirma que o momento de uma força em torno de um ponto é igual à soma dos momentos dos componentes da força em torno do ponto.
O momento de uma força em um ponto é o produto da distância perpendicular do ponto de aplicação e da força aplicada.
Também pode ser determinado resolvendo a força em seus componentes e multiplicando componentes individuais com o braço de momento correspondente.
Considere uma válvula onde um volante é montado em uma tubulação. Quando uma força é aplicada para girar a roda, o momento da força em torno do centro pode ser determinado multiplicando a magnitude da força pela distância perpendicular do centro ao ponto de aplicação.
A força aplicada também pode ser resolvida em seus componentes, e o momento pode ser determinado adicionando os produtos de cada componente de força com sua distância correspondente.

<ol>
	<li>Hibbeler, R.C. (2016). Engenharia Mecânica \u2012 Estática e Dinâmica. Hoboken, Nova Jersey: Pearson Prentice Hall. pág. 132.</li>
</ol>

princípio dos momentos

O princípio dos momentos, também conhecido como teorema de Varignon's, é um conceito fundamental na física e engenharia que descreve o equilíbrio de um corpo rígido sob a influência de forças externas. O princípio afirma que o momento de uma força em relação a um ponto é igual à soma dos momentos dos componentes da força em relação ao mesmo ponto.

O momento é calculado multiplicando a magnitude da força pela distância perpendicular do ponto de aplicação ao ponto em relação ao qual o momento está sendo calculado. Considere uma válvula em que uma manivela está montada em uma tubulação. Quando alguém aplica uma força para girar a manivela, o momento da força em relação ao centro pode ser determinado multiplicando a magnitude da força pela distância perpendicular do centro ao ponto de aplicação da força.

No entanto, o cálculo pode se tornar mais complexo se a força aplicada não for perpendicular à válvula ou tiver múltiplos componentes. Nesse caso, podemos decompor a força em seus vetores componentes e calcular individualmente o momento de cada componente multiplicando-o pela distância perpendicular do ponto de aplicação desse componente ao ponto em relação ao qual o momento está sendo calculado. Uma vez que cada momento tenha sido calculado, podemos somá-los para determinar o momento global da força em relação ao ponto em questão.

O princípio dos momentos pode ser usado em uma ampla gama de aplicações, desde engenharia estrutural até projeto mecânico. Ao calcular os momentos das forças atuando em um sistema ou estrutura, podemos determinar se ele está em equilíbrio ou se irá girar ou mover devido a um desequilíbrio de forças.

Princípio dos Momentos

O princípio dos momentos, também conhecido como teorema de Varignon, é um conceito fundamental em física e engenharia que descreve o equilíbrio de um ...

Education

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

Principle of Moments

resolving forces in moment calculations

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 force can turn an object.

A valve with a hand wheel on a pipeline gives a clear example. When a person pushes on the wheel, the moment about the center depends on the force and the perpendicular distance from the center to where the force is applied. If the force is not perpendicular to the valve, the calculation is less direct.

In that case, the force can be split into component vectors. Each component has its own moment, and each one is found using the perpendicular distance from the point of application of that component to the point of rotation. After the moments are found, they are added together to get the overall moment about the point.

This method is used in structural engineering and mechanical design. It helps show whether a system or structure is in equilibrium. It also shows when an imbalance of forces may cause rotation or motion.

Resolving Forces in Moment Calculations

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Net Moment Sign Convention in 2D Forces

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principle of moments

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...

principle of moments: problem solving

Torque About an Axis in 3D Systems

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Bicycle Torque and Moment About an Axis

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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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Equivalent Couples in Mechanical Systems

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Equivalent Force and Moment Systems

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Resultant Forces in Force and Couple Systems

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simplification of a force and couple system: ii

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Resultant Force and Wrench Motion

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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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Finding Resultant Loads on a Beam

Structural engineering often requires finding the resultant load on a beam with changing force patterns. Here, a beam of length L carries a varying load made from parabolic and trapezoidal load distributions along the x-axis. The goal is to find the total load, where it acts, and the centroid of the combined area so the beam’s response can be predicted. The parabolic load is handled first. A small force element, dR, acts over a short distance, dx, and these elements are integrated across the...

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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 the principle of moments breaks a force into components and uses distance to find rotation in a valve, structure, or other rigid body.

Resolving Forces in Moment Calculations | JoVE K12

O JoVE Core Mechanical Engineering oferece vídeos animados concisos e de fácil compreensão que abrangem tópicos-chave como equilíbrio, forças, análise de treliças e mecânica estrutural. Explore suas aplicações no mundo real e observe esses conceitos em ação por meio de experimentos conduzidos por cientistas.

mechanical engineering

Resolving Forces in Moment Calculations

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