Name: net moment sign convention in 2d forces
Uploaded: 2023-09-22T11:49:20.000Z
Duration: 1 min 31 s
Channel: JoVE

Рассмотрим консольную балку, на которую действуют силы 1000 Н, 600 Н, 750 Н и 500 Н в разных точках B, C, D и E соответственно. Момент, создаваемый в точке А определенной силой, является произведением любой из сил с соответствующим перпендикулярным расстоянием от точки приложения силы до неподвижной точки А.
Здесь силы F1, F2 и F3 создают момент по часовой стрелке, который обычно считается отрицательным, в то время как момент, создаваемый силой F4, является положительным с учетом направления против часовой стрелки.
Результирующий момент от всех четырех сил вычисляется как алгебраическая сумма всех моментов, порожденных каждой силой в системе.
Здесь, поскольку величина результирующего момента отрицательна, он действует по часовой стрелке.
Теперь предположим, что направление силыF3 обратное. Результирующий момент будет положительным, указывая на момент против часовой стрелки вокруг точки А.

<ol>
	<li>Хиббелер, Р.К. (2016). Инженерная механика \u2012 Статика и динамика. Хобокен, Нью-Джерси: Пирсон Прентис Холл. С. 122.</li>
</ol>

Результирующий момент: скалярная формулировка

Resultant Moment: Scalar Formulation

Когда на объект в двумерном пространстве действуют несколько сил, понятие суммарного момента можно использовать для понимания тенденции этих сил вызывать вращательное движение вокруг фиксированной точки. Скалярная формулировка результирующего момента является полезным инструментом в анализе равновесия структур, подвергнутых действию нескольких сил.

Для определения результирующего момента учитываются моменты, вызванные всеми силами в системе в плоскости x-y. Положительные моменты обычно являются против часовой стрелки, так как они направлены вдоль положительной оси z, в то время как отрицательные моменты являются по часовой стрелке. Каждому моменту присваивается знак в зависимости от его направления. Чтобы вычислить результирующий момент, вызванный всеми силами, берется алгебраическая сумма произведений каждой силы и ее соответствующего перпендикулярного расстояния относительно данной точки A.

<img alt="Equation 1" src="/files/ftp_upload/14252/14252_Equation_1v3.svg" style="text-align: center; height: 15px;" />

В расчете используются знаки для моментов. Подставив значения всех сил и их перпендикулярных расстояний в указанное уравнение, если числовой результат этого уравнения является положительным скалярным, то результирующий момент будет против часовой стрелки. Соответственно, результирующий момент будет по часовой стрелке, если результат отрицательный.

Когда на объект в двумерном пространстве действуют множественные силы, концепция результирующего момента может быть использована для понимания тенденции этих сил к ...

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Mechanical Engineering

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Unit 1

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Force System Resultants

Результирующие силы системы

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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 are usually counterclockwise and point along the positive z-axis. Negative moments are clockwise.

The calculation uses the algebraic sum of each force multiplied by its perpendicular distance from point A. This sign convention makes it possible to combine the effects of all the forces into one scalar value. If the final result is positive, the resultant moment is counterclockwise. If the result is negative, the resultant moment is clockwise.

Net Moment Sign Convention in 2D Forces

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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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resultant moment: scalar formulation

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...

moment of a force: vector formulation

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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).

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...

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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...

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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...

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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...

couple

Couple Moment in Force Systems

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Equivalent Couples in Mechanical Systems

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Torque from a Couple: Solving Forces

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Equivalent Force and Moment Systems

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

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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 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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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 to use the scalar form of net moment in 2D force systems. See how sign convention, perpendicular distance, and rotation direction determine the result.

Net Moment Sign Convention in 2D Forces | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

Net Moment Sign Convention in 2D Forces

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