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

1000N, 600N, 750N 및 500N의 힘이 각각 다른 점 B, C, D 및 E에서 작용하는 캔틸레버 빔을 고려하십시오. 특정 힘에 의해 점 A에서 생성된 모멘트는 힘이 가해지는 지점에서 고정 소수점 A까지의 해당 수직 거리를 가진 힘 중 하나의 곱입니다.
여기서, 힘F1,F2,F3 는 시계 방향으로 모멘트를 생성하는데, 이는 일반적으로 음수로 간주되는 반면, 힘 F4 에 의해 생성된 모멘트는 시계 반대 방향을 고려할 때 양수입니다.
네 가지 힘 모두로 인한 결과 모멘트는 시스템의 각 힘에 의해 생성된 모든 모멘트의 대수적 합으로 계산됩니다.
여기서 결과 모멘트의 크기는 음수이기 때문에 시계 방향으로 작용합니다.
이제 힘의 방향 F3 이 반전되었다고 가정합니다. 결과 모멘트는 양수이며, 이는 점 A를 기준으로 시계 반대 방향 모멘트를 나타냅니다.

<ol>
	<li>히벨러, R.C. (2016). Engineering Mechanics \u2012 정역학 및 동역학. 뉴저지 호보켄: 피어슨 프렌티스 홀. 122쪽.</li>
</ol>

합력 모멘트: 스칼라 공식

Resultant Moment: Scalar Formulation

2차원 공간에서 여러 힘이 물체에 작용할 때, 알짜 모멘트의 개념은 고정점에 대한 회전 운동을 유도하는 힘의 경향을 이해하는 데 사용될 수 있습니다. 합력 모멘트의 스칼라 공식은 여러 힘을 받는 구조물의 평형을 분석하는 데 유용한 도구입니다.

합력 모멘트를 결정하기 위해 시스템의 모든 힘에 의해 발생하는 모멘트를 고려합니다. 양의 모멘트는 양의 z축을 따라 방향을 잡기 때문에 일반적으로 시계 반대 방향입니다. 각 모멘트는 방향 감각에 따라 부호가 부여됩니다. 모든 힘에 의한 합력 모멘트를 계산하기 위해 주어진 점 A에 대해 각 힘과 수직 거리의 곱의 대수적 합을 취합니다. 

<img alt="Equation 1" src="/files/ftp_upload/14252/14252_Equation_1v3.svg" style="text-align: center; height: 15px;" />

모멘트에 대한 부호 규칙이 계산에 사용됩니다. 위의 식에서 모든 힘과 수직거리의 값을 대입하면 이 식의 수치 결과가 양의 스칼라이면 합력 모멘트는 반시계 방향이 됩니다. 반대로 결과가 음이면 합력 모멘트는 시계 방향이 됩니다.

여러 힘이 2차원 공간에서 물체에 작용할 때 순 모멘트의 개념을 사용하여 이러한 힘의 경향을 이해할 수 있습니다.

Education

교육

JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Force System Resultants

힘 체계의 합력

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

Moment of Force and Direction Rules

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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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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).

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...

principle of moments: problem solving

Torque About an Axis in 3D Systems

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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...

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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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Couple Moments and the Right-Hand Rule

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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

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Resultant Force and Wrench Motion

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Equivalent Resultant Loads on Beams

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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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