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

モーメントの原理、またはヴァリニョンの定理は、力の作用下での剛体の平衡を説明しています。
これは、ある点に関する力のモーメントは、その点に関する力の成分のモーメントの合計に等しいと述べています。
ある点における力のモーメントは、印加点からの垂直距離と加えられた力の積です。
また、力をその成分に分解し、個々の成分に対応するモーメントアームを掛けることによっても決定できます。
ハンドホイールがパイプラインに取り付けられているバルブを考えてみましょう。ホイールを回転させるために力が加えられると、力の大きさに中心から印加点までの垂直距離を掛けることにより、中心を中心とした力のモーメントを決定できます。
加えられた力は、その成分に分解することもでき、モーメントは、各力成分の積とそれに対応する距離を加算することによって決定できます。

<ol>
	<li>ヒベラー、RC(2016)。エンジニアリングメカニクス \u2012 静力学と力学。 ニュージャージー州ホーボーケン:ピアソンプレンティスホール。132ページ。</li>
</ol>

モーメントの原理

モーメントの原理、またはバリニオンの定理としても知られるものは、物理学や工学において、外部力の影響下で剛体が平衡状態にあることを記述する基本的な概念です。この原理は、ある点に対する力のモーメントは、同じ点における力の成分のモーメントの合計に等しいことを述べています。

モーメントは、点の適用地点から計算されるモーメントの中心までの垂直距離に力の大きさを掛け算することで計算されます。バルブの場所に取り付けられたハンドルが回転するために誰かが力を加えるとき、力のモーメントは、中心から力が加えられる地点までの垂直距離に力の大きさを掛け算することによって求めることができます。

ただし、適用された力がバルブに垂直でない場合や複数の成分を持つ場合、計算はより複雑になる可能性があります。この場合、力を成分ベクトルに分解し、それぞれの成分のモーメントを、その成分の適用地点から計算されるモーメントの中心までの垂直距離に力の大きさを掛け算することで個別に計算することができます。各モーメントを計算した後、対象となる点における力の全体的なモーメントを求めるためにそれらを合計することができます。

モーメントの原理は、構造工学から機械設計まで幅広い応用があります。システムや構造物に作用する力のモーメントを計算することで、その平衡状態を判断したり、力の不均衡による回転や移動するかどうかを判断することができます。

モーメントの原理は、ヴァリニョンの定理とも呼ばれ、物理学と工学の基本的な概念であり、...

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Force System Resultants

力の系の合力

KEY TERMS AND CONCEPTS

主要用語と概念

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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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...

moment of a force: problem solving

Calculating Force Moments in Problem Solving

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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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Moment of Force and Direction Rules

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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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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

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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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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system of forces and couples

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

simplification-of-a-force-and-couple-system-i

Resultant Forces in Force and Couple Systems

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

simplification-of-a-force-and-couple-system-ii

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...

distributed loads

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...

distributed loads: problem solving

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

JoVE Core 機械工学は、平衡、力、トラス解析、構造力学などの重要なトピックをカバーする簡潔でわかりやすいアニメーション ビデオを提供します。実際のアプリケーションを探索し、科学者主導の実験を通じてこれらのコンセプトが実際に動作しているのを目撃してください。

mechanical engineering

Resolving Forces in Moment Calculations

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