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

1000 N、600 N、750 N、500 N の力がそれぞれ異なる点 B、C、D、E で作用する片持ち梁について考えてみます。特定の力によって点Aで生成されるモーメントは、いずれかの力と、力の適用点から固定点Aまでの対応する垂直距離の積です。
ここで、力F1、F2、およびF3は、従来負と考えられていた時計回りのモーメントを生成しますが、力F4によって生成されるモーメントは反時計回りの方向を考慮して正になります。
4つの力すべてによる合力モーメントは、システム内の各力によって生成されるすべてのモーメントの代数的合計として計算されます。
ここでは、結果として生じるモーメントの大きさが負であるため、時計回りに作用します。
ここで、力F3の方向が逆になったとします。結果として得られるモーメントは正になり、点 A の周りの反時計回りのモーメントを示します。

<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。122ページ。</li>
</ol>

結果的なモーメント：スカラー形式

Resultant Moment: Scalar Formulation

複数の力が二次元空間の物体に作用する場合、ネットモーメントという概念を使用して、これらの力が固定点を中心に回転運動を引き起こす傾向を理解することができます。結果的なモーメントのスカラー形式は、複数の力によって受ける構造物の平衡を分析するための有用なツールです。

結果的なモーメントを求めるためには、xy平面内のすべての力によって引き起こされるモーメントが考慮されます。通常、正のモーメントは反時計回りに向かっており、正のz軸に沿って方向を向いています。一方、負のモーメントは時計回りです。各モーメントはその方向を基準にして符号が与えられます。すべての力による結果的なモーメントを計算するには、各力とその各点Aに対する垂直距離の積の代数的な合計が行われます。

<img alt="Equation 1" src="/files/ftp_upload/14252/14252_Equation_1v3.svg" style="text-align: center; height: 15px;" />

モーメントの符号規則が計算に使用されます。上記の方程式においてすべての力とそれらの垂直距離の値を代入した後、この方程式の数値結果が正のスカラーであれば、結果的なモーメントは反時計回りになります。逆に、結果が負であれば、結果的なモーメントは時計回りになります。

2次元空間の物体に複数の力が作用する場合、正味モーメントの概念を使用して、これらの力が...

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

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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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

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mechanical engineering

Net Moment Sign Convention in 2D Forces

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