Name: calculating torque from multiple forces
Uploaded: 2023-09-22T11:49:21.000Z
Duration: 1 min 30 s
Channel: JoVE

モーメントとは、物体に力が加えられたときに、物体が点または軸を中心に回転する傾向です。
重心を通らないボディに加えられた力はモーメントを生成します。ボディに作用するこれらすべてのモーメントのベクトル合計は、結果モーメントと呼ばれます。
2台のトラクターがポールを引っ張ってポールを下ろすと考えてください。ここでは、点AのF1と点BのF2の2つの力が極に作用します。これらの力は、デカルトベクトル形式で表されます。
これらの力は、基準点Oからの距離rAおよびrBで作用します。
これらの力のモーメントは、力の外積と基準点からの垂直距離を使用して計算できます。
結果として生じるモーメントを見つけるために、モーメントM1とM2が追加され、さらにデカルトベクトル形式で表されます。
最後に、ベクトル クロス積を使用して行列式を展開すると、デカルト ベクトルとして極に作用する結果モーメントが決まります。

<ol>
	<li>ラッセルC.ヒベラー。(2016). エンジニアリングメカニクス:静力学とダイナミクス。ピアソン。122-131ページ。</li>
</ol>

結果モーメント：ベクトル形式

物体に力が加わると、その物体が点を中心に回転する傾向をモーメントと呼びます。もし複数の力が物体に作用している場合、体全体に作用するすべての力のモーメントの合計は、系の結果モーメントとして表現することができます。結果モーメントは他のベクトルと同様に加算および減算できるベクトル量と考えることができます。

力の系の結果モーメントは、ベクトル形式で計算することができます。例えば、2つの力F1およびF2がそれぞれ点AおよびBでポールに作用している場合、これらの力の結果モーメントは以下のように表現できます：

MR = (rA x F1) + (rB x F2)

ここで、rAおよびrBは固定点から点AおよびBまでの位置ベクトルです。r x Fの積は力のモーメントとして知られ、行列式形式で表すことができます。位置ベクトルと力ベクトルの外積を考慮することで、力の方向と回転運動を引き起こす点が考慮されます。

この結果モーメントのベクトル形式にはいくつかの実用的な応用があります。例えば、エンジニアは歯車、プーリー、クランクなどの機械部品にかかるトルクを計算するために使用します。また、スポーツ科学では異なる種類の身体活動中の関節にかかるトルクを計算するために広く使用されています。

物体に力が加えられると、物体が点を中心に回転する傾向は、そのモーメントと呼ばれます。複数の力が作用している場合...

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

Resultant Moment: Vector Formulation

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). Here, rA and rB are position vectors from a fixed point to A and B.

The cross product r x F gives the moment of a force. It can also be written in determinant form. This vector form includes both the direction of the force and the point about which rotation occurs.

This method has practical uses in engineering and sports science. Engineers use it to find torque on machine parts such as gears, pulleys, and cranks. It is also used to calculate torques on joints during physical activity.

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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).

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key terms and concepts

Learn how resultant moment uses vector math to combine multiple forces, with examples from poles, machine parts, and sports joints.

Calculating Torque from Multiple Forces | 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

Calculating Torque from Multiple Forces

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