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

Das Moment ist die Tendenz eines Körpers, sich um einen Punkt oder eine Achse zu drehen, wenn eine Kraft auf ihn ausgeübt wird.
Kräfte, die auf einen Körper ausgeübt werden und nicht durch den Schwerpunkt gehen, erzeugen Momente; die Vektorsumme all dieser Momente, die auf einen Körper wirken, wird als resultierendes Moment bezeichnet.
Stellen Sie sich zwei Traktoren vor, die an der Stange ziehen, um sie herunterzunehmen. Hier wirken zwei Kräfte auf den Pol, F1 am Punkt A und F2 am Punkt B. Diese Kräfte werden in der kartesischen Vektorform ausgedrückt.
Diese Kräfte wirken in den Abständen rA und rB vom Bezugspunkt O.
Das Moment dieser Kräfte kann aus dem Kreuzprodukt der Kraft und dem senkrechten Abstand vom Referenzpunkt berechnet werden.
Um das resultierende Moment zu finden, werden die Momente M1 und M2 addiert und in der kartesischen Vektorform weiter ausgedrückt.
Schließlich bestimmt die Erweiterung der Determinanten mit Hilfe des Vektorkreuzprodukts das resultierende Moment, das als kartesischer Vektor auf den Pol wirkt.

<ol>
	<li>Russell C. Hibbeler. (2016). Technische Mechanik: Statik & Dynamik. Pearson. S. 122-131.</li>
</ol>

ergebnierender moment: vektorformulierung

Wenn eine Kraft auf ein Objekt ausgeübt wird, wird die Tendenz des Objekts, sich um einen Punkt zu drehen, als sein Moment bezeichnet. Wenn mehrere Kräfte auf ein Objekt wirken, kann die Summe der Momente aller auf einen Körper wirkenden Kräfte als das resultierende Moment des Systems ausgedrückt werden. Das resultierende Moment kann als Vektorgröße betrachtet werden, die wie jeder andere Vektor addiert und subtrahiert werden kann. Das resultierende Moment eines Systems von Kräften kann durch Vektorformulierung berechnet werden. Wenn wir zum Beispiel zwei Kräfte, F1 und F2, betrachten, die an einem Pfosten an den Punkten A und B wirken, kann das resultierende Moment dieser Kräfte ausgedrückt werden als MR = (rA x F1)+ (rB x F2). wo rA und rB die Positionsvektoren von einem festen Punkt zu den Punkten A und B sind. Das Produkt r x F wird als das Moment der Kraft bezeichnet und kann in Determinantenform ausgedrückt werden. Die Berücksichtigung des Kreuzprodukts des Positionsvektors mit dem Kraftvektor berücksichtigt die Richtung der Kraft und den Punkt, um den sie eine Rotationsbewegung verursacht. Diese Vektorformulierung des resultierenden Moments hat mehrere praktische Anwendungen. Ingenieure verwenden sie zum Beispiel, um das Drehmoment an Maschinenteilen, wie Zahnrädern, Umlenkrollen und Kurbeln, zu berechnen. Es wird auch in den Sportwissenschaften verwendet, um die Drehmomente an Gelenken während verschiedener Arten von körperlicher Aktivität zu berechnen.

Ergebnierender Moment: Vektorformulierung

Wenn eine Kraft auf ein Objekt ausgeübt wird, wird die Tendenz des Objekts, sich um einen Punkt zu drehen, als sein Moment bezeichnet. Wenn mehrere Kräfte auf eine ...

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Force System Resultants

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KEY TERMS AND CONCEPTS

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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.

Calculating Torque from Multiple Forces

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resultant moment: vector formulation

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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couple

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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 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

Calculating Torque from Multiple Forces

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