Name: couple moment in force systems
Uploaded: 2023-09-22T11:49:21.000Z
Duration: 1 min 29 s
Channel: JoVE

Ein Paar ist ein Paar paralleler Kräfte gleicher Größe, die aber in entgegengesetzte Richtungen wirken und durch einen senkrechten Abstand getrennt sind.
Das Paar verursacht eine Rotationskraft, die den Körper um eine Achse senkrecht zur Ebene der Kräfte dreht, und das resultierende Moment wird als Paarmoment bezeichnet.
Erwäge, eine Schraube mit einem Radschlüssel festzuziehen. Ein Kraftpaar entsteht, wenn zwei gleiche und entgegengesetzte Kräfte an den Punkten A und B auf den Schlüssel aufgebracht werden, die durch einen senkrechten Abstand getrennt sind.
Die Positionsvektoren rA und rB werden vom Ursprung eines Koordinatensystems zu den Anwendungspunkten gerichtet.
Das Paarmoment um den Ursprung ist die Summe aus dem Kreuzprodukt der Ortsvektoren und den Kräften.
Die Differenz zwischen den Ortsvektoren rA und rB ist der Ortsvektor r, der den Abstand zwischen den beiden entgegengesetzten Kräften darstellt.
Das Paarmoment hängt nur vom Ortsvektor r zwischen den Kräften ab und nicht von den Ortsvektoren rA und rB. Daher wird es als freier Vektor betrachtet.

<ol>
	<li>Hibbeler, R.C. (2016). Technische Mechanik \u2012 Statik und Dynamik. Hoboken, New Jersey: Pearson Prentice Hall. Seite 154</li>
	<li>Bier, F.P.; Johnston, E.R.; Mazurek, D.F.; Cromwell, P.J. und Self, B.P. (2019). Vektormechanik für Ingenieure \u2012 Statik und Dynamik. New York: McGraw-Hill. Seiten – 120.</li>
</ol>

paar

Ein Paar besteht aus zwei parallelen Kräften gleicher Größe, die jedoch in entgegengesetzte Richtungen wirken. Die Kräfte werden durch einen senkrechten Abstand voneinander getrennt, der als Arm des Paares bezeichnet wird. Das Paar verursacht ein Drehmoment, das den Körper um eine Achse dreht, die senkrecht zur Ebene der Kräfte steht. Das resultierende Moment wird als Paarmoment bezeichnet. Die SI-Einheit für ein Paarmoment ist das Newton-Meter (N-m). Ein typisches Beispiel, um dieses Konzept zu verstehen, ist das Anziehen einer Schraube mit einem Radmutternschlüssel. Ein Kräftpaar entsteht, wenn zwei gleich große und entgegengesetzte Kräfte auf den Schlüssel an den Punkten A und B angewendet werden, die durch einen senkrechten Abstand voneinander getrennt sind. Die jeweiligen Positionsvektoren sind vom Ursprung eines Koordinatensystems zum Anwendungspunkt gerichtet. Das Paarmoment bezüglich des Ursprungs ist die Summe des Kreuzprodukts der Positionsvektoren und der Kräfte. Der Unterschied zwischen den Positionsvektoren beider entgegengesetzter Kräfte ergibt den Positionsvektor r, der den Abstand zwischen den gegenüberliegenden Kräften darstellt. Interessanterweise hängt das Paarmoment nur vom Positionsvektor r zwischen den Kräften ab und nicht von den individuellen Positionsvektoren der beiden Kräfte. Der Positionsvektor r ist unabhängig vom Ursprung. Das bedeutet, dass das Berechnen der Momente derselben Kräfte um einen anderen Punkt das gleiche Ergebnis liefern würde. Das Paarmoment ist ein freier Vektor. Im Gegensatz zum Paarmoment hängt das Moment einer Kraft von der Position ab, an der es gemessen wird. Wenn zwei Paare ein Moment gleicher Größe und Richtung erzeugen, dann sind diese beiden Paare äquivalent. Äquivalente Paare haben unabhängig von ihren Positionen, Richtungen oder Größen das gleiche Drehmoment oder die gleiche Drehwirkung. Die Berechnung des Paarmoments und das Verständnis seiner Auswirkungen sind entscheidend für die Gestaltung stabiler und robuster Systeme, die äußeren Kräften standhalten können.

Paar

Ein Paar ist ein Paar paralleler Kräfte, die gleich groß sind, aber in entgegengesetzte Richtungen. Die Kräfte sind durch einen senkrechten Abstand getrennt, der als ...

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Couple

couple moment in force systems

A couple is a pair of parallel forces that are equal in magnitude and opposite in direction. The two forces are separated by a perpendicular distance called the couple arm. Together, they create a turning effect on a body instead of a net push.

This turning effect is called the couple moment. It rotates the body about an axis that is perpendicular to the plane of the forces. The SI unit for a couple moment is the Newton-meter (N-m).

A common example is tightening a bolt with a lug wrench. In that case, two equal and opposite forces act at points A and B on the wrench. These points are separated by a perpendicular distance, so they form a force couple.

The couple moment about the origin is found by adding the cross products of the position vectors and the forces. The position vector between the two opposing forces is r, which is the distance between them. The couple moment depends only on this vector r, not on the separate position vectors of the forces.

Because r does not depend on the origin, the same couple moment is obtained even if the moments are taken about a different point. This is why a couple moment is a free vector. A moment of a single force is different because it depends on where it is measured.

If two couples create moments with the same magnitude and direction, they are equivalent couples. Equivalent couples have the same torque, or turning effect, even if their positions, directions, or magnitudes differ. Understanding couple moments helps in designing stable systems that can resist external forces.

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key terms and concepts

Learn how a couple creates rotation, why couple moment depends on the distance between forces, and how equivalent couples are identified in force systems.

Couple Moment in Force Systems | JoVE K12

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Couple Moment in Force Systems

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