Name: torque on a bicycle wheel: vector method
Uploaded: 2023-09-22T11:49:21.000Z
Duration: 1 min 29 s
Channel: JoVE

Stellen Sie sich einen Radfahrer vor, der in die Pedale tritt. Wenn eine Kraft auf das Pedal ausgeübt wird, dreht sich die Kurbelwelle so, dass die an der Kurbelwelle befestigte Kette eine Kraft auf die Zahnräder des Rades ausübt.
Beim Festlegen eines Koordinatensystems verläuft die Tangentialkraft auf die Zahnräder entlang der x-Achse, während der Radius der Zahnräder der Momentenarm ist, ausgedrückt als Ortsvektor.
Hier liegt das Kraftmoment um den Punkt O entlang der y-Richtung senkrecht zum Kraft- und Lagevektor und wird als Kreuzprodukt der Orts- und Kraftvektoren ausgedrückt.
Das Kreuzprodukt kann gelöst werden, indem der Koeffizient der Komponenten der Kraft und des Positionsvektors in Form einer Determinante ausgedrückt wird.
Wenn man die Determinante erweitert, wird die Komponente des Moments entlang der x-Achse in Form der y- und z-Komponenten des Kraft- und Lagevektors ausgedrückt.
In ähnlicher Weise kann das Moment einer Kraft, wenn man seine beiden anderen Komponenten in Form von Kraft- und Ortsvektorkomponenten ausdrückt, in kartesischer Vektorform ausgedrückt werden.

<ol>
	<li>Hibbeler, R.C. (2016). Technische Mechanik \u2012 Statik und Dynamik. Hoboken, New Jersey: Pearson Prentice Hall. Seite 146</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 107 - 109</li>
</ol>

moment einer kraft um eine achse: vektor

Wenn eine Kraft auf ein Objekt ausgeübt wird, kann sie dazu führen, dass sich das Objekt um eine Achse dreht. Das Moment einer Kraft, auch als Drehmoment bekannt, misst die Fähigkeit der Kraft, diese Drehung zu verursachen. Im Fall eines Radfahrers, der in die Pedale tritt, verursacht die auf das Pedal ausgeübte Kraft, dass die Kurbelwelle rotiert, was wiederum dazu führt, dass sich das Rad dreht. Das Moment der auf das Pedal ausgeübten Kraft treibt die Rotation des Rades an. Zuerst wird ein Koordinatensystem festgelegt, um zu verstehen, wie das Moment einer Kraft funktioniert. Betrachten Sie das Fahrrad als Beispiel. Legen Sie die x-Achse tangential zum Rad und die y-Achse senkrecht zur x-Achse und nach oben zeigend fest. Die z-Achse kann aus dem Rad herauszeigen. Wenn der Radfahrer eine Kraft auf das Pedal ausübt, rotiert die Kurbelwelle so, dass die an der Kurbelwelle befestigte Kette eine Kraft auf die Achse des Rades ausübt. Die auf die Achse ausgeübte Kraft verläuft dann entlang der x-Achse. Der Radius der Achse ist der Hebelarm, der in Form des Positionsvektors ausgedrückt werden kann. Das Moment der Kraft um den Punkt O verläuft in z-Richtung, senkrecht sowohl zur Kraft als auch zum Positionsvektor. Es wird als das Kreuzprodukt der Positions- und Kraftvektoren ausgedrückt. Das Kreuzprodukt kann gelöst werden, indem die Koeffizientenkomponenten von Kraft und Positionsvektor in Form einer Determinante ausgedrückt werden. Die Determinante kann erweitert werden, um jede Komponente des Kraftmoments zu lösen. Zum Beispiel wird die Komponente des Moments entlang der x-Achse in Bezug auf die y- und z-Komponenten der Kraft und des Positionsvektors ausgedrückt. Ähnlich können die anderen beiden Komponenten des Moments in kartesischer Vektorform ausgedrückt werden. Das Verständnis des Momentes einer Kraft ist in vielen Bereichen der Wissenschaft und Technik wichtig. Es kann uns helfen, die Kräfte auf Objekte wie Zahnräder, Umlenkrollen und Hebel zu berechnen und kann bei der Konstruktion von Maschinen helfen, die Kräfte in Bewegung umwandeln. Im Beispiel des Fahrrads kann das Verständnis des Moments der Kraft helfen, das Design der Kurbelwelle und der Kette zu optimieren, um die auf das Rad ausgeübte Kraft zu maximieren.

Moment einer Kraft um eine Achse: Vektor

Wenn eine Kraft auf ein Objekt ausgeübt wird, kann dies dazu führen, dass sich das Objekt um eine Achse dreht. Das Moment einer Kraft, auch Drehmoment genannt, misst die ...

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Moment of a Force About an Axis: Vector

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 radius acts as the moment arm, and it can be written using the position vector. The moment of the force about point O points in the z-direction because it is perpendicular to both the force and the position vector. It is found using the cross product of the position and force vectors.

The cross product can be calculated by writing the force and position components in determinant form. Expanding the determinant gives the x-, y-, and z-components of the moment. The x-component, for example, depends on the y and z components of the force and position vectors.

Knowing how to find the moment of a force is useful in science and engineering. It helps with problems involving gears, pulleys, and levers. It also supports the design of machines that turn force into motion, including the bicycle crankshaft and chain system.

Torque on a Bicycle Wheel: Vector Method

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Torque About an Axis in 3D Systems

The principle of moments helps solve torque problems in physics and engineering. It describes how forces and moments balance around a pivot point or axis. It is used in many real-life cases, including construction, sports, and everyday actions like opening doors and pushing objects. The problem here uses a pole in a three-dimensional system with a cable attached. When tension acts in the cable, the goal is to find the moment about the z-axis through the base. One method is to project the force...

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Bicycle Torque and Moment About an Axis

The moment of a force about an axis describes how a force can make an object turn around a fixed line. In scalar analysis, the moment is found from the perpendicular distance between the axis of rotation and the line of action of the force. That distance is called the moment arm. A bicycle gives a clear example of this idea. When the cyclist pushes on the pedal, the chain applies a force to the wheel’s axle and makes it rotate. The axis of rotation passes through the axle, and the moment arm...

moment of a force about an axis: vector

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...

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key terms and concepts

Learn how torque, or the moment of a force, makes a bicycle wheel rotate. Follow the vector method, coordinate axes, and cross product step by step.

Torque on a Bicycle Wheel: Vector Method | JoVE K12

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Torque on a Bicycle Wheel: Vector Method

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