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

Pensemos en un ciclista pedaleando una bicicleta. Cuando se ejerce una fuerza sobre el pedal, el cigüeñal gira de tal manera que la cadena unida al cigüeñal ejerce una fuerza sobre los engranajes de la rueda.
Al establecer un sistema de coordenadas, la fuerza tangencial sobre los engranajes está a lo largo del eje x, mientras que el radio de los engranajes es el brazo de momento expresado en términos del vector de posición.
Aquí, el momento de fuerza alrededor del punto O está a lo largo de la dirección y perpendicular tanto al vector de fuerza como al de posición y se expresa como el producto cruzado de los vectores de posición y fuerza.
El producto cruzado se puede resolver expresando el coeficiente de los componentes de la fuerza y el vector de posición en forma de un determinante.
Expandiendo el determinante, la componente del momento a lo largo del eje x se expresa en términos de las componentes y y z del vector de fuerza y posición.
De manera similar, expresando sus otros dos componentes en términos de componentes vectoriales de fuerza y posición, el momento de una fuerza se puede expresar en forma vectorial cartesiana.

<ol>
	<li>Hibbeler, R.C. (2016). Ingeniería Mecánica \u2012 Estática y Dinámica. Hoboken, Nueva Jersey: Pearson Prentice Hall. págs. 146</li>
	<li>Cerveza, F.P.; Johnston, E.R.; Mazurek, D.F.; Cromwell, P.J. y Self, B.P. (2019). Mecánica vectorial para ingenieros: estática y dinámica. Nueva York: McGraw-Hill. págs. 107 - 109</li>
</ol>

momento de una fuerza alrededor de un eje: vector

Cuando se ejerce una fuerza sobre un objeto, puede hacer que ese objeto gire alrededor de un eje. El momento de una fuerza, también conocido como torsión, mide la capacidad de la fuerza para causar esa rotación. En el caso de un ciclista pedaleando una bicicleta, la fuerza ejercida sobre el pedal hace que el cigüeñal gire, lo cual a su vez hace que la rueda gire. El momento de la fuerza ejercida sobre el pedal impulsa la rotación de la rueda. Primero, establezca un sistema de coordenadas para comprender cómo funciona el momento de una fuerza. Considere la bicicleta como ejemplo. Establezca el eje x tangente a la rueda, y el eje y perpendicular al eje x y apuntando hacia arriba. El eje z puede apuntar hacia afuera desde la rueda. Cuando el ciclista ejerce una fuerza sobre el pedal, el cigüeñal gira de manera tal que la cadena unida al cigüeñal ejerce una fuerza sobre el eje de la rueda. La fuerza ejercida sobre el eje está a lo largo del eje x. El radio del eje es el brazo de momento, que se puede expresar en términos del vector de posición. El momento de fuerza alrededor del punto O está en la dirección z, perpendicular tanto a la fuerza como al vector de posición. Se expresa como el producto cruz entre el vector de posición y la fuerza. El producto cruz se puede resolver al expresar el coeficiente de componentes de la fuerza y el vector de posición en forma de un determinante. El determinante se puede expandir para resolver cada componente del momento de fuerza. Por ejemplo, el componente del momento a lo largo del eje x se expresa en términos de los componentes y, y z del vector de fuerza y posición. De manera similar, los otros dos componentes del momento se pueden expresar en forma de vector cartesiano. Comprender el momento de fuerza es importante en muchos campos de la ciencia y la ingeniería. Puede ayudarnos a calcular las fuerzas en objetos como engranajes, poleas y palancas, y puede ayudar en el diseño de máquinas que convierten las fuerzas en movimiento. En el ejemplo de la bicicleta, comprender el momento de fuerza puede ayudarnos a optimizar el diseño del cigüeñal y la cadena para maximizar la fuerza ejercida sobre la rueda.

Momento de una Fuerza alrededor de un Eje: Vector

Cuando se ejerce una fuerza sobre un objeto, puede hacer que ese objeto gire alrededor de un eje. El momento de una fuerza, también conocido como par, mide el ...

Education

Educación

JoVE Core

Mechanical Engineering

Ingeniería Mecánica

Unit 1

Unidad 1

Force System Resultants

Resultantes de Sistemas de Fuerzas

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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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cartesian form for vector formulation

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Torque About an Axis in 3D Systems

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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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