Name: calculating moment with cartesian vectors
Uploaded: 2025-05-22T09:06:02.000Z
Duration: 1 min 26 s
Channel: JoVE

El momento de fuerza se define como el producto cruzado de los vectores de posición y fuerza.
El producto cruzado por el momento se puede expresar en la forma determinante, utilizando vectores unitarios y la forma cartesiana de los vectores de posición y fuerza.
El determinante se expande para determinar la formulación vectorial cartesiana del momento de fuerza.
Considere que se aplica una fuerza de 10 N a una puerta giratoria en un punto dado por el vector de posición en la forma de componentes cartesianos. Aquí, es necesario determinar el momento de fuerza en la formulación del vector.
En este caso, el vector de fuerza es perpendicular al plano y-z , lo que da como resultado que las componentes y y z del vector de fuerza sean cero. Un determinante se construye utilizando el vector de posición y el vector de fuerza.
Finalmente, al expandir el determinante, se determina el momento de la fuerza de la puerta giratoria sobre el eje z.
Aquí, el momento es en la dirección z positiva, lo que implica que la puerta gira en sentido contrario a las agujas del reloj.

<ol>
	<li>Hibbeler, R.C. (2016). Ingeniería Mecánica \u2012 Estática y Dinámica. Hoboken, Nueva Jersey: Pearson Prentice Hall. Págs. 129.</li>
</ol>

forma cartesiana para la formulación vectorial

La forma cartesiana para la formulación vectorial es un proceso para calcular el momento de fuerza utilizando los vectores de posición y fuerza. El momento de fuerza se define como el producto cruz de estos vectores, lo que lo convierte en una cantidad vectorial. La forma

<img alt="Equation 1" src="/files/ftp_upload/14254/14254_ Equation_1v2.svg" style="text-align: center; height: 60px;" />

cartesiana de los vectores de posición y fuerza involucra vectores unitarios, que se pueden usar para expresar el producto cruz en forma de determinante.

El determinante luego se puede expandir para determinar la formulación vectorial cartesiana del momento de la fuerza. <img alt="Equation 2" src="/files/ftp_upload/14254/14254_ Equation_2v2.svg" style="text-align: center; height: 15px;"> Por ejemplo, supongamos que se aplica una fuerza de 10 N a una puerta giratoria a lo largo de la dirección x en un punto dado por el vector de posición r = 0i - 4j + 0k en la forma de componentes cartesianas. En este caso, el vector de fuerza es perpendicular al plano y-z a lo largo del cual se encuentra la puerta, lo que significa que las componentes y, y z del vector de fuerza son cero. Para calcular el momento de la fuerza, se construye un determinante utilizando el vector de posición y el vector de fuerza, F = 10i + 0j + 0k. <img alt="Equation 3" src="/files/ftp_upload/14254/14254_ Equation_3v2.svg" style="text-align: center; height: 60px;"> Finalmente, al expandir el determinante, podemos determinar que el momento de fuerza de la puerta giratoria es igual a 40 N.m sobre el eje z. El momento positivo implica que la puerta gira en sentido antihorario. La forma cartesiana para la formulación vectorial nos permite calcular el momento de fuerza utilizando los vectores de posición y fuerza de manera sencilla.

Forma Cartesiana para la Formulación Vectorial

La forma cartesiana para la formulación de vectores es un proceso para calcular el momento de fuerza utilizando los vectores de posición y fuerza. El momento de la fuerza es ...

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

Cartesian Form for Vector Formulation

calculating moment with cartesian vectors

Calculating moment with Cartesian vectors shows how position and force vectors work together. The moment of force is the cross product of these vectors, so it is a vector quantity. In Cartesian form, unit vectors help write the vectors in component form.

The cross product can be arranged in determinant form. That determinant is then expanded to find the Cartesian vector form of the moment of force. This method gives a clear way to work through the calculation step by step.

A revolving door example shows the process in action. A force of 10 N is applied in the x-direction at the position vector r = 0 i - 4 j + 0 k. The force vector has no y or z components, so it can be written as F = 10 i + 0 j + 0 k.

Using these vectors, the determinant is built and expanded. The result is a moment of 40 N.m about the z-axis. The positive sign means the door rotates counterclockwise.

Calculating Moment with Cartesian Vectors

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cartesian form for vector formulation

Calculating moment with Cartesian vectors shows how position and force vectors work together. The moment of force is the cross product of these vectors, so it is a vector quantity. In Cartesian form, unit vectors help write the vectors in component form. The cross product can be arranged in determinant form. That determinant is then expanded to find the Cartesian vector form of the moment of force. This method gives a clear way to work through the calculation step by step. A revolving door...

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simplification of a force and couple system i

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key terms and concepts

Learn how Cartesian vector form is used to calculate moment of force with unit vectors, determinants, and a revolving door example in a simple step-by-step method.

Calculating Moment with Cartesian Vectors | JoVE K12

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Calculating Moment with Cartesian Vectors

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