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

O momento de força é definido como o produto cruzado dos vetores de posição e força.
O produto vetorial no momento pode ser expresso na forma determinante, usando vetores unitários e a forma cartesiana de vetores posição e força.
O determinante é expandido para determinar a formulação do vetor cartesiano do momento de força.
Considere que uma força de 10 N é aplicada a uma porta giratória em um ponto dado pelo vetor de posição na forma de componentes cartesianos. Aqui, o momento de força na formulação do vetor precisa ser determinado.
Nesse caso, o vetor de força é perpendicular ao plano y-z , o que resulta nos componentes y e z do vetor de força sendo zero. Um determinante é construído usando o vetor posição e o vetor força.
Finalmente, ao expandir o determinante, o momento da força da porta giratória em torno do eixo z é determinado.
Aqui, o momento está na direção z positiva, o que implica que a porta gira no sentido anti-horário.

<ol>
	<li>Hibbeler, R.C. (2016). Engenharia Mecânica \u2012 Estática e Dinâmica. Hoboken, Nova Jersey: Pearson Prentice Hall. pág. 129.</li>
</ol>

forma cartesiana para formulação vetorial

A forma cartesiana para formulação vetorial é um processo para calcular o momento de força usando os vetores posição e força. O momento de força é definido como o produto cruzado desses vetores, tornando-se uma quantidade vetorial. A forma cartesiana dos vetores posição e força envolve vetores unitários, que podem ser usados para expressar o produto cruzado na forma de um determinante.

<img alt="Equation 1" src="/files/ftp_upload/14254/14254_ Equation_1v2.svg" style="text-align: center; height: 60px;" />

O determinante pode então ser expandido para determinar a formulação vetorial cartesiana do momento da força.

<img alt="Equation 2" src="/files/ftp_upload/14254/14254_ Equation_2v2.svg" style="text-align: center; height: 15px;" />

Por exemplo, suponha que uma força de 10 N seja aplicada a uma porta giratória ao longo da direção x em um ponto dado pelo vetor posição r = 0i - 4j + 0k na forma de componentes cartesianas. Neste caso, o vetor força é perpendicular ao plano y-z, ao qual a porta está posicionada, o que significa que as componentes y e z do vetor força são zero. Para calcular o momento de força, é construído um determinante usando o vetor posição e o vetor força, F = 10i + 0j + 0k.

<img alt="Equation 3" src="/files/ftp_upload/14254/14254_ Equation_3v2.svg" style="text-align: center; height: 60px;" />

Finalmente, ao expandir o determinante, podemos determinar que o momento de força da porta giratória é de 40 N.m em relação ao eixo z. O momento positivo implica que a porta gira no sentido anti-horário.

A forma cartesiana para formulação vetorial nos permite calcular o momento de força usando vetores posição e força de maneira direta.

Forma Cartesiana para Formulação Vetorial

A forma cartesiana para formulação vetorial é um processo para calcular o momento de força usando os vetores posição e força. O momento da força é ...

Education

JoVE Core

Mechanical Engineering

Engenharia Mecânica

Unit 1

Unidade 1

Force System Resultants

Resultantes de Sistemas de Forças

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

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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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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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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mechanical engineering

Calculating Moment with Cartesian Vectors

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