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

Kuvvet momenti, konum ve kuvvet vektörlerinin çapraz çarpımı olarak tanımlanır.
Moment için çapraz çarpım, birim vektörler ve Kartezyen konum ve kuvvet vektörleri kullanılarak determinant formda ifade edilebilir.
Kuvvet momentinin Kartezyen vektör formülasyonunu belirlemek için determinant genişletilir.
Kartezyen bileşenler formundaki konum vektörü tarafından verilen bir noktada döner bir kapıya 10 N'luk bir kuvvet uygulandığını düşünün. Burada, vektör formülasyonundaki kuvvet momentinin belirlenmesi gerekir.
Bu durumda, kuvvet vektörü y-z düzlemine diktir, bu da kuvvet vektörünün y ve z bileşenlerinin sıfır olmasına neden olur. Konum vektörü ve kuvvet vektörü kullanılarak bir determinant oluşturulur.
Son olarak, determinantı genişleterek, döner kapının z ekseni etrafındaki kuvvet momenti belirlenir.
Burada, moment pozitif z yönündedir, bu da kapının saat yönünün tersine döndüğünü ima eder.

<ol>
	<li>Hibbeler, R.C. (2016). Mühendislik Mekaniği \u2012 Statik ve Dinamik. Hoboken, New Jersey: Pearson Prentice Salonu. sayfa 129.</li>
</ol>

vektör formülasyonu için kartezien form

Vektör formülasyonunun kartezien formu, konum ve kuvvet vektörlerini kullanarak kuvvet momentini hesaplamak için bir süreçtir. Kuvvet momenti, bu vektörlerin çarpımı olarak tanımlanır ve bir vektör niceliğidir. Konum ve kuvvet vektörlerinin kartezien formu, determinan formunda çapraz çarpımı ifade etmek için kullanılabilen birim vektörler içerir.

<img alt="Equation 1" src="/files/ftp_upload/14254/14254_ Equation_1v2.svg" style="text-align: center; height: 60px;" />

Determinant daha sonra kuvvet momentinin kartezien vektör formülasyonunu belirlemek için genişletilebilir.

<img alt="Equation 2" src="/files/ftp_upload/14254/14254_ Equation_2v2.svg" style="text-align: center; height: 15px;" />

Örneğin, bir dönme kapısına 10 N kuvvetin x-yönünde bir noktaya uygulandığını varsayalım, bu nokta kartezien bileşen formunda r = 0i - 4j + 0k olarak verilmiştir. Bu durumda, kuvvet vektörü, kapının durduğu y-z düzlemine dik bir vektördür, bu da kuvvet vektörünün y ve z bileşenlerinin sıfır olduğu anlamına gelir. Kuvvet momentini hesaplamak için, bir determinantal pozisyon vektörü ve kuvvet vektörü olan F = 10i + 0j + 0k kullanılarak oluşturulur.

<img alt="Equation 3" src="/files/ftp_upload/14254/14254_ Equation_3v2.svg" style="text-align: center; height: 60px;" />

Son olarak, determinantal açarak, dönme kapısının kuvvet momentinin z-eksenine göre 40 N.m eşit olduğunu belirleyebiliriz. Pozitif moment, kapının saat yönünün tersine döndüğünü gösterir.

Vektör formülasyonu için kartezien form, konum ve kuvvet vektörlerini kullanarak kuvvet momentini basit bir şekilde hesaplama olanağı sağlar.

Vektör Formülasyonu için Kartezien Form

Vektör formülasyonu için Kartezyen form, konum ve kuvvet vektörlerini kullanarak kuvvet momentini hesaplamak için bir işlemdir. Kuvvet anı ...

Education

JoVE Core

Mechanical Engineering

Makine Mühendisliği

Unit 1

Ünite 1

Force System Resultants

Kuvvet Sistemleri Bileşkesi

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

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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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

JoVE Core Makine Mühendisliği, denge, kuvvetler, kafes kiriş analizi ve yapısal mekanik gibi temel konuları kapsayan kısa, anlaşılması kolay animasyonlu videolar sunar. Gerçek dünyadaki uygulamalarını keşfedin ve bilim insanlarının önderlik ettiği deneylerle bu kavramların uygulanmasına tanık olun.

mechanical engineering

Calculating Moment with Cartesian Vectors

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