Name: torque about an axis in 3d systems
Uploaded: 2023-09-22T11:49:21.000Z
Duration: 1 min 30 s
Channel: JoVE

3 boyutlu bir sisteme yerleştirilmiş ve kablo takılı bir direk düşünün. Kabloya 15 kN gerilim uygulandığında, tabandan geçen z ekseni ile ilgili momenti belirleyin.
Moment iki yöntem kullanılarak belirlenebilir.
İlk yöntemde, kuvvetin birim vektör boyunca izdüşümünü hesaplayın ve kuvvet vektörünü elde etmek için kuvvetin büyüklüğü ile çarpın.
Orijin hakkındaki moment, konum vektörü ile kuvvetin çapraz çarpımıdır. Z ekseni boyunca moment, orijin etrafındaki momentin nokta çarpımı ve z ekseni boyunca birim vektör ile elde edilebilir.
Alternatif olarak, kuvvet vektörünü bileşenlerine ayırın. Y ekseni ve z ekseni boyunca uzanan bileşenler, sırasıyla z ekseninden geçerken ve z eksenine paralel olduklarında moment uygulamazlar.
X yönündeki gerilim, gerilimin x eksenine göre kosinüs yönü ile çarpılmasıyla elde edilebilir.
Kuvvet denkleminin momentini hatırlayın ve terimleri değiştirerek z ekseni etrafındaki moment belirlenebilir.

<ol>
	<li>Hibbeler, R.C. (2016). Mühendislik Mekaniği \u2012 Statik ve Dinamik. Hoboken, New Jersey: Pearson Prentice Salonu. sayfa 133-138</li>
	<li>Bira, F.P.; Johnston, E.R.; Mazurek, D.F; Cromwell, P.J. ve Öz, B.P. (2019). Mühendisler için Vektör Mekaniği \u2012 Statik ve Dinamik. New York: McGraw-Tepesi. sayfa 96 -99</li>
	<li>Meriam, J.L.; Kraige, L.G. ve Bolton, J.N. (2020). Mühendislik Mekaniği \u2012 Statik. Hoboken, New Jersey: John Wiley. sayfa 78 ve 79</li>
</ol>

anında moment prensibi: problem Çözme

Anlık moment prensibi, fizik ve mühendislikte temel bir kavramdır. Bu, kuvvetlerin ve momentlerin bir nokta veya eksen etrafında dengelemesine atıfta bulunur, ayrıca ayak noktası olarak da bilinir. Bu prensip, inşaat, spor ve kapı açma gibi günlük aktiviteler gibi birçok gerçek hayat senaryosunda kullanılır.

Bir örnek senaryo, bir kablo eklenmiş bir üç boyutlu sistemde yerleştirilmiş bir direğin içerir. Bir gerginlik kablo üzerine uygulandığında, tabanın içinden geçen z-eksenine göre moment belirlenmelidir. Bu problemi çözmek için iki yöntem vardır.

İlk yöntem, kuvvetin birim vektöre göre projeksiyonunu hesaplamak ve kuvvetin büyüklüğüyle çarpmak suretiyle kuvvet vektörünü elde etmeyi içerir. Başlangıçtan itibaren olan moment, konum vektörünün ve kuvvet vektörünün çapraz çarpımı alınarak hesaplanabilir. Moment vektörü belirlendikten sonra, z-eksenine göre moment, başlangıçtan itibaren olan moment ile z-eksenine yönelik birim vektörün nokta çarpımı alınarak değerlendirilebilir.

Alternatif olarak, kuvvet vektörünü bileşenlerine ayrıştırın. y-ekseni ve z-ekseni boyunca olan bileşenler, sırasıyla z-eksenine geçer ve ona paraleldir, dolayısıyla moment uygulamazlar. x-yönündeki gerilme, gerilimi x-eksenine göre yönlendirme kosinüsü ile çarparak hesaplanabilir. Ardından, moment denklemi kullanılabilir ve uygun terimler yerine konarak z-eksenine göre olan moment belirlenebilir.

Anlık moment prensibinin yapıların ve makinelerin davranışını anlamak için önemli olduğunu belirtmek önemlidir. Mühendisler ve tasarımcılar, yaratımlarının stabil, güvenli ve etkili olduğunu sağlamak için bunu çokça kullanır. Kuvvetleri ve momentleri bir ayak noktası etrafında dengeleyerek, bir yapı veya makinenin dayanacağı gerilimi ve gerilmeyi hesaplayabilir ve potansiyel hata noktalarını belirleyebilirler.

Genel olarak, anlık moment prensibi, kuvvetlerle, torklarla ve hareketle ilgili sorunları çözmeye yardımcı olan güçlü bir araçtır. Köprülerin inşa edilmesi, spor tekniklerinin analizi veya sadece bir kapı açılmasıyla ilgili olması fark etmeksizin, her şeyin doğru ve verimli bir şekilde yapılmasını sağlamak için bu prensibi güvenle kullanabilirsiniz.

Anında Moment Prensibi: Problem Çözme

Anlar ilkesi fizik ve mühendislikte temel bir kavramdır. Kuvvetlerin ve momentlerin bir nokta veya eksen etrafında dengelenmesini ifade eder, ...

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

Principle of Moments: Problem Solving

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 along a unit vector to build the force vector. The moment about the origin is then found with the cross product of the position vector and the force vector. After that, the moment along the z-axis is found by taking the dot product of the moment vector with the z-axis unit vector.

A second method is to split the force into components. The y-axis and z-axis components create no moment in this setup. The y-axis component passes through the axis, and the z-axis component is parallel to it. The x-direction tension is found by multiplying the cable tension by the direction cosine with respect to the x-axis. Then the moment of force equation is used to determine the moment about the z-axis.

This kind of analysis is important in structures and machines. Engineers and designers use the principle of moments to check stability, safety, and performance. It helps them estimate the stresses and strains a structure or machine may face and spot possible failure points. The same idea also appears in bridges, sports technique, and simple tasks like opening a door.

Torque About an Axis in 3D Systems

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Torque on a Flywheel: Direction and Size

Torque, or the moment of a force, describes how a force can make an object turn about an axis. It is a vector quantity, so it has both size and direction. This idea is important in physics, mechanics, and engineering. A simple flywheel example shows how torque works. The flywheel rotates about point O when a force is applied to it. The moment arm is the perpendicular distance from point O to the line of action of the force. The moment, in newton-meter (N-m), is found by multiplying the force...

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Calculating force moments in problem solving helps students analyze rotation in mechanical systems. The scalar form of the moment of a force is used to work through these problems step by step. Start by drawing a free-body diagram, or FBD. An FBD is a sketch that shows every force acting on the system. Each force must be identified and included. Next, identify the axis or point about which the moment is calculated. In some problems, that axis or point is given. In other cases, you must choose...

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Net Moment Sign Convention in 2D Forces

Net moment in two-dimensional force systems shows how multiple forces can cause rotation about a fixed point. The scalar formulation helps analyze equilibrium in structures that are acted on by several forces. It focuses on the x-y plane and uses a simple sign rule to describe the direction of rotation. To find the resultant moment, the moments from all forces in the system are considered about a chosen point A. Each moment is assigned a sign based on its sense of rotation. Positive moments...

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The moment of force describes the twisting effect a force can have on an object. It shows why a force may cause rotation instead of straight-line motion. The moment arm is the perpendicular distance from the force’s line of action to the axis of rotation. The moment of force is a vector quantity, not a scalar. Its vector form comes from the cross product of the position vector and the force vector. A cross product gives a vector that is perpendicular to both input vectors. The moment about a...

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...

resultant moment: vector formulation

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Resultant moment describes the total turning effect of multiple forces acting on an object. It shows how several forces can combine to make a body rotate about a point. In physics, moment is the tendency of a force to cause rotation. The resultant moment of a force system is a vector quantity. That means it can be added and subtracted like other vectors. For a system with two forces, F1 and F2, acting on a pole at points A and B, the resultant moment is written as MR = (rA x F1) + (rB x F2).

principle of moments

Resolving Forces in Moment Calculations

The principle of moments, also called Varignon's theorem, explains how a force creates rotation about a point. It is a key idea in physics and engineering. It also helps describe when a rigid body stays in equilibrium under external forces. The moment of a force is found by multiplying the force by the perpendicular distance from the point of application to the point being studied. A larger force or a larger distance gives a larger moment. This makes the idea useful for checking how strongly a...

principle of moments: problem solving

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...

moment of a force about an axis: scalar

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...

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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...

couple

Couple Moment in Force Systems

A couple is a pair of parallel forces that are equal in magnitude and opposite in direction. The two forces are separated by a perpendicular distance called the couple arm. Together, they create a turning effect on a body instead of a net push. This turning effect is called the couple moment. It rotates the body about an axis that is perpendicular to the plane of the forces. The SI unit for a couple moment is the Newton-meter (N-m). A common example is tightening a bolt with a lug wrench. In...

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Couple Moments and the Right-Hand Rule

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Equivalent Couples in Mechanical Systems

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Torque from a Couple: Solving Forces

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Equivalent Force and Moment Systems

Structural systems often experience several forces and couple moments at the same time. Engineers simplify these loading cases by replacing them with an equivalent force and moment system at a chosen point O. This makes the analysis easier while keeping the same external effects on the member. A key idea in this process is the principle of transmissibility. A force is a sliding vector, which means it can be moved anywhere along its line of action without changing how the body behaves...

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Resultant Forces in Force and Couple Systems

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simplification of a force and couple system: ii

simplification-of-a-force-and-couple-system-ii

Resultant Force and Wrench Motion

Resultant force and resultant couple moment describe how several forces and moments act together on a rigid body in three dimensions. When many forces act on an object, they can be replaced by one equivalent force. The moments from those forces can also be combined into one equivalent couple moment. In some cases, the resultant force and the resultant couple moment are not mutually perpendicular. That means the angle between them is not 90 degrees. To study this situation, the couple moment is...

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Load Distribution on Shelves and Dams

Load distribution helps engineers describe how force spreads across a surface or structure. A distributed load is a continuous force per unit area, rather than a single point force. It is a common idea in many practical situations. A bookshelf full of stacked books is one simple example. The weight of the books is spread along the shelf, so the pressure changes across the surface. This pressure is measured in Newtons per square meter, or Pascals. A hydroelectric dam gives another clear...

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Finding Resultant Loads on a Beam

Structural engineering often requires finding the resultant load on a beam with changing force patterns. Here, a beam of length L carries a varying load made from parabolic and trapezoidal load distributions along the x-axis. The goal is to find the total load, where it acts, and the centroid of the combined area so the beam’s response can be predicted. The parabolic load is handled first. A small force element, dR, acts over a short distance, dx, and these elements are integrated across the...

distributed loads: problem solving

Equivalent Resultant Loads on Beams

Equivalent resultant loads on beams can be found by breaking a distributed load into smaller regions. This makes the beam easier to analyze. Each region can then be handled on its own before the results are combined. The magnitude of the equivalent resultant load for each region comes from the area of that region. In this setting, area represents the force applied by the distributed load over that part of the beam. After finding the force for each region, the position of each resultant load...

key terms and concepts

Learn how the principle of moments is used to find torque about the z-axis in a 3D cable-and-pole setup using cross products and force components.

Torque About an Axis in 3D Systems | 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

Torque About an Axis in 3D Systems

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