Name: couple moment work in rotation
Uploaded: 2023-09-22T11:49:20.000Z
Duration: 1 min 12 s
Channel: JoVE

거리만큼 떨어져 있는 두 점에 작용하는 두 개의 동일하고 반대되는 힘이 있는 강체를 생각해 보십시오.
이 커플은 힘에 그들 사이의 거리를 곱한 것과 같은 순간을 만들어냅니다. 결과적으로 강체는 최종 위치에 도달하기 위해 변환과 회전을 거칩니다.
번역하는 동안 한 힘의 작용은 다른 힘의 작용과 동일하고 반대입니다. 따라서 번역 중에 두 힘이 수행하는 순 작업은 0입니다.
그러나 회전하는 동안 힘 중 하나로 인한 각도 변위는 동일한 선형 변위를 제공하여 작업을 초래합니다.
각도 변위(angular displacement)라는 용어로 작업을 표현하고 커플 모멘트의 규모에 대한 표현을 사용하면 커플 모멘트와 회전 각도에 따라 수행되는 최종 작업량을 알 수 있습니다.
커플 모멘트와 회전 각도가 같은 의미를 갖는다면 커플 모멘트가 수행하는 작업은 긍정적입니다.
반대로, 만약 그들이 반대의 감각을 가지고 있다면, 수행된 작업은 부정적이다.

<ol>
	<li>히벨러, R.C. (2016). 엔지니어링 역학: 정적. 14판, 뉴저지: 피어슨. 섹션 11.1, 582쪽.</li>
	<li>Meriam, J.L., Kraige, L.G. 및 Bolton, J.N. (2016). Engineering Mechanics: Statics and Dynamics(정역학 및 동역학). 여덟 번째 판, 싱가포르 : John Wiley & Sons. 393-394쪽.</li>
	<li>Beer, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. 및 Self, B.P. (2016). 엔지니어를 위한 벡터 역학. 제 11 판, 뉴욕 : McGraw-Hill Education. 섹션 10.1A, 577쪽</li>
</ol>

우력 모먼트의 작업

Work of a Couple Moment

기계공학은 운동, 에너지, 힘을 연구하는 학문이며, 기계 시스템의 설계, 제작 및 유지보수와 관련이 있습니다. 이 분야에서 중요한 개념 중 하나는 일정한 거리로 분리된 강체의 두 점에서 작용하는 동일하고 반대인 두 힘에 의해 생성되는 우력 모멘트입니다.
강체가 커플로 인해 미분 변위를 겪을 때, 강체의 운동은 두 부분으로 나눌 수 있습니다: 두 점을 최종 위치로 동일하게 변환하고 그 중 하나를 중심으로 회전합니다. 변환하는 동안 두 힘은 같은 양의 변위를 겪지만 방향은 반대입니다. 따라서, 부호는 반대지만 크기는 동일한 힘이 한 일은 0이 됩니다.
그러나 회전하는 동안 힘은 각도 변위를 일으켜서 0이 아닌 일을 합니다. 회전하는 동안의 일은 우력 모멘트의 크기와 회전 각도의 곱으로 계산할 수 있습니다.
우력 모멘트와 회전각이 같은 감각이면 우력 모멘트가 한 일은 양수입니다. 반대로 우력 모멘트와 회전각이 반대 감각이면 수행한 일은 음수가 됩니다.
두 순간이 하는 일은 기계 시스템을 설계할 때 고려해야 할 필수 요소입니다. 엔지니어는 시스템이 제대로 작동하는지 확인하기 위해 회전 중에 수행할 작업의 양과 우력 모멘트의 크기 및 방향을 고려합니다.

기계 공학은 운동, 에너지 및 힘에 대한 연구를 포함하며 기계 공학의 설계, 제조 및 유지 관리와 관련이 있습니다.

Education

교육

JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Virtual Work

가상일

KEY TERMS AND CONCEPTS

주요 용어 및 개념

couple moment work in rotation

Mechanical engineering studies motion, energy, and force, and it uses the idea of a couple moment to describe how two equal and opposite forces act on a rigid body. A couple moment is created when those forces act at two points on the body that are separated by a distance.

When a rigid body moves because of a couple, its displacement can be split into two parts. First, the two points move by the same amount to their final positions. Then the body rotates about one of those points.

During the translation part, each force moves the same distance but in the opposite direction. Because the forces are equal in magnitude and opposite in sign, the work done in this step is zero.

The rotation part is different. Here, the force produces an angular displacement, so the work is not zero. The work done by the couple moment equals the magnitude of the couple moment times the angle of rotation.

The sign of the work depends on direction. If the couple moment and the rotation angle have the same sense, the work is positive. If they have opposite senses, the work is negative. Engineers use this idea when they design mechanical systems, since the amount of work during rotation matters, along with the size and direction of the couple moment.

Couple Moment Work in Rotation

work

Work in Force and Motion

Work connects force, motion, and energy in mechanics. It happens when a force acts on an object and the object moves along the line of action of that force. Work can also be described as energy transfer caused by applying a force, which leads to a change in the object’s motion or position. Work is calculated as the force multiplied by the part of the displacement in the same direction as the force. It can also be written as the dot product of the applied force and the object’s displacement. In...

work of a couple moment

Mechanical engineering studies motion, energy, and force, and it uses the idea of a couple moment to describe how two equal and opposite forces act on a rigid body. A couple moment is created when those forces act at two points on the body that are separated by a distance. When a rigid body moves because of a couple, its displacement can be split into two parts. First, the two points move by the same amount to their final positions. Then the body rotates about one of those points. During the...

virtual work

Virtual Work in Force Equilibrium

Virtual work is a mechanics principle used to check equilibrium with imaginary motion. If a body is in static or dynamic equilibrium, the total virtual work from external forces and couple moments must be zero for any virtual displacement. A virtual displacement is an imagined small movement. It can be a shift or a rotation. The virtual work done by a force equals the force dotted with the virtual displacement in the force’s direction. For a couple moment, virtual rotational work is found by...

virtual work for a system of connected rigid bodies

virtual-work-for-a-system-of-connected-rigid-bodies

Finding Forces with Virtual Work in Linked Bodies

Virtual work helps find forces in a system of connected rigid bodies. It is a useful method when several links move together and the system is in equilibrium. In that case, the total virtual work is zero. To analyze the system, start with a free-body diagram. Use one independent coordinate to describe the link configuration. Then mark the deflected position that comes from a positive virtual displacement. This makes the small change in position clear before any calculations begin. Next,...

principle of virtual work: problem solving

principle-of-virtual-work-problem-solving

Virtual Work for Finding Unknown Forces

The principle of virtual work helps find unknown forces and moments in equilibrium problems. It is an important idea in mechanics and engineering. The method uses a small, hypothetical motion called a virtual displacement. If the system is in equilibrium, the work done by the forces during that displacement is zero. To apply this principle, the positions of the internal and external forces must be written in terms of one common coordinate parameter. That parameter can be an angle, a distance,...

mechanical efficiency of real machines

Friction’s Role in Machine Efficiency

Mechanical efficiency shows how well a machine turns input work into output work. It is calculated as the ratio of output work to input work. An ideal machine has an efficiency of one, which means the input work equals the output work. Real machines are never perfectly ideal because some energy is lost. Friction is one of the main causes of that loss. In a toggle vise used to compress wooden blocks, the sliding block rubs against the horizontal plane and creates friction. To find the...

conservative forces

Conservative Forces and Path-Independent Work

Conservative forces are forces whose work depends only on an object’s starting and ending positions. The path between those positions does not change the amount of work done. This idea is important in mechanical engineering because it helps describe how energy moves through a system. A conservative force also conserves energy in the sense that its work is path independent. Gravity is one example. Electrostatic forces and springs modeled by Hooke’s law are also examples. A ball rolling down a...

potential energy

Gravitational and Elastic Energy Stored

Gravitational and elastic potential energy are forms of stored energy from conservative forces. A conservative force, such as gravity or an elastic force, gives a body the capacity to do work. This capacity is measured as potential energy and depends on the body’s position relative to a fixed reference point, or datum. For gravitational potential energy, the datum is the level where the energy is taken as zero. If a body is above this reference plane, its weight has positive gravitational...

potential-energy criterion for equilibrium

potential-energy-criterion-for-equilibrium

Stable Equilibrium Through Potential Energy

Potential energy helps determine when a mechanical system is stable at equilibrium. When a system is acted on by gravitational and elastic forces, its total potential function is the algebraic sum of gravitational potential energy and elastic potential energy. If the system is already in equilibrium and is given a small displacement, the work done on the system equals the negative of the change in potential energy between the starting and ending positions. For a virtual displacement, which is...

stability of equilibrium configuration

Types of Equilibrium in Mechanical Systems

Types of equilibrium in mechanical systems are stable, neutral, and unstable. These three cases help explain how a structure or object responds when it is pushed slightly away from balance. They are important for predicting whether a system will return to its original position, stay where it is, or move farther away. Stable equilibrium occurs when a system returns toward its original position after a small displacement. In this case, the potential energy is at a minimum. A cantilever beam...

one-degree-of-freedom system

Spring-Mass Motion and Energy Stability

A one-degree-of-freedom system uses a single independent variable to describe its state and behavior. In mechanical engineering, this kind of model helps explain how parts in a larger system respond to force. It also gives engineers a way to predict motion before a design is built in real life. A simple harmonic oscillator is one example of a one-degree-of-freedom system. A mass attached to a spring moves along one axis, and that position determines the system’s state. The spring force makes...

stability of equilibrium configuration: problem solving

stability-of-equilibrium-configuration-problem-solving

Equilibrium Stability Through Potential Energy

Stability of equilibrium in physics and engineering can be studied by using a system’s potential energy. An equilibrium configuration is a state where the system can remain at rest. Stability describes whether the system tends to return to that state after a small disturbance. Problem solving begins by finding the equilibrium points of the system. This is done by setting the derivative of the potential energy function equal to zero and solving for the independent variable values that satisfy...

key terms and concepts

Learn how a couple moment does zero work during translation but non-zero work during rotation, and how sign depends on the direction of rotation.

Couple Moment Work in Rotation | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

Couple Moment Work in Rotation

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