Name: rigid body force balance in equilibrium
Uploaded: 2023-09-22T11:49:22.000Z
Duration: 1 min 28 s
Channel: JoVE

강체는 외부 힘의 영향으로 변형되지 않습니다.
회전목마가 수직 반경 거리 r에서 외력 F를 받아 점 O에 대한 힘의 모멘트를 생성한다고 생각해 보십시오.
회전목마에 여러 힘이 작용하면 회전목마에 작용하는 모든 외부 힘의 합이 0일 때 평형 상태가 얻어집니다.
평형의 다른 조건은 점 O에 대한 모든 순간의 합이 0과 같아야 한다는 것입니다.
점 A에서 모멘트를 측정할 때 점 O에서의 모멘트와 수직 거리 및 적용된 힘의 교차 제품의 합으로 표현할 수 있습니다.
이러한 조건은 신체가 정적 평형 상태에서 평행 이동 또는 회전 운동을 겪지 않도록 합니다.
여기서는 강체 내부의 힘이 동일한 크기를 가지며 반대 방향으로 작용하여 뉴턴의 운동 제3법칙으로 인해 서로를 상쇄하기 때문에 외부 힘만 고려됩니다.

<ol>
	<li>맥주, F.P.; 존스턴, ER; 마주렉, D.F; 크롬웰, PJ 및 셀프, BP (2019). 엔지니어를 위한 벡터 역학 \u2012 Statics and Dynamics. 뉴욕 : McGraw-Hill. 170쪽</li>
</ol>

평형 조건

Conditions of Equilibrium

평형은 강체가 어떠한 병진운동이나 회전운동을 받지 않는 상태를 말합니다. 이 상태는 강체에 작용하는 힘과 우력이 0일 때 얻어집니다. 외력의 시스템이 0에 해당하는 순효과를 얻을 때 강체는 평형상태에 있는 것으로 간주됩니다.
내력은 신체 내에서 동등한 쌍과 반대 쌍으로 발생하여 사실상 서로 상쇄되기 때문에 평형 조건에 고려되지 않습니다. 결과적으로 이러한 내력은 강체의 전반적인 운동이나 운동 변화에 기여하지 않습니다. 평형은 외력과 신체에 작용하는 모멘트의 균형에 의해 결정되며, 이는 병진 운동이나 회전 운동을 일으키는 원인입니다.
평형을 이루기 위한 필요충분조건은 합력과 모멘트를 0과 같게 설정함으로써 결정될 수 있습니다. 또한 벡터 방정식은 각 힘과 모멘트를 직사각형 성분으로 분해함으로써 6개의 스칼라 방정식으로 대체할 수 있습니다. 이는 외력의 x, y, z 방향 성분이 균형을 이루고 있으며, 외력의 x, y, z축 모멘트도 균형을 이루고 있음을 의미합니다. 강체가 평형을 이루면 외력의 시스템은 몸에 병진운동이나 회전운동을 하지 않습니다. 
강체에 대한 평형방정식을 작성하려면 먼저 물체에 작용하는 모든 힘을 확인한 다음 해당하는 자유 물체도를 그려야 합니다. 구조물에 작용하는 힘 외에 구조물의 지지물에 작용하는 반응을 고려해야합니다. 각 반응을 정확하게 확인하면 알려지지 않은 힘과 반응을 해결하는 데 도움이 될 수 있습니다.
평형조건에 대한 지식은 강체와 관련된 문제를 분석하는 데 매우 중요합니다. 알려지지 않은 힘과 반응을 결정하고 평형에 필요하고 충분한 조건을 사용함으로써 강체의 거동을 예측할 수 있습니다.

평형(Equilibrium)은 강체가 평행 이동 또는 회전 운동의 영향을 받지 않는 상태를 나타냅니다. 이 상태는 힘과 ...

Education

교육

JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Equilibrium of a Rigid Body

강체의 평형

KEY TERMS AND CONCEPTS

주요 용어 및 개념

rigid body force balance in equilibrium

Rigid body equilibrium depends on a balance of external forces and moments. A rigid body is in equilibrium when it has no translational motion and no rotational motion. This happens when the net force and the net couple acting on the body are both zero.

Internal forces are not used when checking equilibrium. These forces act in equal and opposite pairs inside the body, so they cancel each other. Because of that, they do not affect the overall motion or change in motion of the rigid body.

The external forces and moments determine whether the body stays balanced. These are the forces that can cause translation or rotation. The necessary and sufficient conditions for equilibrium are found by setting the resultant force and the resultant moment equal to zero.

The vector equations for equilibrium can also be written as six scalar equations. Each force and moment is resolved into rectangular components. This means the external force components in the x, y, and z directions must balance, and the moments about the x, y, and z axes must also balance.

To write equilibrium equations for a rigid body, first identify all forces acting on it. Then draw a free-body diagram. The reactions from supports must also be included. Correctly identifying each reaction helps solve unknown forces and reactions in structures.

Rigid Body Force Balance in Equilibrium

conditions of equilibrium

Rigid body equilibrium depends on a balance of external forces and moments. A rigid body is in equilibrium when it has no translational motion and no rotational motion. This happens when the net force and the net couple acting on the body are both zero. Internal forces are not used when checking equilibrium. These forces act in equal and opposite pairs inside the body, so they cancel each other. Because of that, they do not affect the overall motion or change in motion of the rigid body. The...

support reactions

Types of Structural Supports

Types of structural supports control how a coplanar force system moves and reacts under load. A coplanar force system is a set of forces that all lie in the same plane. The supports create reactions at the point of contact. These reactions help keep a structure stable under external forces. Supports work by stopping translation with an equal and opposite force. They can also stop rotation by applying a couple moment in the opposite direction. In structural design, these reactions are important...

internal forces and center of gravity

Forces Inside a Body and Balance

Internal forces and the center of gravity help explain how objects stay in balance. These mechanics ideas matter for structures, machines, and vehicles that must remain stable under different loads and conditions. Internal forces are created inside a body when its particles interact. They can appear as tension, compression, or shear forces. These forces act in collinear pairs with equal magnitude and opposite direction. Between connected parts, they cancel each other and help keep the body in...

alternative sets of equilibrium equations

alternative-sets-of-equilibrium-equations

Equilibrium Conditions for a Supported Plate

Equilibrium conditions for a supported plate are used to describe when forces and moments balance. In this state, the plate has no net movement and no rotation. Engineers use these equations to study how structures behave under external loads. In many cases, the standard equilibrium equations are enough. But some systems need an alternative set of equations to match the geometry of the support points. A rectangular plate supported at points A, B, and C is one example. For this plate, the...

two force member

Two-Force Body Equilibrium

A two-force body is a rigid body acted on by only two external forces. In equilibrium, those two forces must have the same magnitude, the same line of action, and opposite directions. This balance is what keeps the body at rest. For a plate with forces F1 and F2 applied at points A and B, equilibrium means the sum of moments about any axis is zero. If moments are summed about point A, the moment from F2 must be zero. That means the line of action of F2 must pass through point A. The same idea...

three force member

Solving a Three-Force Member Example

A three-force member is a rigid body acted on by three forces at three points. The forces must have concurrent lines of action. If the forces are parallel, their lines of action stay parallel instead. A dumpster provides the example used here. It is connected to a pin support at point A and to a pin on a hydraulic cylinder at point B. The hydraulic cylinder acts as a two-force member in equilibrium. The dumpster weight acts through the center of gravity, and the support reaction acts at point...

equations of equilibrium in three dimensions

equations-of-equilibrium-in-three-dimensions

Checking Force Balance in 3D Structures

Checking force balance in 3D structures is a key step when a system is at rest. The vector and scalar equations of equilibrium are used to test whether a body is stable and will not collapse or fall apart. These equations give a clear way to study the forces acting on a body. The vector equations of equilibrium require the vector sum of all external forces on a body to equal zero. They also require the vector sum of the couple moments and the moments of all forces about a point to equal zero.

support reactions in three dimensions

3D Support Types for Stability and Motion

Support reactions in three dimensions keep structures stable and in equilibrium. They stop unwanted translation and rotation, so a design can handle external forces safely and work as intended. These reactions are important in many structures and systems. A ball and socket joint is one support that allows free rotation about any axis. It does not provide a moment that resists turning. At the same time, it restricts motion in space with three reaction forces along the three dimensions. A...

constraints and statical determinacy

Constraints in Structural Equilibrium

Constraints in structural engineering control how a body can move and help keep it in mechanical equilibrium. A constraint is a restriction on motion. When the right number of constraints is used, the system can stay balanced with the fewest supports needed. A system with the proper number of supports is called statically determinate. In that case, the unknown reaction forces can be found from equations of equilibrium. These systems are the easiest to analyze and design because the forces can...

key terms and concepts

Learn how rigid body equilibrium is determined by balanced external forces and moments, free-body diagrams, and support reactions in high school physics.

Rigid Body Force Balance in Equilibrium | 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

Rigid Body Force Balance in Equilibrium

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