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

A rigid body does not undergo any deformation under the influence of external forces.
Consider a merry-go-round subjected to an external force F at a perpendicular radial distance r, which results in the moment of a force about point O.
If multiple forces act on the merry-go-round, the equilibrium condition is obtained when the sum of all external forces acting on it is zero.
The other condition of equilibrium states that the sum of all moments about point O must equal zero.
When the moment is measured at point A, it can be expressed as the sum of the moment at point O and the cross product of perpendicular distance and the applied force.
These conditions ensure that the body does not undergo any translational or rotational motion in static equilibrium.
Only external forces are considered here since the internal forces within the rigid body have the same magnitude and act in opposite directions, canceling each other due to Newton&#39;s third law of motion.

conditions of equilibrium

Conditions of Equilibrium

Equilibrium refers to a state where a rigid body is not subjected to any translational or rotational motion. This state is achieved when the force and couple acting on a rigid body equal zero. When the system of external forces results in a net effect equivalent to zero, the rigid body is considered to be in equilibrium.
Internal forces are not considered for conditions of equilibrium because they occur in equal and opposite pairs within the body, effectively canceling each other. As a result, these internal forces do not contribute to the overall motion or change in motion of the rigid body. Equilibrium is determined by the balance of external forces and moments acting on the body, as they are responsible for causing translational or rotational motion.
The necessary and sufficient conditions for equilibrium can be determined by setting the resultant force and moment equal to zero. Additionally, the vector equations can be replaced with six scalar equations by resolving each force and moment into its rectangular components. This implies that the components of the external forces in the x, y, and z directions are balanced, and the moments of the external forces about the x, y, and z axes are also balanced. If a rigid body is in equilibrium, the system of external forces imparts no translational or rotational motion to the body.
To write the equilibrium equations for a rigid body, first, identify all the forces acting on the body and then draw the corresponding free-body diagram. Besides the forces applied to a structure, consider the reactions exerted on the structure by its supports. Correctly identifying each reaction can help solve the unknown forces and reactions.
Knowledge of equilibrium conditions is crucial in analyzing problems related to rigid bodies. By determining the unknown forces and reactions and using the necessary and sufficient conditions for equilibrium, it is possible to predict the behavior of rigid bodies.

Equilibrium refers to a state where a rigid body is not subjected to any translational or rotational motion. This state is achieved when the force and ...

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JoVE Core

Mechanical Engineering

Unit 1

Equilibrium of a Rigid Body

KEY TERMS AND CONCEPTS

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

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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