Equilibrium of Rigid Bodies

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## Introduction:

Rigid bodies are those in which the distance between particles remains constant in the face of external forces. So, when studying the equilibrium of rigid bodies, we are primarily interested in defining the behavior of these constituent particles under changing conditions of force or torque. Because we are interested in the equilibrium of rigid bodies in motion, we must consider both translational and rotational motion.

A rigid body is a multi-particle system. It is not necessary for each particle of a rigid body to behave similarly to the other particle. Every particle behaves differently depending on the type of motion.

## Overview:

The term “equilibrium” refers to any point where the total amount of external force or torque is zero. This point could be anywhere close to the center of mass. The linear momentum of a rigid body in translational motion is changed by an external force. While the external torque in rotational motion can change the rigid body’s angular momentum. The linear momentum and angular momentum of a rigid body remain constant over time in mechanical equilibrium.

This means that the body under the influence of an external force has neither linear nor angular acceleration. If the total force on a rigid body is zero, the linear momentum remains unchanged despite the change in time. If the total torque on a rigid body is zero, the body exhibits rotational equilibrium because the angular momentum does not change with time.

### Dynamic Equilibrium:

Dynamic equilibrium is defined as the state of a given system in which the reversible reaction occurring in it stops changing the ratio of reactants and products, but there is substantial movement between the reactants and the products.

This movement happens at the same rate, and there is no net change in the reactant/product ratio. Only reversible reactions have dynamic equilibrium. In the case of dynamic equilibrium, both reactants and products transition at the same rate, resulting in no net change. Reactants and products are produced at such a rapid rate that their concentration remains constant. The ratio of products to reactants remains constant in this equilibrium, but there is a reaction movement, i.e. from reactants to products. We can represent the equilibrium constant using constant forward and backward reactions based on these equilibria. Systems in steady states include those that exhibit dynamic equilibrium.

### Static Equilibrium:

Static equilibrium refers to any system in which the sum of the forces and torques on all of the system’s particles is zero. Simply put, it is the state of equilibrium of a system whose components are at rest. The physical state in which a system’s components are at rest and the net force through the system is zero is referred to as static equilibrium. When all of the forces acting on an object are balanced and the object is not moving in relation to the relative plane, the object is said to be in static equilibrium.

An object that is in static equilibrium cannot move. This is due to the fact that all of the forces acting on it balance each other out. This idea is crucial in the design of rigid structures. These rigid structures range from a house’s floor system to a massive suspension bridge. Furthermore, under all loading conditions, these rigid structures must maintain static equilibrium.

The fundamental and basic condition for static equilibrium is that an object must not be in motion, whether translational or rotational. In addition, an object in translational equilibrium does not move from one location to another. An object in rotational equilibrium, on the other hand, is not rotating around an axis. Translational equilibrium requires that the vector sum of all external forces be zero. Furthermore, the magnitude and direction of external forces cancel each other out. Rotational equilibrium requires that all external torques cancel each other out. Static equilibrium is unquestionably a useful analytical tool. Most notably, when two forces act on a static equilibrium object, they add up to zero.

## Translational equilibrium:

An object can experience translational motion (the movement that changes its position) as well as rotational motion (motion that changes its angle). If the velocity of an object’s translational motion is constant, it is said to be in translational equilibrium.

An object in translation equilibrium is one that is not moving or is moving in a straight line at a constant velocity. To be in translational equilibrium, the net force acting on the object must be zero (recall Newton’s first law: an object does not accelerate if no unbalanced forces act on it).

When the net total force on an object in a system is zero, the object is said to be in equilibrium with the system. Because there is no increase or decrease in speed in equilibrium, the velocity is constant and there is no acceleration.

The torques or moments at any point on the object or system must also sum to zero.

When the torque is equal to zero, the system is said to be in rotational equilibrium. Because the object does not move in this case, it is also referred to as static equilibrium. Because the net force is zero in translational equilibrium, there is no acceleration.

Also read: Conservation of Mechanical Energy

Question: What is the equilibrium of a body?

Answer: A system is said to be in a stable state of equilibrium when, when displaced from equilibrium, it experiences net force or torque in the opposite direction of the displacement.

Question: How is your body balanced?

Answer: When a system is out of balance and shifts, it enters a stable equilibrium and generates a net force or torque in the opposite direction of the shift.

Question: What is the difference between Translational Motion and Rotational Motion?

Answer: The primary distinction between Translational Motion and Rotational Motion is that Translational Motion involves the sliding of an object in one or more of the three dimensions x,y,z, whereas Rotational Motion involves the continuous rotation of an object around an internal axis. Translational motion occurs when every line in the body remains parallel to its original position, whereas rotational motion occurs when the body rotates around a fixed axis.

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