Hi readers, I hope you are all well. In this post, we discuss the main topic, equilibrium. Equilibrium can play a fundamental role in the modern and different fields of science. In physics, engineering, or also in chemistry the concept of equilibrium describes and provides information about forces that can be applied to the system. In physics, the equilibrium describes the balanced forces and the torque that can be acted on the system or the body. if the body is at rest or in a motion state, equilibrium explains and provides information about the forces that can act in both types of situations persons.

Equilibrium plays a vital role in understanding the forces and the torque because equilibrium provides stability to the system, also it stabilizes the person who is in the state of rest or motion because in both conditions forces always act on it, so for their stabilization equilibrium plays an essential role.

In this post, we can discuss the equilibrium definitions, their types, first equilibrium condition, second equilibrium condition, mathematical expressions, their applications, examples, and related phenomena.

## Definition of equilibrium:

Equilibrium can be defined as:

"The state in which the body is in the state of balance, or the body is in the state of motion or rest with uniform velocity and no net change occurs on it."

Simply equilibrium is a state in which the system or the body is at the condition of balance under the action of forces but there is no net change occurring. Every system achieves equilibrium at some conditions because, without an equilibrium state, the system or the object can't do its work properly.

### Types of equilibrium:

There are two main types of equilibrium which are common and they are given there:

Mechanical equilibrium

Thermal equilibrium

Their description is given there:

#### Mechanical equilibrium:

Mechanical equilibrium is the main type of equilibrium and it can be defined as:

In the system or an object mechanical equilibrium occurs when there is no force, torque net force, or acceleration acting on the object or the system.

Mechanical equilibrium occurs during the state of motion mostly. Mechanical equilibrium can be divided into two types which are also the main types of equilibrium and they are given below:

Static equilibrium

Dynamic equilibrium

These are the further divisions of the mechanical equilibrium Details are given there:

##### Static equilibrium:

Static equilibrium can be defined as:

"static equilibrium can achieved by the body when the body is at rest and all forces which can act on the body including torque and acceleration sum is equal to zero."

##### Dynamic equilibrium:

Dynamic equilibrium can be defined as:

"Dynamic equilibrium can be achieved by the body when the body moves with a constant velocity and the all forces and torque which can be acted on the body their sum is equal to zero.”

#### Thermal equilibrium:

Thermal equilibrium can be defined as:

"The two objects or the two or more systems can achieve the state of thermal dynamics when no exothermic or endothermic heat exchange occurs and with some condition or time both systems can be reached to the same temperature."

These are the major types of equilibrium but the types of equilibrium in physics are given there:

### In physics the types of equilibrium:

The types of equilibrium in physics with their uses and examples are given there:

Dynamic equilibrium

Radiative equilibrium

Thermal equilibrium

Static equilibrium

Chemical equilibrium

Their detailed definitions, mathematical expressions, formulas, and examples are given there:

#### Dynamic equilibrium:

Dynamic equilibrium can be achieved by the body when the body moves with a constant velocity and all forces and torque which can be acted on the body their sum are equal to zero. In dynamic equilibrium all forces which can be acted on the object are balanced. Mostly dynamic equilibrium can be used to understand or determine the objects that can be moved without acceleration.

##### Mathematical expression:

As we know in dynamic equilibrium the all forces sum is equal to 0 then it can be written as:

F = 0

Or the sum of torque is also equal to zero, hence it can be written as:

𝛕 = 0

##### For instance:

The body or object can be rotated around its axis with uniform angular velocity and no acceleration can be calculated or measured and all sum of forces that can be acted are 0

The car that can be moved with uniform linear velocity on a straight road, and not change their speed then the force which can be acted to maintain the road friction or air friction can be produced through the driving force which can be produced through the engines.

The paratrooper can also fly in the sky due to the dynamic equilibrium which stabilizes them to fly in the sky efficiently.

The airplane can also fly with a state of dynamic equilibrium because it can fly with constant speed and the weight and thrust force can balance the drag force by balancing their forces it can fly efficiently.

#### Radiative equilibrium:

Radiative equilibrium is the state that can be achieved by the system or the object by absorbing the radiation or emitting the radiation at the same time and rate through equal emitting and absorbing radiation of the system and the object can achieved the dynamic equilibrium state efficently.

##### Mathematical expression:

Rate of absorption of radiation = rate of emission of radiation

##### For instance:

Stars can also maintain their lifecycle phase by emitting or absorbing radiation and achieving radioactive equilibrium. the stars produce energy through the nuclear fusion reaction and it can also radiate the absorbing energy into space and maintain gain radiative equilibrium.

The temperature or radiation can come from the sun and is maintained in the earth by radiative equilibrium because the earth absorbs all solar radiation and emits infrared radiation on the surface of the earth.

#### Thermal equilibrium:

The two objects or two or more systems can achieve the state of thermal dynamics when no exothermic or endothermic heat exchange occurs and with some condition or time, both systems can reach the same temperature. thermal equilibrium concepts are essential in thermodynamics and also in their laws.

##### Representation:

The temperature of the object and the system that can achieve the thermal equilibrium can represented through the symbol T.

##### Mathematical expression:

No heat exchange occurs in the system when they achieve the thermal equilibrium then it can be written as:

T1 = T2 = T3=........ = Tn

##### For instance:

For the two metal spoons, one is cold or the other is hot but if we check after some time then it can be observed that both metal spoons have the same temperature because both of them achieve thermal equilibrium.

If we leave the hot cup of tea or coffee in the room or open environment, then after some time we can observe that the hot cup of tea or coffee temperature becomes equal to the room or environment temperature,

#### Static equilibrium:

Static equilibrium can achieved by the body when the body is at rest and all forces that can act on the body including torque and acceleration sum are equal to zero. In the static equilibrium state, the object always remains at rest so that's why the static equilibrium can be used to determine or understand those objects that can't move and always remain at rest. Simply static means rest so static equilibrium can only achieved by those objects or systems that can't be moved.

##### Mathematical expression:

As we know in static equilibrium the all forces sum is equal to 0 then it can be written as:

F = 0

F represents the sum of all forces that can be acted on the body or object.

Or the sum of torque is also equal to zero, hence it can be written as:

𝛕 = 0

𝛕 represents the sum of all torques that can be acted on the body or object.

##### For instance:

The book can be lying on the table or at rest, then the forces that can be acted on the table are maintained or normalized through the gravitational force that can be acted on the book which is lying on the table

The bridge that can be used for traffic is always in a static state, then it can maintain its static equilibrium by balancing the forces and the weight or load that act on the bridge.

#### Chemical equilibrium:

In chemical reactions, chemical equilibrium can be achieved, when the forward and the reverse reaction rates are the same under the same conditions, and when the concentration of the products and the reactants can't be changed during the reaction then this state can be achieved. Mostly in chemistry, the chemical equilibrium can be used to determine or understand the concentration of reaction but in physics sometimes it can be used.

##### Mathematical expression:

The rate of forward reaction = the rate of reverse reaction

##### For instance:

The solution of the salt becomes in the equilibrium or saturation state when the rate of salt dissolution is equal to the rate of precipitation. But if we can provide the temperature to the solution of salt then we can change their equilibrium state also.

When we close the container in which hydrogen iodide solution is present, then this solution can achieve the equilibrium state easily because, in the closed container, we can't change the conditions and can't change the temperature or concentration of the reactant and product amount.

## Condition of equilibrium:

Two main conditions are essential for achieving the equilibrium state. If the object and the system can't follow these two main conditions then it can't achieve the equilibrium state. The two conditions for the equilibrium state are given there:

The first condition of equilibrium ( equilibrium of forces)

A second condition of equilibrium ( equilibrium of torque

in the previous post, we can discuss the first condition of equilibrium and now we can discuss the detail of the second condition of equilibrium.

### The second condition of equilibrium:( equilibrium of torque)

The second condition of equilibrium can also referred to as the equilibrium of torque. According to the second condition, the all torque that can be acted on the body, their sum is always equal to zero. If the object or system follows this condition then it means that the body can't rotate around its axis and can't do the rotational motion.

##### Definition:

The second condition of equilibrium is defined as:

The sum of all vector torque that can be acted on the object or the system is always equal to zero. Because this condition describes that the object or the system can't do the rotational motion around their axis.

𝛕 = 0

𝛕 represented the sum of all torque that can be acted on the body.

#### Mathematical expression:

As we know the torque is equal to the position vector or the distance from the axis of rotation and the vector product of force F and the sin θ are the angle between the r and f. The it can be mathematically represented as:

𝛕 = r F sin θ

Then if the sum of all torque is equal to zero it proves that the body which can be moved with rotational motion is at the equilibrium state and all forces have become zero and it can be written as:

𝛕 = 0

#### Important note:

When all forces that can be acted on the object in one plane or are coplanar then we can apply the condition of equilibrium we stabilized or maintained them.

All forces can be passed through one point which is the line of action and the body moves around into its axis within the line of action.

By choosing the axis we can calculate the torque efficiently and the position of the object and the position of the axis is arbitrary.

#### Significance of the second equilibrium condition in physical applications:

The second condition of equilibrium or the equilibrium of forces is essentially used to determine or understand those systems or objects that can do the rotational motion.

This condition is the base in the field of dynamics because in this field we can deal with different types of motion. In mechanics, it can help to analyze the structures and the components that can be used in the designing of the system which can do the rotational motion, and also analyze how they achieve the equilibrium state by balancing the forces and the load which can be acted on them.

##### Examples:

The seesaw can pivot in the center. Two children with different weights sit on both sides but they can show the equilibrium state when the torque that can be acted on is equal to zero by balancing the load or forces that can be acted on the swing.

The ladder can stand with the support of the wall. The ladder may fall but if it becomes at the equilibrium state by balancing the forces then it can't fall.

### Applications of the equilibrium of torque:

The second condition of equilibrium can follow many different fields of science and it can be used in many different applications that can be used in daily life some explanations are given there:

Every day situations

Structural engineering

Mechanical system

##### In everyday situations:

In our daily lives, the second condition of equilibrium can be used to balance or stabilize many different things. All systems can be managed or stabilized due to equilibrium. For instance, the picture can be hung with the hook and the weight of the picture or sign can be balanced through the hook. Torque can also be produced by the picture and it can be balanced by following the second condition of equilibrium.

##### Structural engineering:

In the field of engineering, engineers can design or choose the components that can manage the rotational motion with equilibrium and manage all forces or torque that can be acted on it. Engineers always prefer to choose those components that can efficiently work and remain in the equilibrium state. For instance, the cantilever beam can be designed by the engineers, they calculate the all torque that can be acted on it and then also analyze that they can able to bear the load or ensure that the beam is at an equilibrium state or not move around their axis to produced torque.

##### Mechanical system:

The second equilibrium can be used in the field of mechanics in which the components are designed to work properly without error. The second condition of equilibrium can also used for checking the proper functioning of the machines and also for their safety and for increasing their efficacy to do work properly. For instance, the gear systems that are used in the vehicles are designed by the engineers, they can be designed by ensuring the components can balance all forces and the torque must be equal to 0.

#### Advanced concepts and ideas about the second condition of equilibrium:

With time and with the development of modern science and technology equilibrium can be used in many different new topics with new concepts and ideas that can be presented through modern research. Some modern concepts and ideas about the second condition of the equilibrium are given there:

Equilibrium in the quantum system

Metastable equilibrium

Equilibrium in the dynamic systems

##### Equilibrium in the quantum system:

The second condition of the equilibrium can also now be used in the quantum system because in the quantum system the probabilities and managed or stabilized efficiently. The superpositions and the quantum tunneling can also be understood or determined through the second condition of the equilibrium. For instance, the electrons that can distributed in the conductors, the energy, and the distribution of the electrons can be managed or stabilized by using or following the conditions of the equilibrium.

##### Metastable equilibrium:

The second condition of equilibrium can be used in the metastable, in this, the larger or smaller distribution can be managed or stabilized efficiently. For instance, the pencils that we can use can also be balanced on the tip, but if a small disturbance occurs the pencil can fall and distribute the equilibrium state easily.

##### Equilibrium in the dynamic system:

In the dynamic system, the equilibrium occurs when it follows the second condition of the equilibrium. If we understand the equilibrium of torque then we can analyze or stabilize all control systems or dynamic systems. For instance, the satellites can be moved around their axis, and in the orbit, their stabilization can be managed by following the second condition. Because the second condition of the equilibrium maintained to move in orbit or doesn't allow them to move irregularly in the other orbits.

#### Advanced topics applications in which the second condition of equilibrium is used:

The advanced topics in which the second condition of equilibrium is used are given there:

Equilibrium in elastic system

Equilibrium in the three-dimension

Multiple forces equilibrium in the system

##### Practical examples:

Some practical examples in which the second condition of equilibrium is used are given there:

Aerospace engineering

Architectures

Building designs

Robotics

Automotive engineering

#### Conclusion:

The equilibrium of torque, which is also referred to as the second condition of the equilibrium is the essential or fundamental concept in the dynamics or mechanics in which the system and the object can do the rotational motion. If we can apply the second condition of equilibrium we can stabilize the different applications in daily life or mechanics. In the era of the modern sciences, equilibrium is essential in every system for working properly and for better output efficiency. by understanding this article or post or understanding the second condition of equilibrium it is easy to balance the objects in the physical world and also in the major fields of science.