The 2 conditions of equilibrium in physics are fundamental concepts. They play a pivotal role in engineering disciplines like mechanical, civil, robotics, automotive, etc.

Introduction

Ever wondered why a tightrope walker holding a long stick stays balanced or why a bus does not tip over when turning a corner? It all comes down to controlling the centre of mass and centre of gravity, which help maintain equilibrium.

The concept of equilibrium is found in many walks of life including social sciences and natural or practical sciences. However, in physics equilibrium describes the state in which a system is either at rest or moving with constant velocity, with no net force or torque (or moment) acting on it.

Understanding the equilibrium, conditions of equilibrium, and stability is also crucial in;

• analysing the stability of a building
• solving problems in mechanics
• designing a bridge etc.

What is Equilibrium?

In mechanics, equilibrium is defined as,

“the state of an object or a system, where all the forces and torques acting on the system balance each other, resulting in no acceleration.”

Examples of Equilibrium

1. A hanging sign

2. A ladder against a wall

3. A beam supported on two pillars

Types of Equilibrium

Based on the state of an object, there are two primary types of equilibrium.

• Static Equilibrium
• Dynamic Equilibrium

Static Equilibrium

In static equilibrium, the system is at rest whereas all forces and torques acting on it sum to zero.

Examples

1. A Book Resting on a Table

• The weight of the book is balanced by the upward normal force of the table.
• Net force and net torque acting on the book is zero, so it remains at rest.

2. A Balanced Seesaw

• Equal forces applied at equal distances from the pivot ensure no motion or rotation.
• The seesaw remains stationary.

3. A Suspended Scenery

• The downward force of gravity is balanced by the tension in the cables.
• The scenery remains motionless.

4. A Ladder Leaning Against a Wall

• Forces from gravity, the wall, and the ground balance each other.
• No motion or rotation occurs.

5. A Bridge at Rest

• The forces from the weight of the bridge and the vehicles are balanced by the reactions at the supports.
• The bridge remains stationary.

Dynamic Equilibrium

In a dynamic equilibrium, the system moves with constant velocity while the net forces and torques are still zero.

Examples

1. A Car Moving at Constant Velocity

• The driving force of the engine balances air resistance and friction.
• The car moves in a straight line without acceleration.

2. A Parachutist Falling at Terminal Velocity

• Air resistance equals the force of gravity.
• The parachutist falls at a constant speed without acceleration.

3. A Ship Sailing at Constant Speed

• The thrust from the engines balances water resistance and wind drag.
• The ship moves steadily through the water.

4. A Planet Orbiting the Sun

• The gravitational pull of the Sun balances the centripetal force needed for the orbit.
• The planet maintains a constant orbital speed.

5. A Conveyor Belt Moving Boxes at a Constant Rate

• The force applied by the motor balances friction and the weight of the boxes.
• The boxes move smoothly and steadily.

Conditions of Equilibrium

For a system to be in equilibrium, two main conditions must be satisfied.

1^st Condition of Equilibrium (Translational Equilibrium)

The first condition of equilibrium is also called translational equilibrium and is stated as,

“for an object to be in translational equilibrium, the net force acting on it must be equal to zero.”

Mathematical Formulation

Mathematically, it is expressed as;

This means the vector sum of all forces acting on the system must be equal to zero. In component form, this can be written as:

Here, are the components of forces in the , respectively.

2^nd Condition of Equilibrium (Rotational Equilibrium)

The second condition of equilibrium is also called rotational equilibrium and is stated as,

“for a body to be in rotational equilibrium, the net torque acting on the system must be equal to zero.”

Mathematical Formulation

Mathematically, it is expressed as:

OR

For an in-depth understanding of click here, and for click here.

Why We Need the 2^nd Condition of Equilibrium?

The first condition of equilibrium and the second condition of equilibrium address different aspects of the stability of a body. While the first condition is related to linear stability (), the second condition ensures rotational stability ().

So, even if the first condition is satisfied, the body could still rotate due to unbalanced torques.

Scenario

Consider a uniform seesaw system on which force(s) is (are) acting at equidistance from the pivot.

Case 1

If a force is applied on either end, the system will rotate. It is because,

Case 2

If two forces of equal magnitude are applied on both ends in the opposite direction, the system will rotate. It is because,

Case 3

If two forces of equal magnitude are applied on both ends in the same direction, the system will not rotate. It is because,

Deduction

In a nutshell, these two conditions ensure complete equilibrium, making the body stable and motionless (static equilibrium, ) or moving uniformly without rotation (dynamic equilibrium, ).

These two conditions work together to achieve both linear and rotational stability, which are critical for maintaining the balance and uniform behavior of any system.

Stability

It is defined as,

“the ability of a system to return to its original position or state after being disturbed from its inertial state.”

Types of Stability in Equilibrium

Based on stability, equilibrium can be classified into three categories.

1. Stable Equilibrium

A stable equilibrium is the one in which a system returns to its original equilibrium position after a small disturbance.

Key Characteristics

• The centre of gravity (CoG) is at its lowest possible position.
• Any displacement increases the potential energy of the system.
• Restoring forces or torques brings the system back to equilibrium.

Example

When a marble inside a bowl is displaced, it rolls back to the centre.

2. Unstable Equilibrium

An unstable equilibrium is the one in which a system moves further away from its original equilibrium position after a small disturbance.

Key Characteristics

• The CoG is at its highest possible position.
• Any displacement decreases the potential energy of the system.
• No restoring forces or torques exist to bring the system back to equilibrium.

Example

A slight displacement to a marble balanced on top of an inverted bowl causes it to roll further away.

3. Neutral Equilibrium

A neutral equilibrium is the one in which a system remains in its new position after being disturbed.

Key Characteristics

• The CoG remains at the same height regardless of displacement.
• The potential energy of the system does not change with displacement.
• There are no restoring or destabilizing forces or torques acting.

Example

A marble on a flat horizontal surface. It stays wherever it is placed.

Deduction

These characteristics of equilibrium states help us to distinguish between the stability types and explain their behaviour under disturbances.

Applications of Equilibrium

Equilibrium concepts are applied in various fields, such as:

• Civil Engineering: Ensuring the stability of structures like buildings, bridges, and dams.
• Physics: Solving problems in mechanics and understanding natural phenomena.
• Mechanical Engineering: Analysing machines and mechanisms.
• Robotics: Designing stable and balanced robots.

Tips for Solving Equilibrium Problems

Generally, there are 5 key steps involved in solving problems related to equilibrium.

1. Free-Body Diagram: Draw a diagram showing all the forces and their directions.

2. Coordinate System: Choose a convenient coordinate system to resolve forces.

3. Equilibrium Equations: Write equations for translational and rotational equilibrium.

4. Solve Systematically: Solve the equations step by step to find unknowns.

5. Check Units and Directions: Verify the consistency of units and the direction of forces and torques.

Conclusion

The conditions of equilibrium form the backbone of mechanics and engineering. By ensuring that the net forces and torques acting on a system are zero, we can analyse and design stable systems capable of withstanding various loads.

Stability and equilibrium are interwind concepts in physics. Whether in static or dynamic scenarios, mastery of equilibrium principles helps solve real-world problems.

Frequently Asked Questions (FAQs)

What are the 2 conditions of equilibrium in physics?

The two conditions are:

• Translational Equilibrium: The net force acting on the system must be zero ().
• Rotational Equilibrium: The net torque acting on the system must be zero ().

What is translational equilibrium?

Translational equilibrium occurs when the vector sum of all forces acting on a system equals zero, ensuring no linear acceleration.

What is rotational equilibrium?

Rotational equilibrium occurs when the sum of all torques acting on a system equals zero, preventing any rotational acceleration.

Why are the two conditions of equilibrium important?

They ensure a system is completely stable, addressing both linear and rotational motion. Without satisfying both conditions, an object may still rotate or accelerate even if one condition is met.

How are the conditions of equilibrium applied in real-world scenarios?

They are used in structural engineering (e.g., buildings, bridges), designing machinery, and understanding stability in objects like seesaws or ladders.

What is the difference between static and dynamic equilibrium?

• Static Equilibrium: The object is at rest with all forces and torques balanced.
• Dynamic Equilibrium: The object moves at constant velocity with no net force or torque.

What happens if the first condition of equilibrium is satisfied but not the second?

The system may not translate but could still rotate due to unbalanced torques.

What role does the centre of gravity play in equilibrium?

The position of the centre of gravity influences stability. Systems are more stable when the centre of gravity is low and within the base of support.

Can equilibrium occur in a system with external forces?

Yes, equilibrium can occur as long as the external forces and torques balance each other.

What are some examples of equilibrium in everyday life?

• A ladder leaning against a wall.
• A hanging sign balanced by tension in cables.
• A balanced seesaw with equal forces on both sides.