Short Answer:

The three types of equilibrium — stable, unstable, and neutral equilibrium — describe how a body behaves when slightly disturbed from its original position. In stable equilibrium, the body returns to its original position after being disturbed. In unstable equilibrium, the body moves farther away from its original position when disturbed. In neutral equilibrium, the body remains in its new position after being disturbed. The movement of the center of gravity (C.G.) determines which type of equilibrium a body is in.

Detailed Explanation :

Stable, Unstable, and Neutral Equilibrium

In Engineering Mechanics, the study of equilibrium is essential to understand the stability of a body or structure under the action of forces. When several forces act on a body, it may either remain at rest, move, or rotate depending on how these forces balance each other.

A body is said to be in equilibrium when all the external forces and moments acting on it are balanced, meaning there is no resultant force or moment causing motion. However, when a body in equilibrium is slightly disturbed from its position, its response to this disturbance determines the type of equilibrium it possesses.

There are three main types of equilibrium:

Stable Equilibrium
Unstable Equilibrium
Neutral Equilibrium

These types depend on how the center of gravity (C.G.) of the body moves relative to its original position when the body is slightly displaced. Let us study each in detail.

Stable Equilibrium

A body is said to be in stable equilibrium if, after being slightly disturbed from its original position, it tends to return to that position automatically.

In this case, when the body is disturbed, its center of gravity (C.G.) rises to a higher position. Due to the gravitational force acting downward, the body tries to come back to its original lowest position, thereby restoring its equilibrium.

Condition for Stable Equilibrium:

The center of gravity must rise when the body is disturbed and fall back to the original position when released.

Examples:

A pendulum hanging at rest (its C.G. is lowest at the equilibrium position).
A ball resting at the bottom of a bowl.
A cone resting on its base.

Explanation:
When a ball is placed at the bottom of a bowl and slightly displaced, its C.G. moves upward. The gravitational force tends to bring it back to the lowest point, restoring equilibrium. This is because the original position corresponds to the lowest potential energy, and the body always tends to return to the position of minimum potential energy.

Practical Importance:
Stable equilibrium is preferred in engineering and construction since it ensures stability and safety. Structures like bridges, towers, vehicles, and machines are designed so that their center of gravity remains low to achieve stable equilibrium.

Unstable Equilibrium

A body is said to be in unstable equilibrium if, after being slightly disturbed from its position, it moves further away from its original position instead of returning to it.

In this case, when the body is displaced slightly, its center of gravity (C.G.) is lowered instead of being raised. As a result, the gravitational force acts in the direction of the disturbance, causing the body to move even farther away.

Condition for Unstable Equilibrium:

The center of gravity must fall when the body is disturbed.

Examples:

A ball balanced on the top of a hill.
A cone resting on its tip.
A pencil standing vertically on its sharp end.

Explanation:
When a ball placed on top of a hill is slightly displaced, its C.G. moves downward. The gravitational pull then causes it to roll further down the hill, moving farther away from its original position. Hence, equilibrium is lost, and the body becomes unstable.

Practical Importance:
Unstable equilibrium is usually undesirable in engineering, as it leads to collapse or imbalance. However, it can be useful in certain dynamic systems, such as rockets, drones, and balancing mechanisms, where controlled instability allows for easier maneuvering.

Neutral Equilibrium

A body is said to be in neutral equilibrium if, after being slightly disturbed, it remains in its new position and does not return to or move away from its original position.

In this condition, the center of gravity (C.G.) neither rises nor falls when the body is disturbed; it remains at the same level.

Condition for Neutral Equilibrium:

The center of gravity remains at the same height when the body is disturbed.

Examples:

A ball resting on a flat surface.
A wheel rolling on a level ground.
A cylinder lying on its curved surface.

Explanation:
When a ball is placed on a flat surface and moved slightly, it rolls to a new position but stays at the same height. The C.G. remains constant, and the body experiences no restoring or disturbing moment. Hence, it stays in the new position, maintaining neutral equilibrium.

Practical Importance:
Neutral equilibrium is desirable in systems that require smooth motion, such as wheels, bearings, and rotating parts, where stability and continuous movement are equally important.

Difference between Stable, Unstable, and Neutral Equilibrium

The three types of equilibrium differ in the behavior of the center of gravity during disturbance:

In Stable Equilibrium, C.G. rises when disturbed and returns to its original position.
In Unstable Equilibrium, C.G. falls when disturbed, causing the body to move further away.
In Neutral Equilibrium, C.G. remains at the same level during displacement.

This relationship between the center of gravity and the body’s movement determines the type of equilibrium.

Applications in Engineering

Structural Engineering:
- Buildings, bridges, and towers are designed for stable equilibrium to resist wind, vibration, and external loads.
Mechanical Engineering:
- Moving parts like bearings and shafts are designed for neutral equilibrium to enable smooth rotation.
Vehicle Design:
- Vehicles have a low center of gravity to ensure stable equilibrium and prevent overturning.
Marine Engineering:
- Ships and submarines are analyzed for equilibrium to ensure that they return to their upright position after tilting.
Robotics and Aerospace:
- Controlled unstable equilibrium is used for responsive systems that require quick adjustments.

Importance of Understanding Equilibrium Types

Helps ensure stability and safety in designs.
Allows engineers to predict how systems behave under different loading conditions.
Essential for machine design, civil structures, and automotive systems.
Forms the foundation for advanced topics like vibration analysis and stability control.

Conclusion

In conclusion, stable, unstable, and neutral equilibrium describe the behavior of a body when disturbed from its position.

In stable equilibrium, the body returns to its original position.
In unstable equilibrium, it moves further away.
In neutral equilibrium, it stays in the new position.
The movement of the center of gravity plays a crucial role in determining these states. Understanding these types of equilibrium helps engineers design structures and machines that are safe, reliable, and well-balanced under different conditions.