Short Answer:

A rigid body is a solid body in which the distance between any two points remains constant, even when external forces are applied. It means that a rigid body does not deform, bend, or change its shape or size during motion.

In reality, every material body experiences some deformation, but for the purpose of mechanical analysis, if the deformation is very small and can be neglected, the body is treated as a perfectly rigid body. Examples include gears, pulleys, shafts, and connecting rods used in machines.

Detailed Explanation :

Rigid Body

A rigid body is an ideal concept used in mechanics to simplify the study of motion and forces. It is defined as a body whose shape and size remain unchanged when external forces or moments act upon it. In other words, all points in a rigid body move in such a way that the relative distance between any two points remains fixed at all times.

In real life, no material is perfectly rigid because every solid deforms to some extent under load. However, in engineering analysis, when the deformation is too small to affect the results, it is neglected, and the body is assumed to be rigid. This assumption simplifies calculations and is widely used in the study of statics, dynamics, and kinematics.

Definition

A rigid body can be defined as:

“A body which does not undergo any change in shape or size when a force is applied on it is called a rigid body.”

Mathematically, if two points  and  are on a rigid body and their distance is , then even after any motion or force acts on the body:

This means that the body does not stretch, compress, or bend under the action of external forces.

Characteristics of a Rigid Body

1. Constant Shape and Size:
   The shape and size of a rigid body do not change under the action of external forces.
2. No Deformation:
   The distance between any two particles of the body remains constant, meaning it does not deform or strain.
3. Mass Distribution:
   The total mass of the body remains the same, and it is uniformly distributed.
4. Fixed Relative Position:
   All points in the rigid body maintain fixed relative positions with respect to one another during motion.
5. Simplified Analysis:
   It is an idealization used to make the analysis of forces and motion easier, neglecting small deformations.

Motion of a Rigid Body

A rigid body can have two types of motion depending on how the forces are applied and how the body moves:

1. Translational Motion:
   In translational motion, every point in the body moves in the same direction and covers the same distance in equal intervals of time.
   Example: A car moving straight on a road or a block sliding on a smooth surface.
2. Rotational Motion:
   In rotational motion, all particles of the body move in circular paths around a fixed axis, and the distances of these particles from the axis remain constant.
   Example: A rotating wheel, ceiling fan, or gear.

Sometimes, a rigid body can undergo combined motion, which includes both translation and rotation, such as a rolling wheel.

Equations of Motion for a Rigid Body

In engineering mechanics, the motion of a rigid body is described using both linear and angular parameters:

• Linear motion: , where  is the net force,  is the mass, and  is the linear acceleration.
• Rotational motion: , where  is the moment of force (torque),  is the moment of inertia, and  is the angular acceleration.

These equations help in studying the dynamics of machines and mechanical systems made up of rigid components.

Examples of Rigid Bodies

1. Gears:
   The teeth of a gear are assumed to remain rigid when transmitting motion and force.
2. Pulleys:
   In a pulley system, the pulley is treated as a rigid body while analyzing belt tension.
3. Flywheel:
   A flywheel rotating about its axis is considered a rigid body in rotational motion.
4. Shafts and Cranks:
   Machine elements like shafts, cranks, and rods are assumed to be rigid while transmitting power.
5. Vehicles or Structures:
   The chassis of a vehicle or a steel structure is considered rigid for load analysis.

Difference Between Real Body and Rigid Body

Property	Real Body	Rigid Body
Deformation	Experiences some deformation under force	Does not deform at all
Shape and Size	May change slightly	Remains constant
Practicality	Exists in real life	Ideal concept for analysis
Example	Rubber ball, metal rod	Gear, pulley (for analysis)

From the above comparison, it is clear that the rigid body is an idealized model used for simplifying the study of mechanics.

Applications in Engineering

1. Mechanism Design:
   In machines, components like levers, links, and gears are treated as rigid bodies for analysis.
2. Statics:
   Used in calculating support reactions, equilibrium conditions, and stability of structures.
3. Dynamics:
   Used to study rotational and translational motion of parts like wheels, flywheels, and shafts.
4. Kinematics:
   Helps in analyzing the movement of mechanisms without considering deformation.
5. Structural Engineering:
   In analyzing trusses, frames, and beams, members are often assumed to be rigid for simplified analysis.

Assumptions in Rigid Body Analysis

1. The body is perfectly solid and cannot deform.
2. The effect of internal forces causing deformation is neglected.
3. The motion of the body is described only by translation and rotation.
4. The applied forces act uniformly on the body.

These assumptions make the mathematical analysis simple and accurate enough for most engineering applications.

Conclusion

A rigid body is an ideal body whose size and shape remain unchanged under the action of external forces. The distance between any two points of a rigid body remains constant at all times, making it easy to analyze motion and equilibrium. Although no material is perfectly rigid in reality, the rigid body assumption is widely used in mechanical and structural engineering to simplify calculations in kinematics, dynamics, and statics. It serves as a fundamental concept in the study of mechanical systems and machine design.