Short Answer:

Rotational motion is the motion of a body in which all its particles move in circular paths around a fixed axis. In this type of motion, every point in the body maintains a constant distance from the axis of rotation, and the body turns through an angle about this axis.

Examples of rotational motion include the spinning of a fan, rotation of a wheel, movement of a flywheel, and the motion of Earth about its own axis. It is an important concept in mechanics, used to study machines and components that rotate or revolve.

Detailed Explanation :

Rotational Motion

Rotational motion occurs when a rigid body turns about a fixed line or axis. Every particle of the body moves in a circular path with the center of the circle lying on this axis. In other words, when a body spins or rotates such that all its parts move in circles around a central line, the motion is known as rotational motion.

Unlike linear motion, where the entire body moves along a straight line, in rotational motion, the body turns or revolves about an axis. The axis may be fixed (like a fan blade) or moving (like a rolling wheel). The study of rotational motion is essential in mechanical engineering, as many machine components like gears, pulleys, turbines, and engines involve rotation.

Definition

Rotational motion can be defined as:

“The motion of a body about a fixed axis in which every point of the body moves in a circular path with its center on that axis is called rotational motion.”

For example, a ceiling fan rotates about its central shaft, and every point on the blade follows a circular path around the shaft.

Mathematically, in rotational motion, every point of the body has the same angular displacement, angular velocity, and angular acceleration, although their linear velocities differ because they depend on the radius from the axis.

Important Terms Related to Rotational Motion

To understand rotational motion properly, it is important to know the following related quantities:

1. Axis of Rotation:
   It is an imaginary line about which the body rotates. Every point on the body moves in a circle whose center lies on this axis.
2. Angular Displacement (θ):
   It is the angle described by a rotating body about the axis between its initial and final position.
   It is measured in radians (rad).
3. Angular Velocity (ω):
   It is the rate of change of angular displacement with respect to time.

The SI unit of angular velocity is radians per second (rad/s).

1. Angular Acceleration (α):
   It is the rate of change of angular velocity with respect to time.

The SI unit of angular acceleration is radians per second squared (rad/s²).

1. Moment of Inertia (I):
   It is the property of a rotating body that resists changes in its angular velocity. It is analogous to mass in linear motion and depends on the distribution of mass about the axis of rotation.
2. Torque (T):
   It is the turning effect of a force acting on a body about an axis of rotation. It is given by:

where  is the applied force, and  is the perpendicular distance from the axis.

Equations of Rotational Motion

Rotational motion is similar to linear motion, and its equations are analogous to those of straight-line motion. The equations for uniform angular acceleration are:

Where,
= initial angular velocity,
= final angular velocity,
= angular acceleration,
= angular displacement,
= time.

These equations are useful for calculating the angular quantities of rotating bodies such as gears, wheels, or flywheels.

Relation Between Linear and Rotational Motion

There is a direct relationship between the linear and angular quantities in rotational motion. If a point on a rotating body is at a distance  from the axis, then:

• Linear velocity,
• Linear acceleration,

This means that the farther the point is from the axis, the greater its linear speed, even though its angular speed is the same as other points.

Examples of Rotational Motion

1. Ceiling Fan:
   Each blade of the fan rotates around the central shaft, showing rotational motion.
2. Wheel of a Car:
   The wheel rotates about its axle when the car moves forward.
3. Earth’s Rotation:
   The Earth rotates about its axis once every 24 hours, causing day and night.
4. Flywheel in an Engine:
   It stores rotational energy and maintains uniform speed.
5. Gears and Turbines:
   In machines, gears and turbines undergo rotational motion to transmit and convert mechanical energy efficiently.

Types of Rotational Motion

1. Uniform Rotational Motion:
   When the body rotates with constant angular velocity, it is called uniform rotational motion.
   Example: A fan running at a constant speed.
2. Non-Uniform Rotational Motion:
   When the angular velocity changes with time, it is called non-uniform rotational motion.
   Example: A ceiling fan when it starts or stops.

Applications in Engineering

Rotational motion is a fundamental concept in mechanical engineering and is used in the design and analysis of rotating systems such as:

• Engines and turbines (to convert energy into mechanical work)
• Gear trains and pulleys (for power transmission)
• Flywheels and shafts (for storing and maintaining energy)
• Wheels and rotors (for motion and stability)
• Centrifugal pumps and compressors (for fluid motion through rotation)

Understanding rotational motion helps engineers design machines that operate efficiently with balanced and smooth motion.

Conclusion

Rotational motion is the motion of a rigid body about a fixed axis where every point in the body moves in a circular path around that axis. It involves important parameters such as angular displacement, angular velocity, angular acceleration, and moment of inertia. The study of rotational motion is essential in mechanical engineering as it forms the basis of the working of rotating machines like turbines, engines, fans, and wheels. It helps in understanding torque, energy transfer, and the stability of mechanical systems.