# Rotational Motion and Conservation of Momentum

## Rotational Motion

The rigid body moving in such a way that all its particles move with a common angular velocity and about an axis is called rotational motion. Few examples of rotational motion are the earth rotating about its axis at a fixed speed and the flywheel of the sewing machine rotating at varying speed. The particles follow a circular path in rotational motion. The angular velocity or the speed of rotation remains the same in a uniform circular motion. The particles follow a circular path along a plan that is perpendicular to the axis and has a centre on the same axis. In rotational motion, different particles show different points of motion.

## Axis of rotation

The axis of rotation is of three types. The first type is the rotation about a fixed axis. The examples of rotation along a fixed axis are ceiling fan, rotation of planets and opening and closing of the door. The second type is the rotation about an axis of rotation. It includes both translational and **rotational motion**. Rolling of a ball is an example of this category. The next type is the rotation about an axis in rotation.

## Angular Momentum

Angular momentum depends on the rotational velocity of the object and its rotational inertia. The angular momentum L is proportional to the moment of inertia I and the angular speed ω. Rotational inertia is the property of a body that can be rotated. It tells how difficult it is to change the rotational velocity of the object around a rotational axis. The rotational inertia depends on the mass of the body. Let us take the example of a tennis ball of mass m rotating at radius r from the axis of rotation. The rotational inertia or moment of inertia of the ball is given by I=mr2.

## Conservation of Angular Momentum

The law of conservation of angular momentum states that if the external torque acting on the body is zero then the angular momentum is a constant. Let’s take the example of an ice-skater spinning and changing her rotational velocity by holding her arms outwards or pulling them inwards. When she pulls her arms in, her rotational inertia is reduced. Since external torque is zero on the ice skater, there is **conservation of momentum** as the angular velocity increases.

## Examples of Conservation of angular momentum

- When a planet revolving in an elliptical orbit around the sun comes closer to the sun, its speed increases. This is because as the planet comes closer to the sun, its moment of inertia decreases and according to the law of conservation of angular momentum its angular velocity increases.
- When a diver jumps from the springboard, he curls his body by rolling his arms and legs in. By doing so he increases his angular velocity and decreases the moment of inertia to conserve the angular momentum.
- In a tornado as the air rushes towards the centre, the moment of inertia of the air decreases. To conserve the angular momentum, the angular speed of the air increases.