Question

A man standing on a table rotating about the central axis pulls his hands holding the dumbbells towards his chest. How does the angular velocity change?

Answer 1

Hint: The rate of change of an object's position concerning a frame of reference is its velocity, which is a function of time. A specification of an object's speed and direction of motion is referred to as velocity.

Complete step by step solution:
Angular velocity or rotational velocity, also known as angular frequency vector in physics, is a vector measure of rotation rate that refers to how fast an object rotates or revolves relative to another point, i.e. how quickly the angular position or orientation of an object changes with time.
Angular velocity can be divided into two categories. The rate at which a point object revolves around a fixed origin or the time rate at which its angular position changes relative to the origin, is referred to as orbital angular velocity. In contrast to orbital angular velocity, spin angular velocity refers to how fast a rigid body rotates concerning its center of rotation and is independent of the choice of origin.
In the above question, When the man pulls his hands towards his chest, the moment of inertia decreases, and angular velocity increases due to the conservation of angular momentum.
When an object spins in a closed system with no external torques applied to it, its angular momentum remains constant. The conservation of angular momentum explains how an ice skater's arms and legs accelerate as they approach the vertical axis of rotation. When the net torque is zero, angular momentum is conserved or constant.

Note:
The magnitude of angular velocity, the rate at which an object rotates or revolves, is measured by a pseudovector, with its direction perpendicular to the instantaneous plane of rotation or angular displacement. The right-hand rule is used to specify the orientation of angular velocity.