Question

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

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Solution

**Angular velocity:**

- Angular velocity or rotational velocity, also known as angular frequency vector, is a vector measure of rotation rate that refers to how fast an object rotates or revolves relative to another point, i.e. how suddenly the angular position or orientation of an object changes with time.
- It 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 can rotate concerning its center of rotation and is independent of the choice of origin.
- Now 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 acting on it, its angular momentum remains constant.
- The conservation of angular momentum explains to us how an ice skater's arms and legs accelerate as they come close to the vertical axis of rotation.
- When the net torque is zero, angular momentum is conserved or constant.
- The rate of change of an object's position concerning a frame of reference is its velocity, which is a function of time.
- When the man pulls his hands towards the chest, the moment of inertia will decrease and due to the conservation of angular momentum, angular velocity will increase.
- The magnitude of angular velocity, the rate at which an object rotates, is measured by a pseudovector, its direction perpendicular to the instantaneous plane of rotation or angular displacement.
- The right-hand rule is used to specify the orientation of the angular velocity

**Thus, angular velocity will increase when a man standing on a table rotating about the central axis pulls his hands holding the dumbbells towards his chest.**

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