Question

A horizontal platform is rotating with uniform angular velocity around the vertical axis passing through its centre. At some instant of time a viscous fluid of mass m is dropped at the centre and is allowed to spread out and finally fall. The angular velocity during this period:
A. decreases continuously
B. decrease initially and increases again
C. remains unaltered
D. increases continuously

Answer 1

We will use the concept of conservation of angular momentum in this question, as the angular momentum is conserved, so the moment of inertia decreases. And we all know that moment of inertia is inversely proportional to the angular velocity.

Complete answer:
When the fluid spreads out, the moment of inertia of the system is increased. If we apply conservation of angular momentum.
$I\omega = {I_1}{\omega _1}$
As $I$ increases due to water spreading out, the angular velocity decreases. When water level falls, $I$ decreases resulting in increased angular velocity.Therefore, the angular velocity decreases initially and then increases again.

The rate of change of angular displacement that describes the angular speed or rotational speed of an object and the axis around which the item is revolving is known as angular velocity. The amount of change in the particle's angular displacement over time is referred to as angular velocity.

The angular velocity vector's trajectory is parallel to the plane of rotation, in the direction specified by the right-hand rule. The pace at which an object or particle spins around a given centre point, or, in other words, how much angular distance does an object cover around anything over time, is measured in angle per unit time.

Hence, the correct option is B.

Note: Angular momentum is directly proportional to the orbital angular velocity vector ω of the particle, where the constant of proportionality is moment of inertia (which depends on both the mass of the particle and its distance from COM), i.e. $L = I\omega$ , where $L$ is the angular momentum, $I$ is the moment of inertia and $\omega$ is the angular velocity.