A horizontal platform is rotating with uniform angular velocity ω around the vertical axis passing through its centre. At some instant of time, a viscous liquid of mass m is dropped at the centre and is allowed to spread out and finally fall. The angular velocity during this period.

When a horizontal platform rotates uniformly around a vertical axis passing through its center, the addition of a viscous liquid at its center will affect its motion. After the liquid has been dropped, it spreads outward due to the rotation of the platform and the forces of centrifugation. The movement of the liquid away from the axis of rotation causes a change in the overall distribution of mass, thus increasing the moment of inertia of the platform.

The principle of conservation of angular momentum tells us that if the torques exerted on a system are zero, the total angular momentum of the system is constant. However, this is dependent both on the moment of inertia and angular velocity, so when the moment of inertia increases due to spreading of liquid, the angular velocity has to reduce for maintaining constant angular momentum. This causes a continuous decrease in the rotation speed of the platform as long as the liquid continues spreading outward.

The angular velocity does not remain constant or increase because the redistribution of mass always increases the moment of inertia. This process ensures that the rotation of the platform slows down uniformly over time, illustrating how angular momentum conservation governs such interactions. Thus, the angular velocity of the platform decreases continuously as the liquid spreads outward and eventually falls off.

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