When sand is poured on a rotating disc what happen to its angular velocity ? explain

When sand is poured on a rotating disc, its angular velocity increases due to the law of conservation of angular momentum. To understand this concept, let's break it down step by step:

1. Law of Conservation of Angular Momentum: Angular momentum is a property of a rotating object which depends on two factors - the moment of inertia (a measure of how mass is distributed in an object) and the angular velocity (how fast the object is rotating). The law of conservation of angular momentum states that if no external torque acts on a rotating object, then its angular momentum remains constant.

2. Initial State: Let's assume that the disc is initially rotating at a certain angular velocity. At this point, the disc has a certain moment of inertia and angular momentum.

3. Pouring Sand: When sand is poured onto the rotating disc, the sand particles adhere to the surface due to friction. As a result, the moment of inertia of the system (the disc + sand) increases since the sand particles contribute to the total mass and distribution of mass in the system.

4. Conservation of Angular Momentum: According to the law of conservation of angular momentum, if no external torque acts on the system, the initial angular momentum must be equal to the final angular momentum. Since the moment of inertia increased by adding sand, in order to maintain the same angular momentum, the angular velocity must increase.

So, when sand is poured on the rotating disc, its angular velocity increases to compensate for the increased moment of inertia and maintain the conservation of angular momentum.