Question

When sand is poured on a rotating disc, its angular velocity will be:
A. Decrease
B. Increase
C. Remain constant
D. None of these

Answer 1

Use the formula for angular momentum of an object. This law gives the relation between mass of object, radius of the circular path and angular velocity of the object. Use the law of conservation of angular momentum and check whether the angular velocity of the rotating disc with sand should be increased, decreased or kept the same in order to have the same angular momentum as that of the rotating disc.

Formula used:
The angular momentum $L$ of an object is given by
$L = mr{\omega ^2}$ …… (1)
Here, $m$ is the mass of the object, $\omega$ is angular velocity of the object and $r$ is radius of the circular path of the object.

Complete answer:
We have given that the sand is poured on a rotating disc. We have asked about the angular velocity of the disc when the sand is poured on the rotating disc. We know that according to the law of conservation of angular momentum, the initial and final angular momentum of the rotating disc should be the same.

From equation (1), we can conclude that the angular momentum of an object depends on the mass of the object, velocity of the object and radius of the circular path. Hence, when the sand is poured over the rotating disc, the total mass of the disc along with sand increases.The radius of the rotating disc remains the same even after pouring sand over it.

Hence, to have the angular momentum of the rotating disc and sand system same as that of the angular momentum of rotating disc, the angular velocity of the rotating disc should be decreased.Therefore, on pouring sand over the rotating disc, the angular velocity of the rotating disc decreases.

Hence, the correct option is D.

Note: The students may also use the formula for angular momentum in terms of linear velocity of the rotating disc and show that the linear velocity of the rotating disc and sand should be decreased to conserve the angular momentum. Since the linear and angular velocities are proportional to each other, the angular velocity also should be decreased.