Question

A disc is rotating with angular speed $\omega$. If a child sits on it, what is conserved :-

• A. linear momentum
• B. angular momentum
• C. kinetic energy
• D. potential energy

Answer 1

The Correct Option is B

To determine what is conserved when a child sits on a rotating disc, we must consider the physical principles involved. The scenario involves rotational motion, so the concept of angular momentum is key.

Angular momentum is defined as the product of the moment of inertia and angular velocity. The formula for angular momentum \(L\) for a rotating object is:

\(L = I \cdot \omega\)

where:

• \(L\) = angular momentum
• \(I\) = moment of inertia
• \(\omega\) = angular speed

In the absence of external torques, angular momentum is conserved according to the law of conservation of angular momentum. This means that the total angular momentum of a system remains constant if no external forces are acting on it.

When the child sits on the rotating disc, the system's moment of inertia changes due to the added mass of the child. As a result, the angular speed \(\omega\) will adjust to keep the angular momentum \(L\) constant, provided no external torque is acting on the system.

Now, let’s evaluate the options:

• Linear momentum: The child sitting on the disc does affect the linear momentum, which is not conserved in this rotational scenario without an external reference.
• Angular momentum: This is conserved because no external torque is acting on the system, as previously explained.
• Kinetic energy: Kinetic energy is not necessarily conserved because it can transform between rotational and translational forms, and changes can occur due to internal forces.
• Potential energy: This is not relevant to the conservation question here, as there is no change in height or gravitational influence directly affecting energy conservation.

The correct answer is that angular momentum is conserved when a child sits on the rotating disc, given no external torques act on the system.