A disc is rotating with angular velocity `omega`. If a child sits on it, what is conserved?

Options

A. Linear momentum
B. Angular momentum
C. kinetic energy
D. Moment of inertia

Answer

To solve the problem, we need to analyze the situation when a child sits on a rotating disc. The key concepts involved are angular momentum, moment of inertia, and the effects of external forces.

### Step-by-Step Solution:

1. **Identify the System**:
We have a disc rotating about its center with an initial angular velocity \( \omega \). When a child sits on the disc, we need to determine what physical quantity remains conserved.

2. **Understand the Forces Acting**:
When the child sits on the disc, the gravitational force \( mg \) acts downward on the child. This force is directed towards the center of the disc, which means it does not create any torque about the axis of rotation.

3. **Determine External Torque**:
Since the gravitational force acts parallel to the axis of rotation, it does not exert any torque on the system. Therefore, the net external torque acting on the system is zero.

4. **Apply the Conservation of Angular Momentum**:
According to the principle of conservation of angular momentum, if no external torque acts on a system, the angular momentum of that system remains constant. Therefore, the angular momentum before the child sits on the disc will equal the angular momentum after the child sits down.

5. **Analyze Moment of Inertia**:
When the child sits on the disc, the moment of inertia of the system increases because the child adds mass to the disc. The moment of inertia \( I \) is given by \( I = I_{disc} + m_{child} r^2 \), where \( r \) is the distance from the axis of rotation to where the child is sitting.

6. **Relate Angular Momentum and Angular Velocity**:
The angular momentum \( L \) of the system is given by \( L = I \omega \). Since \( I \) increases when the child sits down, and \( L \) is conserved, the angular velocity \( \omega \) must decrease to keep \( L \) constant.

7. **Conclusion**:
The quantity that remains conserved when the child sits on the disc is the angular momentum. Therefore, the answer to the question is that angular momentum is conserved.

### Final Answer:
**Angular momentum is conserved.**

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