If a person standing on a rotating disc stretches out his hands, the angular speed will

Options

A. increase
B. decrease
C. remain same
D. None of these

Explanation

To solve the problem of what happens to the angular speed of a rotating disc when a person standing on it stretches out their hands, we can analyze the situation using the principles of rotational motion and conservation of angular momentum.

### Step-by-Step Solution:

1. **Understanding Angular Momentum**:
- Angular momentum (L) of a system is given by the product of the moment of inertia (I) and the angular velocity (ω):
\[ L = I \cdot \omega \]
- For a rotating system, if no external torque acts on it, the angular momentum remains constant.

2. **Identifying the Initial State**:
- Initially, the person is standing on the disc with their hands at their sides. At this point, the system has a certain moment of inertia (I_initial) and a certain angular speed (ω_initial).

3. **Stretching Out Hands**:
- When the person stretches out their hands, they effectively increase their moment of inertia (I_final) because the mass distribution is now further from the axis of rotation.

4. **Applying Conservation of Angular Momentum**:
- Since there is no external torque acting on the system, we can apply the conservation of angular momentum:
\[ L_{initial} = L_{final} \]
- This gives us:
\[ I_{initial} \cdot \omega_{initial} = I_{final} \cdot \omega_{final} \]

5. **Relating Initial and Final States**:
- Rearranging the equation allows us to express the final angular speed (ω_final) in terms of the initial angular speed (ω_initial):
\[ \omega_{final} = \frac{I_{initial}}{I_{final}} \cdot \omega_{initial} \]

6. **Conclusion**:
- Since the moment of inertia increases when the person stretches out their hands (I_final > I_initial), it follows that:
\[ \omega_{final} < \omega_{initial} \]
- Therefore, the angular speed of the disc decreases when the person stretches out their hands.

### Final Answer:
The angular speed of the disc will decrease when the person standing on it stretches out their hands.