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 question about the effect of a person stretching out their hands while standing on a rotating disc, we can analyze the situation using the principles of rotational motion, particularly focusing on angular momentum and moment of inertia.

### Step-by-Step Solution:

1. **Understanding the System**:
- A person is standing on a rotating disc. Initially, the person has their hands close to their body.

2. **Moment of Inertia**:
- The moment of inertia (I) of a body is defined as \( I = \sum m_i r_i^2 \), where \( m_i \) is the mass of each part of the body and \( r_i \) is the distance from the axis of rotation.
- When the person stretches out their hands, the distribution of mass changes. The hands are now further away from the axis of rotation, which increases the moment of inertia.

3. **Conservation of Angular Momentum**:
- Angular momentum (L) is given by the equation \( L = I \cdot \omega \), where \( \omega \) is the angular speed.
- In the absence of external torques (as stated in the problem), angular momentum must be conserved. This means that the initial angular momentum must equal the final angular momentum: \( L_{initial} = L_{final} \).

4. **Analyzing Changes**:
- Initially, let’s denote the moment of inertia as \( I_1 \) and the angular speed as \( \omega_1 \).
- After the person stretches their hands, the moment of inertia increases to \( I_2 \) (where \( I_2 > I_1 \)).
- Since angular momentum is conserved, we have:
\[ I_1 \cdot \omega_1 = I_2 \cdot \omega_2 \]
- Rearranging gives:
\[ \omega_2 = \frac{I_1 \cdot \omega_1}{I_2} \]

5. **Conclusion**:
- Since \( I_2 > I_1 \), it follows that \( \omega_2 < \omega_1 \). Therefore, the angular speed decreases when the person stretches out their hands.

### Final Answer:
The angular speed will **decrease**.