A man spinning in free space changes the shape of his body, eg. By spreading his arms or curling up. By doing this, he can change his.

Options

A. moment of inertia
B. angular momentum
C. angular velocity
D. rotational kinetic energy

Answer

To solve the problem, we need to understand the relationship between the shape of a spinning body, its moment of inertia, and its angular velocity, based on the principle of conservation of angular momentum.

### Step-by-Step Solution:

1. **Understanding Angular Momentum Conservation**:
- In the absence of external torques, the angular momentum of a system remains constant. This is expressed mathematically as:
\[ L = I \cdot \omega \]
where \( L \) is angular momentum, \( I \) is the moment of inertia, and \( \omega \) is the angular velocity.

2. **Initial and Final States**:
- Let’s denote the initial moment of inertia and angular velocity as \( I_i \) and \( \omega_i \), respectively. When the man is curled up, he has a certain moment of inertia and angular velocity.
- When he spreads his arms and legs, his moment of inertia increases, denoted as \( I_f \), while his angular velocity changes to \( \omega_f \).

3. **Applying Conservation of Angular Momentum**:
- According to the conservation of angular momentum, we have:
\[ I_i \cdot \omega_i = I_f \cdot \omega_f \]

4. **Analyzing the Change in Moment of Inertia**:
- When the man curls up, his moment of inertia \( I_i \) is smaller. When he spreads his arms, \( I_f \) increases. Since angular momentum is conserved, an increase in moment of inertia must lead to a decrease in angular velocity:
\[ I_f > I_i \implies \omega_f < \omega_i \]

5. **Conclusion**:
- By changing his shape (spreading arms or curling up), the man can change his angular velocity. Specifically, spreading his arms increases his moment of inertia and decreases his angular velocity.

### Final Answer:
The man can change his **angular velocity** by changing the shape of his body.