The mass of a flywheel is concentrated at its rim

Options

A. to obtain a strong wheel
B. to decrease the moment of inertia
C. to increase the moment of inertia
D. to obtain the stable equilibrium

Answer

To solve the question regarding why the mass of a flywheel is concentrated at its rim, we will analyze the implications of mass distribution on the moment of inertia and the overall performance of the flywheel.

### Step-by-Step Solution:

1. **Understanding Flywheel Design**:
- A flywheel is a mechanical device that stores rotational energy. Its design is crucial for its performance, particularly in applications requiring stability and energy storage.

2. **Moment of Inertia**:
- The moment of inertia (I) is a measure of an object's resistance to changes in its rotational motion. It depends on the mass distribution relative to the axis of rotation. The formula for the moment of inertia for a point mass is given by:
\[ I = m r^2 \]
- Here, \(m\) is the mass and \(r\) is the distance from the axis of rotation.

3. **Effect of Mass Distribution**:
- If the mass of the flywheel is concentrated at the rim, the radius \(r\) is maximized. This maximization leads to a higher moment of inertia because:
\[ I \propto m \cdot r^2 \]
- Therefore, concentrating mass at the rim increases the moment of inertia significantly compared to if the mass were distributed closer to the center.

4. **Torque and Angular Acceleration**:
- Torque (\(\tau\)) is related to moment of inertia and angular acceleration (\(\alpha\)) by the equation:
\[ \tau = I \cdot \alpha \]
- A higher moment of inertia means that for a given torque, the angular acceleration will be lower. However, it also means that the flywheel can store more energy and maintain a more stable rotation.

5. **Conclusion**:
- The primary reason for concentrating the mass at the rim of the flywheel is to **increase the moment of inertia**. This design choice enhances the flywheel's ability to store energy and maintain stability during rotation. Thus, the correct answer to the question is:
- **C. To increase the moment of inertia.**