A person is standing on the edge of a circular platform, which is moving with constant angular speed about an axis passing through its centre and perpendicular to the plane of platform. If person is moving along any radius towards axis of rotation then the angular velocity will:

Options

A. decrease
B. remain unchanged
C. increase
D. data is insufficient

Answer

To solve the problem, we need to analyze the situation where a person is moving towards the axis of rotation on a circular platform that is rotating with a constant angular speed. We will use the principle of conservation of angular momentum to understand how the angular velocity changes as the person moves.

### Step-by-Step Solution:

1. **Understanding the System**:
- We have a circular platform rotating about its center with a constant angular speed \( \omega \).
- The person is initially at the edge of the platform, at a distance \( R \) from the axis of rotation.

2. **Initial Moment of Inertia**:
- The moment of inertia \( I \) for the person standing at the edge (distance \( R \)) is given by:
\[ I_1 = m R^2 \]
- Here, \( m \) is the mass of the person.

3. **Final Moment of Inertia**:
- As the person moves towards the center, let’s say they move to a distance \( R_1 \) (where \( R_1 < R \)).
- The new moment of inertia when the person is at distance \( R_1 \) is:
\[ I_2 = m R_1^2 \]

4. **Conservation of Angular Momentum**:
- Since there are no external torques acting on the system, the angular momentum before and after the person moves must be conserved:
\[ I_1 \omega = I_2 \omega_2 \]
- Substituting the expressions for \( I_1 \) and \( I_2 \):
\[ m R^2 \omega = m R_1^2 \omega_2 \]

5. **Simplifying the Equation**:
- The mass \( m \) cancels out from both sides:
\[ R^2 \omega = R_1^2 \omega_2 \]
- Rearranging gives us:
\[ \omega_2 = \frac{R^2}{R_1^2} \omega \]

6. **Analyzing the Result**:
- Since \( R_1 < R \), the ratio \( \frac{R^2}{R_1^2} \) is greater than 1.
- Therefore, \( \omega_2 > \omega \).

7. **Conclusion**:
- As the person moves towards the axis of rotation, the angular velocity \( \omega_2 \) increases. Thus, the angular velocity will increase as the person moves towards the center.

### Final Answer:
The angular velocity will **increase** as the person moves along any radius towards the axis of rotation.

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