A person is standing on a rotating table with metal spheres in his hands. If he withdraws his hands to his chest, then the effect on his angular velocity will be.

Options

A. increase
B. decrease
C. remain same
D. can't say

Explanation

To solve the question regarding the effect on the angular velocity when a person standing on a rotating table withdraws his hands to his chest, we can follow these steps:

### Step 1: Understand the Concept of Angular Momentum
Angular momentum (L) is defined as the product of the moment of inertia (I) and angular velocity (ω):
\[ L = I \cdot \omega \]
In a closed system with no external torques, angular momentum is conserved.

### Step 2: Analyze the Situation
Initially, the person is holding metal spheres in his hands, which contributes to the moment of inertia of the system. When he withdraws his hands to his chest, he effectively reduces the distance of the spheres from the axis of rotation, which decreases the moment of inertia (I).

### Step 3: Apply the Conservation of Angular Momentum
Since there are no external forces acting on the system, the angular momentum before and after the person withdraws his hands must be equal:
\[ L_{\text{initial}} = L_{\text{final}} \]
This can be expressed as:
\[ I_{\text{initial}} \cdot \omega_{\text{initial}} = I_{\text{final}} \cdot \omega_{\text{final}} \]

### Step 4: Relate Moment of Inertia and Angular Velocity
As the person withdraws his hands, the moment of inertia decreases:
\[ I_{\text{final}} < I_{\text{initial}} \]
To keep the angular momentum constant, if the moment of inertia decreases, the angular velocity must increase:
\[ \omega_{\text{final}} > \omega_{\text{initial}} \]

### Step 5: Conclusion
Thus, when the person withdraws his hands to his chest, the angular velocity of the rotating table will increase.

### Final Answer
The effect on his angular velocity will be that it increases.

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