A person is sitting on a rotating chair which is rotating with some angular velocity. Person is sitting on the chair with his arms folded. Now he slowly stretches his arm then

Options

A. Angular momentum of the system decreases (
B. Angular momentum of the system increases
C. Angular momentum remains constant
D. Angular speed of the system increases

Explanation

To solve the problem step by step, we will analyze the situation of the person on the rotating chair and how stretching the arms affects angular momentum and angular speed.

### Step 1: Understand the Initial Conditions
Initially, the person is sitting on a rotating chair with folded arms. At this point, the system has a certain moment of inertia (I₁) and angular velocity (ω₁).

### Step 2: Identify the Change
When the person stretches their arms, the distribution of their mass changes. The arms being extended means that the mass is now further from the axis of rotation, which increases the moment of inertia (I₂) of the system.

### Step 3: Apply the Conservation of Angular Momentum
Since there are no external torques acting on the system, the angular momentum (L) must be conserved. The angular momentum is given by the product of moment of inertia and angular velocity:
\[ L = I \cdot \omega \]
Thus, we have:
\[ I₁ \cdot ω₁ = I₂ \cdot ω₂ \]

### Step 4: Analyze the Relationship Between I and ω
From the conservation of angular momentum:
\[ I₁ \cdot ω₁ = I₂ \cdot ω₂ \]
Since we established that I₂ > I₁ (because the person stretched their arms), we can rearrange the equation:
\[ ω₂ = \frac{I₁}{I₂} \cdot ω₁ \]
Since I₂ > I₁, it follows that:
\[ ω₂ < ω₁ \]
This means that the angular velocity decreases when the person stretches their arms.

### Step 5: Conclusion
The angular momentum remains constant (conserved) while the angular speed decreases. Therefore, the correct answer is that the angular momentum remains constant, and the angular speed decreases.

### Final Answer
- Angular momentum remains constant.
- Angular speed decreases.

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