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This is a classic problem that uses the principle of **conservation of angular momentum**.

### Solution:
When Student A pulls his arms closer to his body, his **moment of inertia** decreases. According to the principle of conservation of angular momentum, if no external torques are acting on the system, the **angular momentum** will remain constant.

Mathematically, angular momentum \( L \) is given by:
\[
L = I \cdot \omega
\]
where:
- \( I \) is the moment of inertia,
- \( \omega \) is the angular velocity.

Since angular momentum is conserved, we have:
\[
I_1 \omega_1 = I_2 \omega_2
\]
where:
- \( I_1 \) and \( \omega_1 \) are the initial moment of inertia and angular velocity (with arms extended),
- \( I_2 \) and \( \omega_2 \) are the final moment of inertia and angular velocity (with arms pulled in).

When Student A pulls his arms in:
- \( I_2 < I_1 \) (since the mass is closer to the axis of rotation),
- To keep \( I_1 \omega_1 = I_2 \omega_2 \) constant, \( \omega_2 \) must increase as \( I_2 \) decreases.

### Conclusion:
When Student A pulls his arms in, his angular velocity \( \omega \) increases. This is because the decrease in moment of inertia requires an increase in angular velocity to maintain the same angular momentum.

Would you like further details or have questions?

### Related Questions:
1. What would happen if Student A extended his arms again after pulling them in?
2. How does the distribution of mass affect the moment of inertia in a rotating body?
3. If friction is present in the system, how would that affect the conservation of angular momentum?
4. How can we calculate the exact change in angular velocity if we know the initial and final moments of inertia?
5. What are some practical applications of the conservation of angular momentum in real-world physics?

### Tip:
Remember, pulling mass closer to the axis of rotation decreases the moment of inertia, leading to an increase in angular velocity for a closed system.

Student A is sitting on a rotating chair with arms stretched out, holding two weights. Student B gives Student A a push to start rotating. After Student A begins rotating, he pulls his arms in, bringing the weights closer to his body. What will happen to the angular velocity of Student A when he pulls his arms in? Explain your answer using the conservation of angular momentum, where I1ω1 = I2ω2.

Understand how pulling arms in affects angular velocity through the principle of conservation of angular momentum. This problem explains the relationship between moment of inertia and angular velocity for a rotating system, ideal for high school physics students in Grades 11-12.

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