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This problem revolves around the concept of **conservation of angular momentum**. Here’s how to approach the solution:

1. **Angular Momentum Conservation Principle**: The conservation of angular momentum states that if there is no external torque acting on a rotating system, its angular momentum remains constant. Mathematically, this is expressed as:
   \[
   I_1 \omega_1 = I_2 \omega_2
   \]
   where \( I \) is the moment of inertia and \( \omega \) is the angular velocity.

2. **Moment of Inertia and Angular Velocity Relationship**: The moment of inertia, \( I \), depends on how mass is distributed relative to the axis of rotation. When Student A pulls his arms in (reducing the distance of the weights from his body), he decreases the moment of inertia \( I \) because the mass is now closer to the axis of rotation.

3. **Effect on Angular Velocity**: Since angular momentum \( L = I \omega \) is conserved, a decrease in \( I \) must be compensated by an increase in \( \omega \). Therefore, as Student A pulls his arms in, his angular velocity \( \omega \) increases to keep the product \( I \omega \) constant.

4. **Conclusion**: When Student A brings the weights closer to his body, his angular velocity \( \omega \) increases due to the decrease in his moment of inertia \( I \). This effect is why we observe a faster spin in scenarios where a rotating object reduces its moment of inertia.

Would you like further details or have any questions?

Here are five related questions to explore this topic further:
1. What are real-life applications of the conservation of angular momentum?
2. How does the distribution of mass affect the moment of inertia in various shapes?
3. Can you describe a scenario where angular momentum is not conserved?
4. What are the differences in moment of inertia between a figure skater spinning with arms extended versus arms folded?
5. How does angular velocity change if external torque is introduced?

**Tip:** Remember, reducing the distance of mass from the axis of rotation always decreases the moment of inertia and typically increases rotational speed if no external torque is applied.

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 the effect on angular velocity when a rotating student pulls their arms in while holding weights. This problem illustrates the conservation of angular momentum principle, showing how reducing the moment of inertia increases angular velocity. Suitable for high school students studying physics.

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