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To solve this problem, we need to analyze the diver's moment of inertia and angular speed at each position (1, 2, and 3) given the conditions of angular momentum conservation.

### Understanding Moment of Inertia and Angular Speed

1. **Moment of Inertia (I)**: The moment of inertia depends on how spread out the mass is from the rotation axis. A fully extended position (like position 3) has a larger moment of inertia than a tucked position (like position 2).
   
2. **Angular Speed (ω)**: According to the conservation of angular momentum, \( L = I \cdot \omega \), where \( L \) (angular momentum) is constant. Thus, if the moment of inertia \( I \) is large, the angular speed \( \omega \) will be small, and vice versa.

### Solution

#### Part (a): Order by Moment of Inertia (Largest to Smallest)

1. **Position 3 (Fully Extended)**: This has the largest moment of inertia because her body is fully extended.
2. **Position 1 (Beginning to Tuck)**: This has an intermediate moment of inertia as she starts tucking but is not in a full tuck yet.
3. **Position 2 (Full Tuck)**: This has the smallest moment of inertia since her mass is closest to the axis of rotation.

**Answer for Part (a)**: Order from largest to smallest moment of inertia: **Position 3, Position 1, Position 2**.

#### Part (b): Order by Angular Speed (Largest to Smallest)

Due to conservation of angular momentum:
- **Position 2 (Full Tuck)**: With the smallest moment of inertia, position 2 will have the highest angular speed.
- **Position 1 (Beginning to Tuck)**: This position will have an intermediate angular speed.
- **Position 3 (Fully Extended)**: This has the lowest angular speed due to the highest moment of inertia.

**Answer for Part (b)**: Order from largest to smallest angular speed: **Position 2, Position 1, Position 3**.

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### Additional Questions

1. Why does the conservation of angular momentum affect the diver's angular speed?
2. How does changing the body’s configuration impact the rotational motion in diving?
3. Can we calculate the specific angular speeds if given the values of moments of inertia?
4. What are other examples where moment of inertia affects angular speed?
5. How would air resistance impact the conservation of angular momentum in this scenario?

#### Tip:
For rotational motion problems, always start by identifying which quantities are conserved (like angular momentum) and how body configuration impacts moment of inertia and angular speed.

A diver does a backflip off a 3-meter board, as shown in the diagram. Assume the diver’s angular momentum is conserved as she moves from position 1 to 2 to 3. At position 1 she is beginning to tuck her body, at position 2 she is in a full tuck, and just before entering the water at position 3 she is fully extended.

Part (a): Order the images of the diver from largest to smallest moment of inertia.

Part (b): Order the images of the diver from largest to smallest angular speed.

Explore how to analyze a diver's moment of inertia and angular speed during a backflip off a 3-meter board. This physics problem involves the conservation of angular momentum, where the diver changes her body position from fully extended to fully tucked. Determine the correct order of the diver’s positions based on moment of inertia and angular speed, suitable for high school students in Grades 10-12.

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