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.

Would you like further details on any part of this explanation?

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.