Please refer to the picture to help answer the questions. A ice skater goes into a spin standing vertically with his arms outstretched horizontally. We can crudely model his torso and legs as a cylinder with radius 0.1m and mass 52 kg and each arm is a rod with mass 4 kg and length 0.9 m. The skater will initially spin at 2.0 rad/s. Question 1: what is the moment of inertia of the skater's torso and legs. Please answer in kg m^2. Question 2: What is
Please refer to the picture to help answer the questions.
A ice skater goes into a spin standing vertically with his arms outstretched horizontally. We can crudely model his torso and legs as a cylinder with radius 0.1m and mass 52 kg and each arm is a rod with mass 4 kg and length 0.9 m. The skater will initially spin at 2.0 rad/s.
Question 1: what is the moment of inertia of the skater's torso and legs. Please answer in kg m^2.
Question 2: What is the moment of inertia of one of the skater's arms? Please answer in kg m^2.
Question 3: What is the total moment of inertia of the skater? Please answer in kg m^2
![### Rotational Inertia
#### Diagram Explanation
This image illustrates two different formulas for the moment of inertia \( I \), which is a measure of an object's resistance to changes in its rotational motion.
1. **Left Diagram: Rod Rotating About an End**
- **Formula:**
\[
I = \frac{1}{3} ML^2
\]
- **Description:**
- The diagram shows a rod of length \( L \) with its rotational axis at one end. The moment of inertia is defined by the formula \( \frac{1}{3} ML^2 \), where \( M \) is the mass of the rod and \( L \) is its length.
2. **Right Diagram: Solid Cylinder Rotating About Its Central Axis**
- **Formula:**
\[
I = \frac{1}{2} MR^2
\]
- **Description:**
- The diagram depicts a solid cylinder with radius \( R \), rotating about its central axis. The moment of inertia for this shape is given by the formula \( \frac{1}{2} MR^2 \), where \( M \) is the mass of the cylinder and \( R \) is its radius.
These formulas are essential for understanding how the distribution of mass affects an object's rotational dynamics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F043a0ede-8e66-4ff6-855d-c3c5ac86ef03%2Fbbb1fcf3-0a4d-4360-ad5a-0e640242b537%2F1ixhdth_processed.jpeg&w=3840&q=75)
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Can you please help me answer the last three parts of this same problem.
Question 4: What is the skater's
Question 5: The skater pulls his arms in to his chest and now he can be approximted as just a cylinder. What is his new moment of inertia? Please answer in kg m^2
Question 6: How fast is he spinning now that his arms are pulled in? Assume no external torque acts on him as he spins. Please answer in rad/s
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