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To solve the problem, we will calculate the total moment of inertia and the total angular momentum of the system based on the provided information.

### Step 1: Understanding the problem
The setup includes:
1. **Cylinder**
   - Radius (\(R_{\text{cylinder}}\)) = 5 meters
   - Mass (\(M_{\text{cylinder}}\)) = 100 kilograms

2. **Person**
   - Radius of path (\(R_{\text{person}}\)) = 5 meters
   - Mass (\(M_{\text{person}}\)) = 50 kilograms

The tasks involve:
1. **Calculating the moment of inertia (\(I\))** of the system:
   - Moment of inertia of the cylinder (\(I_{\text{cylinder}}\)).
   - Moment of inertia of the person (\(I_{\text{person}}\)) treated as a single particle.

2. **Total angular momentum (\(L\))** of the system:
   - Using angular velocity (\(\omega\)).

---

### Step 2: Moment of Inertia Calculations

1. **Cylinder's Moment of Inertia**:
   The cylinder is a solid cylinder rotating about its axis, so its moment of inertia is:
   \[
   I_{\text{cylinder}} = \frac{1}{2} M_{\text{cylinder}} R_{\text{cylinder}}^2
   \]
   Substituting the values:
   \[
   I_{\text{cylinder}} = \frac{1}{2} \times 100 \, \text{kg} \times (5 \, \text{m})^2
   \]
   \[
   I_{\text{cylinder}} = \frac{1}{2} \times 100 \times 25 = 1250 \, \text{kg·m}^2
   \]

2. **Person's Moment of Inertia**:
   The person is treated as a particle at a radius of 5 meters, so the moment of inertia is:
   \[
   I_{\text{person}} = M_{\text{person}} R_{\text{person}}^2
   \]
   Substituting the values:
   \[
   I_{\text{person}} = 50 \, \text{kg} \times (5 \, \text{m})^2
   \]
   \[
   I_{\text{person}} = 50 \times 25 = 1250 \, \text{kg·m}^2
   \]

3. **Total Moment of Inertia**:
   Adding the moments of inertia of the cylinder and the person:
   \[
   I_{\text{total}} = I_{\text{cylinder}} + I_{\text{person}}
   \]
   \[
   I_{\text{total}} = 1250 + 1250 = 2500 \, \text{kg·m}^2
   \]

---

### Step 3: Angular Momentum Calculation

1. The angular momentum of a system is given by:
   \[
   L = I_{\text{total}} \cdot \omega
   \]
   Here, \(\omega\) (angular velocity) needs to be provided or recorded from the simulation. Once \(\omega\) is known, the total angular momentum can be computed using the above formula.

---

### Summary of Results:
- **Moment of Inertia of the Cylinder**: \(1250 \, \text{kg·m}^2\)
- **Moment of Inertia of the Person**: \(1250 \, \text{kg·m}^2\)
- **Total Moment of Inertia**: \(2500 \, \text{kg·m}^2\)
- **Total Angular Momentum**: Dependent on the value of \(\omega\).

Let me know the angular velocity (\(\omega\)) if you have it, or share additional details so we can proceed to compute \(L\). Would you like further clarification or assistance

Calculate the total moment of inertia and angular momentum of a cylinder-person system, given a cylinder radius of 5 meters, mass of 100 kilograms, and a person of mass 50 kilograms at a radius of 5 meters.

Learn how to calculate the moment of inertia and angular momentum for a rotating cylinder-person system. This problem involves key physics concepts like rotational motion, angular velocity, and moment of inertia. Perfect for high school and college physics students.

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