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