# Step 1: Calculate the Mass of the Leg The leg's mass is typically estimated as a percentage of the total body weight. For an average adult, the leg (including the thigh, shank, and foot) is about **16%** of total body weight. \[ \text{Mass of leg} = \text{Body weight} \times .16 = 80\,\text{kg} \times .16 = 12.8\,\text{kg} \] **Explanation:** We multiply the total body mass by .16 to estimate the mass of one leg. --- # Step 2: Calculate the Center of Mass and Moment of Inertia ### Center of Mass The center of mass (COM) of the leg is typically about **43.3%** of the leg length from the proximal end (hip). \[ \text{COM distance from proximal end} = .433 \times .435\,\text{m} = .188\,\text{m} \] **Explanation:** We use anthropometric data to find the COM location as a fraction of leg length. --- ### Moment of Inertia (About Proximal End) The moment of inertia of the leg about the hip (proximal end) is: \[ I = m k^2 \] where \( k \) is the radius of gyration, about **32.2%** of leg length. \[ k = .322 \times .435\,\text{m} = .140\,\text{m} \] \[ I = 12.8\,\text{kg} \times (.140\,\text{m})^2 = 12.8 \times .0196 = .251\,\text{kg}\cdot\text{m}^2 \] **Explanation:** The radius of gyration is a standard percentage of leg length. Squaring it and multiplying by the leg mass gives the moment of inertia. --- # Final Answers - **Center of mass distance from proximal end:** \( .188\,\text{m} \) - **Moment of inertia about proximal end:** \( .251\,\text{kg}\cdot\text{m}^2 \)