For a composite body made of a solid cylinder and a solid sphere, how do you calculate the total moment of inertia about the same axis?

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Q: For a composite body made of a solid cylinder and a solid sphere, how do you calculate the total moment of inertia about the same axis?

Solution: The total moment of inertia of a composite body about the same axis is the sum of the individual moments of inertia.

Steps: 5

Step 1: Identify the shapes in the composite body. In this case, we have a solid cylinder and a solid sphere.
Step 2: Find the moment of inertia formula for each shape. The moment of inertia for a solid cylinder about its central axis is (1/2) * m * r^2, and for a solid sphere, it is (2/5) * m * r^2.
Step 3: Calculate the moment of inertia for the solid cylinder using its mass (m_c) and radius (r_c). Use the formula: I_cylinder = (1/2) * m_c * r_c^2.
Step 4: Calculate the moment of inertia for the solid sphere using its mass (m_s) and radius (r_s). Use the formula: I_sphere = (2/5) * m_s * r_s^2.
Step 5: Add the two moments of inertia together to find the total moment of inertia for the composite body. Use the formula: I_total = I_cylinder + I_sphere.