For a composite body made of a solid cylinder and a solid sphere, how do you cal

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?

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?

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.

Moment of Inertia – The moment of inertia is a measure of an object's resistance to rotational motion about a given axis.
Composite Bodies – A composite body is made up of two or more distinct shapes, and the total moment of inertia is calculated by summing the individual moments of inertia of each shape.
Parallel Axis Theorem – If the axis of rotation is not through the center of mass, the parallel axis theorem may need to be applied to find the correct moment of inertia.