Example 11.6 determined the moment of inertia of a solid cube. Now you will find the moment of inertia of a hollow cube, where the wall thickness is much smaller than the cube height.
a. Consider a thin square plate of height h and mass mp. Show that the moment of inertia of such a plate, relative to its center of mass G and expressed in a body frame B attached to the plate, is
b. A hollow cube can be modeled as a structure built of six thin plates. For one of the plates, find the moment of inertia relative to the center of the cube O.
c. Sum the contributions of all the plates to find the moment of inertia of the cube about its center of mass. Be careful to consider the rotation of the plates with respect to one another.
