(30 points) Find the inertia tensors for the following rigid bodies. Set the center of mass to be the origin of coordinates. Choose the orientation of the coordinate system wisely so that the axes coincide with the principal axes. You need to justify your selections by showing that the off-diagonal terms vanish. a. Four identical point masses (mass =m for each one) connected by massless rods (length =l for each one) to form an equilateral tetrahedron. b. A plank, with dimensions l,w,h and mass M. c. A thin disk, with radius r and mass M.
