1. A wedge of a sphere of radius 29 cm (similar to one segment of an orange) is oriented so that the axis is aligned with the z-axis, one face is in the xz plane, and the other is inclined at an angle of = 53o, as shown. The wedge is made of metal having a density of 7500 kg/m3. In the co- ordinate system shown, compute a) Ixx, b) Iyy, and c) Izz.
2. In the coordinate system shown, compute a) Ixy, b) Ixz, and c) Iyz.
3. What are the principal moments of inertia (i.e., the eigenvalues) for this object? List them from smallest to largest.
4. Determine the unit eigenvector (i.e., having a magni- tude of 1) corresponding to the first eigenvalue listed in the previous problem. Find the version that has a positive x- component. Enter a) the x-component, b) the y-component, and c) the z-component of the eigenvector.
5. Determine the unit eigenvector corresponding to the second eigenvalue listed in the previous problem. Find the version that has a positive z-component. Enter a) the x- component, b) the y-component, and c) the z-component of the eigenvector.
6. Determine the unit eigenvector corresponding to the third eigenvalue listed in the previous problem. Find the ver- sion such that the cross product of your first eigenvector with your second eigenvector equals your third. Enter a) the x- component, b) the y-component, and c) the z-component of the eigenvector.