1) a. Write the integral for the moment of inertia for a solid cylinder of a uniform density p, radius a, and height h in Cartesian (xyz) coordinates for rotation about z axis (assume the base of the cylinder is in xy-plane. Do not integrate, just show the integral with the limits of integration); b. write the same integral in cylindrical coordinates, integrate, and calculate the moment of inertia of the solid cylinder about z axis; C. calculate the moment of inertia of a cylindrical shell (radius a, height h, mass M) in cylindrical coordinates (hint: there is the side surface and two disks (bases) that will rotate about z axis). 1) a. Write the integral for the moment of inertia for a solid cylinder of a uniform density p, radius a, and height h in Cartesian (xyz) coordinates for rotation about z axis (assume the base of the cylinder is in xy-plane. Do not integrate, just show the integral with the limits of integration); b. write the same integral in cylindrical coordinates, integrate, and calculate the moment of inertia of the solid cylinder about z axis; C. calculate the moment of inertia of a cylindrical shell (radius a, height h, mass M) in cylindrical coordinates (hint: there is the side surface and two disks (bases) that will rotate about z axis)