You are handed a rod that is four times as dense on one side as it is on the other side, and two times as dense in the middle as it is on the least dense side. Further, you are told that the density varies quadratically. The mass of the rod is M and the length is L. Write your answers only in terms of these constants. (a) What is the moment of inertia about an axis that passes through the midpoint of the rod (and is perpendicular to the length of the rod)?
(b) What is the moment of inertia about an axis that passes through one of the ends of the rod (and is perpendicular to the length of the rod)?