1. The problem statement, all variables and given/known data First, there's a slender rod with length L that has a mass per unit length that varies with distance from the left end, where x=0, according to dm/dx = yx where y has units of kg/m^2. (a) Calculate the total mass of the rod in terms of y and L (Which I've already done and is .5yL^2) (b) Use I = ∫r^2*dm to calculate the moment of inertia of the rod for an axis at the left end, perpendicular to the rod. Express your answer in terms of total mass M and length L. (c) Repeat b for an axis at the right end, perpendicular to the rod. Express your answer in terms of total mass M and length L. Second, a thin, uniform rod is bent into a square of side length a. If the total mass is M, find the moment of inertia about an axis through the center and perpendicular to the plane of the square. 2. Relevant equations I= ∫r^2 dm. Ip = Icm + Md^2 (parallel-axis theorem) 3. The attempt at a solution For the square I tried to use the Parallel-Axis Theorem by calculating the moment of inertia of a corner with 2 sides coming out of it. Using the Parallel-axis theorem to move the center to the middle and then doubling it to account for the two other sides. That got me 4Ma^3/3+Ma^2/2 which is wrong. For the rod of variable mass, I tried to use the integrals ∫r^2*y*L and ∫r^2*y*(L-x) but those didn't work. What should I have done?