1. The problem statement, all variables and given/known data My textbook says that I = (1/3)ML^2 for a slender uniform rod, and I = (1/2)MR^2 for a uniform solid cylinder. So let's say that there is cylinder that is a thin disk with M = 5kg, and R = 7m. And let's say that a thin rod also is 5kg and has a length of 7m. Why don't both objects have the same inertia? 2. Relevant equations Inertia for a thin uniform rod is I = (1/3)ML^2. Inertia for a thin uniform cylinder is I = (1/2)MR^2. 3. The attempt at a solution My textbook says that some point mass circling an axis has the same inertia as a thin ring of the same mass (if this isn't true, then my issue in this thread is irrelevant). So I will divide the mass of the rod into infinitesimally small masses dm. I should be able to do the same for the cylinder with each infinitely thin ring equaling dm. Apparently, a ring can be thought of as a point mass. Then the disk can be thought of as a thin rod with the same mass and the same length as the other. But rods and cylinders have different formulas.