1. The problem statement, all variables and given/known data Derive the moment of inertia of a solid, uniform density, disk rotating about a diameter using vertical rods. Diagram: http://i.imgur.com/TQIjz.png Only the radius of the circle and the inertia of a thin rod is given 2. Relevant equations Inertia of thin vertical rod = m*r^2 σ= area density M= Total mass I= inertia dm= infinitesimal amount of mass dI= infinitesimal amount of inertia A= total area R= radius of the circle 3. The attempt at a solution This is the method given in my class. Because calculus 1 is the only prerequisite we can not use double integrals. I of rod = m*x^2 dI= dm*x^2 dm=σ*da da= 2y*dx σ= M/A A=pi*R^2 σ= M/(pi*R^2) dm=M/(pi*R^2) * 2y*dx dI= M/(pi*R^2) * 2y*x^2 * dx From here we have to put y in terms of x which I think must be done using the Pythagorean theorem so: y=(R^2-x^2)^(1/2) subbing in we get: dI= M/(pi*R^2) * 2(R^2-x^2)^(1/2) * x^2 * dx This is why I get stuck because I am not quite sure how to integrate that. What is should come out to be is I = 1/4 MR^2. If anyone can offer an explanation it would be very appreciated.