I've been staring at this problem for quite a while now, and I don't really know how to approach it. Any guidance would be greatly appreciated. What we have is a rotating cylinder to create artificial gravity (equivalent gravitation acceleration of ag where a is a constant). We are asked to determine the limit on the radius in terms of the elastic limit, E, the density of the material, rho, and the desired fractional gravity, ag. There was a hint given to assume the cylinder wall is "thin" and start by considering forces on a small segment of a ring rotating with angular velocity omega. Considering limit of delta (theta) goes to 0 would be useful. The only thing i've got out of this is that the force has to equal the centipetal force, and so ag = mr(omega)^2. I don't know how to deal with the elastic limit, or get the omega out of the equation. Any help would be great!