inertia of a solid cylinder

With a couple of assumptions, I arrived the solution as follow:


圖片參考：http://i187.photobucket.com/albums/x22/cshung/7008081102927.png

both answers are correct. Strict Calculation VS Conceptual Induction.

2008-08-19 12:46:59 補充：
ar! 原來一個係 Andrew, 一個係 physics8801! 兩個都係我心目中的高手呢~

Actually, this problem could be answered by common sense based on the basic concept of physics without the need to go through rigorous mathematical derivation.

To maximize the moment of inertia, the substance in rotation should be as far from the axis of rotation as possible. In that case, the cylinder should be thin enough so as to 'squeeze' its volume to to large distance from the centre. As such, the cylinder would look like a thin disc with large radius.

To minimize the moment of inertia, the substance should ve as close as to the axis of rotation as possible. In this case, the cylinder would look like a thick cylinder with small radius.