How Do You Calculate the Moment of Inertia for a Disk Rotated Off-Center?

[Sweeney91]

Hi, I just got of a test that had a question about moment of inertia on it. The question "Calculate the moment of inertia of a thin uniformed disk that is being rotated about an axis of rotation". This axis is halfway between the center of the disk and the outer perimeter. The mass of the disk is M and the radius of the disk is R. The question that came to me while taking the test was "is because a quarter of the disk is above the axis of rotation and the rest of the circle is below it do you subtract the moment of inertia of the little part (part above axis of rotation) away from the moment of inertia of the big part (part below axis of rotation). The question above isn't worded exactly as is was on the test, but I worded it in a way I felt easies to understand. I'm not trying to cheat or anything, I just want to know my theory was correct or not. I asked a few fellow students and none of them could give me a definitive answer. I googled almost everything, but I couldn't fine an example similar to this. I feel this is the best way to get the answer that I am seeking. If possible please answer the question above, and then let me know if I was on the right track.

 

[gneill]

What does "above" and "below" mean in this context? Coordinate axes are arbitrary. What if you turned the diagram upside down? Would you then subtract the larger portion from the smaller and get a negative moment of inertia? How about if you turned it sideways? Would it make sense for orientation to affect the result?

You could try doing the math for your idea to see if the result matches what the known answer is. Do you know how to apply the parallel axis theorem?