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a) Determine the location of an axis perpendicular to the rod) which minimizes the moment of inertia of the system.

The answer is "with M1 at the origin x = M2*L/(M1+M2)

I know that I = Sum of ( M1*r1^2)

However, how do we know that M1 is at origin? I know that M1 + M2 is the total mass of the system. I know L is the length between the two points. But I don't know why the answer is above. I think I am missing something in understanding this but I don't know what.

b) Verify that the moment of inertia about this axis can be obtained by determine I about an axis through M2 and then using the parallel-axis theorem.

I know that I = I_cm + Mh^2 , where h is the distance between the axis, M is the total mass (M1+M2). Is the distance between the axis L? How do I use this to verify the moment of inertia.