Moments of Inertia object problem

[Momentum09]

Homework Statement

Consider 3 objects of equal masses but different shapes: a solid disk (radius R), a thin ring (radius R), and a thin hollow square (side 2R). The ring and the square are hollow and their perimeters carry all the mass, but the disk is solid and has uniform mass density over its whole area. Compare the three objects' moments of inertia when rotated around their respective centers of mass. Rank their moments of inertia from greatest to least.

Homework Equations

I know that for the disk, I = 1/2MR^2, and for the ring, MR^2.

The Attempt at a Solution

I don't know about the hollow square...can someone please give a hint? Thanks!

 

[Dick]

To do the square look up the moment of inertia of a rod through it's center and then use the parallel axis theorem. Four times.

 

[Dick]

PS. If you are clever you don't really have to compute the moment of inertia of all of these things. Think about the definition of moment of inertia. The disks mass is inside of the radius of the ring. The rings mass is inside the square.

 

[Momentum09]

I got it! Thank you so much!