Do Solid Cylinders and Cylindrical Sections Have the Same Rotational Inertia?

[Zarathustra1]

Let's assume for a moment that we have two objects: a solid cylinder rotating about the center, and a section of a cylinder with a given angle rotating about the center of the would-be cylinder (had it been a full cylinder). They have an equal radii, and we will modify their mass-densities in such a way that the cylinder and the cylindrical section have equal masses.

We can conclude that the mass distribution across the radius is equal in both objects. As such, would it be safe to assume they have the same rotational inertias?

If I did my math correctly, then yes. I attempted to derive a formula for the rotational inertia of a cylindrical section, and it turned out to be same formula for that of a full cylinder: .5MR^2. I was a little intrigued to see that the angle measure canceled out in the process, but it sort of makes sense. Anyone want to verify this?

(Although this question occurred to me after doing a related homework problem, it isn't a homework problem itself, so I hope this is the proper forum for this question.)

 

[binarybob0001]

Is this section of a cylinder rotating about its center of mass? Is the section shaped sort of like a piece of pie?