How Does Drilling a Hole Affect the Rotational Inertia of a Disk?

[gills]

Homework Statement

A disk of radius R has an initial mass M. Then a hole of radius (1/4)R is drilled, with its edge at the disk center (The center of mass of the cutout is in the x positive direction). Find the new rotational inertia about the central axis.

Hint: Find the rotational inertia of the missing piece, and subtract it from that of the whole disk. You'll need to determine what fraction of the missing mass is of the total M and use the parallet-axis theorem.

Homework Equations

Parallel-axis theorem:
I = I_cm + md^2

Rotational Inertia of solid disk:
I = (1/2)MR^2

The Attempt at a Solution

My attempt thus far is not very good. I having trouble getting the mass of the small disk. Any advice?

 

[mjsd]

assuming uniform distribution of mass, you need to work out the ratio between the two disks. note A=\pi r^2 and you are given two different r's. after that follow the hints and you should be right