Finding Center of Mass - Plate with hole

[Bryon]

Homework Statement

https://wug-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/DuPage/phys2111/fall/homework/Ch-09-Momentum/plate_with_hole/3.gif

A uniform circular plate of radius 11 cm has a circular hole of radius 3 cm cut out of it. The center of the plate is at the origin of the coordinate system and the center of the hole is located along the x-axis a distance 4 cm from the origin.

What is the position of the center of mass of the plate with the hole in it?

Homework Equations

center mass = (m1x1 + m2x2)/ (m1 + m2)

Im really stumped with this one. I was thinking at first to find the total area of the plate and then subtract that from the area of the hole. I am at a loss with this one.

 

[mgb_phys]

Almost right - imagine the hole as equivalent to a piece of metal that size/shape/position on the opposite side of the balnace.

 

[Bryon]

This one is really getting me. The center of mass will be away from the hole. Now to translate into coordinates.

 

[mgb_phys]

Imagine the force * distance downward for the mass of the entire plate, now imagine the hole is a mass * force upward

 

[Bryon]

So you essentially subract the larger mass from the other? I still don't see how to translate that into coordinates.