Finding Center of Mass - Plate with hole

1. Oct 19, 2009

Bryon

1. The problem statement, all variables and given/known data

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 [Broken]

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?

2. Relevant 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.

Last edited by a moderator: May 4, 2017
2. Oct 19, 2009

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.

3. Oct 19, 2009

Bryon

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

4. Oct 19, 2009

mgb_phys

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

5. Oct 19, 2009

Bryon

So you essentially subract the larger mass from the other? I still dont see how to translate that into coordinates.