Tuesday, March 9, 2010

What is the center of mass of a square sheet of metal with a circular whole cut in one corner?

The sheet of metal is square with sides 49cm, and the diameter of the circle is 24.5cm and is in the top right corner so that it is in part of the top right corner of 1/4 of the square sheet of metal, , how do i find the center of mass?What is the center of mass of a square sheet of metal with a circular whole cut in one corner?
Calculate the area of the uncut square (A1), and of the circle (A2). Calculate the location of the circle's center.


Set origin at center of square CM1, let CM2 = vector to circle's center.


CM = (m1CM1-m2CM2)/(m1-m2)


m1CM1 = 0


CM = -m2CM2/(m1-m2)


Since mass is proportional to area, CM = -A2CM2/(A1-A2). CM will be located in the lower left quadrant.

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