Center of area

1. Jul 23, 2006

teng125

a square with dimensions (a x a),a quater circle is cut out which has the radius r.Find the center of area of the remaining part.
i found the coordinate for the removed quater circle which is a-4r/3pi ,
but i don't know how to find the cenroid of the remaining part.

anybody pls help

thanx

2. Jul 23, 2006

Andrew Mason

The centre of area is the same as the centre of mass of a sheet of uniform thickness and density.

The centre of mass of two objects is the point at which the products of the distance to the centre of mass x mass of each object sum to zero.

$$m_1R_1 + m_2R_2 = 0$$

The mass of the object is its area x mass/area ($m=\sigma A$)

Think of the sheet as a whole sheet superimposed with a quarter circle of negative mass. The centre of mass of the full sheet is its centre. If you can work out the centre of area or mass of the quarter circle, then it is just a simple matter of using the above equation.

AM