ABSTRACT
If the boundary of a plane surface is an irregular curve, the integral in relation (C.1) may have to be evaluated numerically.
(C.3)
(C.4)
(C.5)
jIf a plane surface has an axis of symmetry x for every infinitesimal area dA with a jpositive coordinate measured from the axis of symmetry x , there is an area dA
iwith a negative coordinate x and vice versa (see Fig. C.2a). Thus, the first moment of the surface about its axis of symmetry is zero. Moreover, if a plane surface has a point of symmetry for every infinitesimal area dA with a position vector r measured from the point of symmetry, there is an area dA with a position vector !r and vice versa (see Fig. C.2b). Hence, the first moment of a surface about any axis passing through its point of symmetry is zero. Consequently, if a surface has an axis or a point of symmetry, its centroid lies on the axis of symmetry or i s the poin t of symmetr y. Thus, if an area has two axes of symmetry, its centroid is the intersection of the two axes of symmetry. In the table of the inside of the back cover of the book we give the coordinates of the centroids of certain plane surfaces.
