To discuss the concept of the center of gravity, center of mass, and the centroid

To show how to determine the location of the center of gravity and centroid for a system of discrete particles and a body of arbitrary shape

To use the theorems of Pappas and Guldinus for finding the area and volume for a surface of revolution

To present a method for finding the resultant of a general distributed loading and show how it applies to finding the resultant of a fluid

9.1 - Center of Gravity and Center of Mass for a System of Particles

Center of Gravity The center of gravity G is a point which locates the resultant weight of a system of particles, if a body is in gravitational field; if not, center of gravity is a center of inertia of the body (= a system of particles). To show how to determine this point consider the system of n particles fixed within a region of space. The weights of a particle comprise a system of parallel forces which can be replaced by a single (equivalent) resultant weight having the defined point G of application.

The resultant weight must be equal to the total weight of all n particles; that is:

W_R=ΣW