Statics/Center of Gravity and Centroid (contents)

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: