To Find the centre of gravity of different shapes

To Find the centre of gravity of different shapes

Centre of  gravity

The center of gravity is a geometric property of any object. The center of gravity is the average location of the weight of an object. 

Centroid

In geometry, the centroid, geometric center, or barycenter of a plane figure or two-dimensional shape X is the intersection of all straight lines that divide X into two parts of equal moment about the line. Informally, it is the "average" (arithmetic mean) of all points of X. The definition extends to any object X in n-dimensional space: its centroid is the intersection of all hyperplanes that divide X into two parts of equal moment.

Procedure

The centroid of a uniform two-dimensional lamina, such as (a) below, may be determined, experimentally, by using a plumbline and a pin to find the center of mass of a thin body of uniform density having the same shape. The body is held by the pin inserted at a point near the body's perimeter, in such a way that it can freely rotate around the pin; and the plumb line is dropped from the pin (b). The position of the plumbline is trace on the body. The experiment is repeated with the pin inserted at a different point of the object. The intersection of the two lines is the centroid of the  (c).

Conclusions