**Branch :**First Year-Engineering Syllabus

**Subject :**Elements of Mechanical Engineering

## Center of mass and Center of Gravity

**Center of mass and Center of Gravity:**** **Consider a uniform rod of length L. When the rod is placed horizontally, each particle of the rod is pulled by the gravitional force of the earth. The sum of all three forces will be equal to the total weight of the rod.

Consider two systems: One is the rod AB of weight W and other is a concentrated weight W, at a distance 1/3 L from point A.

These two systems are equivalent as far as the net gravitational pull is concerned, but the moment of the gravitational forces of the two systems about point A is different.

If a concentrated weight of W is put at a distance of 1/2 L from point A, then the moment of gravitational pull in uniform rod as well as the new system will be same.

In this case, not only the weight but the first moment of an element of a quantity about an origin is defined d as the product of its position vector with the element physical quantity itself.

With the concept of first moment, we define the centroid centre of mass and centre of gravity