Saturday, January 2, 2016

Centre of Mass Mathematical Derivation

Center of mass is a point of a body or a system which represents the actual motion of a body or a system. There need not any mass at the center of mass point physically. For a body, it can be out side the body and it can be inside the system. If different point of a body are having complicated and different kinds of motion, the real motion of the body is exhibited by center of mass.

The algebraic sum of moments about the center of mass of a system is equal to zero. Different particles of the body exhibits and applies moment on the center of mass particles in different directions but their algebraic sum is equal to zero.

Moment is defined as the product of mass and distance of the point about the center of mass.

We can derive mathematical expression for the center of mass of a system using the concept that the algebric sum of moments is equal to zero.

The location of center of mass of a system depends on the reference point from which we are measuring the center of mass of the system.

Let us consider a system of two particles having different masses. From a reference point these two particles are at two different distances. Let us assume that the cenere of mass of the system is some where between them and we can equate the moments about that point with all other points.

By simplifying the mathematical equations  as shown in the  video, we can get the mathematical expression as shown below.

When ever the reference position changes the value of cenrte of mass appears like changes with respect to that point.

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