Moment, Centre of mass and Centroid

Moment of force is tendency of the force to twist or rotate an object. A measure of the body's resistance to the angular acceleration, which is equal to:

1)    The product of the mass of a particle and square of its distance from a reference.

2)    The sum of the products of each mass element of a body multiplied by square of its distance from an axis.

3)    The sum of the products of each element of an area multiplied by square of its distance from a coplanar axis.

As a rotating body spins about an external or internal axis, it opposes any change in the body's speed of rotation that can be caused by a torque. It can be defined as the sum of the products obtained by multiplying the mass of each particle of matter in a given body by the square of its distance from the axis of rotation. The moment of inertia of a figure about a line is the sum of the products formed by the magnitude of each element by the square of its distance from the line. The moment of inertia of the figure is sum of the moments of inertia of its parts.

The center of mass is the mean location of all mass in the system. In the case of the rigid body, the position of center of mass is fixed in the relation to the body. The position of center of mass is a point in space among them which can not correspond to position of any individual mass. The center of mass of a body does not coincide generally with its geometric center. The center of mass (and center of gravity in a uniform gravitational field) is the average of all points, weighted by the specific weight. If the physical object has uniform density, then its center of mass is same as the centroid of its shape. The center of mass of a 2-particle system lies on the line connecting particles. The center of mass is closer to massive object.