Moment, Centre of mass and Centroid

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

• The product of the mass of a particle and the square of its distance from a reference.
• The sum of the products of each mass element of a body multiplied by the square of its distance from an axis.
• The sum of the products of each element of an area multiplied by the square of its distance from a coplanar axis.

As a rotating body spins about an external or internal axis (either fixed or unfixed), it opposes any change in the body's speed of rotation that may be caused by a torque. It is 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 (area or mass) about a line is the sum of the products formed by multiplying the magnitude of each element (of area or of mass) by the square of its distance from the line. The moment of inertia of a figure is the sum of moments of inertia of its parts.

The center of mass or mass center is the mean location of all the mass in a system. In the case of a rigid body, the position of the center of mass is fixed in relation to the body. In the case of a loose distribution of masses in free space. the position of the center of mass is a point in space among them that may not correspond to the position of any individual mass. The center of mass of a body does not generally coincide 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 local density or specific weight. If a physical object has uniform density, then its center of mass is the same as the centroid of its shape. The center of mass of a two-particle system lies on the line connecting the particles. The center of mass is closer to the more massive object.