centerofgravity

Center of gravity is the point in a body at which the total weight can be considered to act for purposes of analyzing translational motion and equilibrium. In a uniform gravitational field, the center of gravity coincides with the center of mass—the average position of the body's mass. In a nonuniform gravitational field or when buoyant or inertial effects are present, the center of gravity and the center of mass may differ.

For calculation, the center of gravity is obtained by weighting positions by the local weight. For discrete forces, R = sum(wi ri) / sum(wi), where wi are the weights and ri their position vectors. For a continuous body with density ρ(r), the center of gravity is R = (1/W)∫ r dm, with W = ∫ dm. If the material is homogeneous, dm = ρ dV and the center of gravity equals the geometric centroid of the body; if density varies, the CG shifts toward regions with larger weight.

Determination methods include static balance and suspension tests. In practice, a body can be balanced on a fulcrum and the point of balance identified, or it can be suspended from a point and the line of action of gravity traced (plumb line method). Experimental methods are often used for irregular shapes.

Applications span engineering and design: stability analysis for vehicles and ships, orientation of aircraft, structural loading, robotics, and biomechanics. The concept is distinct from the geometric centroid when density is not uniform or external forces alter the effective weight distribution.