Statics

Centroid

Aka. centre of area, geometric centre. The point where the area of a figure is assumed to be concentrated. Defined for a 2D shape.

Located on the axes of symmetry, if one exists.

Center of gravity

The point where the mass of an object is concentrated. Defined for a 3D shape.

First moment of area

Measure of spatial distribution of a shape in relation to an axis.

Here:

• - Centroid’s coordinate
• - Centroid’s coordinate
• - Total area

About an axis of symmetry, first moment of area is .

Second moment of area

Aka. area moment of inertia. Describes how the cross-sectional area of a shape is distributed relative to an axis.

Not to be confused with moment of inertia.

Always positive.

For common shapes

Shape	Description
Rectangle or Parallelogram	Base . Height . About centroidal axis parallel to base.
Triangle	Base . Height . About base.
Triangle	Base . Height . About centroidal axis parallel to base.
Circle	Diameter . About centroidal axis.

The product of moment of area about x,y axes

The polar moment of area about z axis

Radius of gyration

Moment of inertia

Describes the resistance of a body to changes in its rotational motion.