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The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object in -dimensional space is the intersection of all hyperplanes that divide into two parts of equal moment about the hyperplane.
A right circular hollow cylinder (or cylindrical shell) is a three-dimensional region bounded by two right circular cylinders having the same axis and two parallel annular bases perpendicular to the cylinders' common axis, as in the diagram. Let the height be h, internal radius r, and external radius R.
Regular polygons; Description Figure Second moment of area Comment A filled regular (equiliteral) triangle with a side length of a = = [6] The result is valid for both a horizontal and a vertical axis through the centroid, and therefore is also valid for an axis with arbitrary direction that passes through the origin.
Thin circular loop of radius r and mass m.. = = = This is a special case of a torus for a = 0 (see below), as well as of a thick-walled cylindrical tube with open ends, with r 1 = r 2 and h = 0 Thin, solid disk of radius r and mass m.
A right circular cylinder is a cylinder whose generatrices are perpendicular to the bases. Thus, in a right circular cylinder, the generatrix and the height have the same measurements. [ 1 ] It is also less often called a cylinder of revolution, because it can be obtained by rotating a rectangle of sides r {\displaystyle r} and g {\displaystyle ...
This article uses the standard notation ISO 80000-2, which supersedes ISO 31-11, for spherical coordinates (other sources may reverse the definitions of θ and φ): . The polar angle is denoted by [,]: it is the angle between the z-axis and the radial vector connecting the origin to the point in question.
The centroid of many figures (regular polygon, regular polyhedron, cylinder, rectangle, rhombus, circle, sphere, ellipse, ellipsoid, superellipse, superellipsoid, etc.) can be determined by this principle alone. In particular, the centroid of a parallelogram is the meeting point of its two diagonals. This is not true of other quadrilaterals.
A star prism is a nonconvex polyhedron constructed by two identical star polygon faces on the top and bottom, being parallel and offset by a distance and connected by rectangular faces. A uniform star prism will have Schläfli symbol {p/q} × { }, with p rectangles and 2 {p/q} faces. It is topologically identical to a p-gonal prism.
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