List of centroids

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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. Informally, it is the "average" of all points of . For an object of uniform composition, the centroid of a body is also its center of mass. In the case of two-dimensional objects shown below, the hyperplanes are simply lines.

2-D Centroids[edit]

For each two-dimensional shape below, the area and the centroid coordinates are given:

Shape Figure Area
rectangle area Block centroid axes.svg
General triangular area Triangle centroid 1.svg
Isosceles-triangular area Altitude of isosceles triangle.svg
Right-triangular area Centroid of a triangle.svg
Circular area Centre de gravite disque.svg
Quarter-circular area[1] Centroid of a quarter circle.svg
Semicircular area[2] Centroid of a semicircle.svg
Circular sector Centroid of a circular sector.svg
Circular segment Centroid of a circular segment.svg
Quarter-circular arc The points on the circle and in the first quadrant
Semicircular arc The points on the circle and above the axis
Arc of circle The points on the curve (in polar coordinates) , from to
elliptical area Ellipse-def0.svg
Quarter-elliptical area Centroid of a quarter ellipse.svg
Semielliptical area Centroid of a semiellipse.svg
Parabolic area The area between the curve and the line
Semiparabolic area

The area between the curve and the axis, from to

Half Parabolic Segment Centroid.png
Parabolic spandrel The area between the curve and the axis, from to
General spandrel The area between the curve and the axis, from to

3-D Centroids[edit]

For each three-dimensional body below, the volume and the centroid coordinates , are given:

Shape Figure Volume
Cuboid a, b = the sides of the cuboid's base
c = the third side of the cuboid
Right-rectangular pyramid a, b = the sides of the base
h = the distance is from base to the apex
General triangular prism b = the base side of the prism's triangular base,
h = the height of the prism's triangular base
L = the length of the prism
see above
for general
triangular base
Isoscele triangular prism b = the base side of the prism's triangular base,
h = the height of the prism's triangular base
L = the length of the prism
Right-triangular prism b = the base side of the prism's triangular base,
h = the perpendicular side of the prism's triangular base
L = the length of the prism
Right circular cylinder r = the radius of the cylinder
h = the height of the cylinder
Right circular solid cone r = the radius of the cone's base
h = the distance is from base to the apex
Solid sphere r = the radius of the sphere
Solid hemisphere r = the radius of the hemisphere
Solid semi-ellipsoid of revolution around z-axe a = the radius of the base circle
h = the height of the semi-ellipsoid from the base cicle's center to the edge
Solid paraboloid of revolution around z-axe a = the radius of the base circle
h = the height of the paboloid from the base cicle's center to the edge
Solid ellipsoid a, b, c = the principal semi-axes of the ellipsoid
Solid semi-ellipsoid around z-axe a, b = the principal semi-axes of the base ellipse
c = the principal z-semi-axe from the center of base ellipse
Solid paraboloid around z-axe a, b = the principal semi-axes of the base ellipse
c = the principal z-semi-axe from the center of base ellipse

See also[edit]

References[edit]

  1. ^ "Quarter Circle". eFunda. Retrieved 23 April 2016.
  2. ^ "Circular Half". eFunda. Retrieved 23 April 2016.

External links[edit]