Centroid (Geometric)

The Center of Mass of a 2-D planar Lamina or a 3-D solid. The mass of a Lamina with surface density function is

(1)

The coordinates of the centroid (also called the Center of Gravity) are

(2)

(3)

Figure
Parabolic Segment
Semicircle

In 3-D, the mass of a solid with density function is

(4)

(5)

(6)

(7)

Figure
Cone
Conical Frustum
Hemisphere
Paraboloid
Pyramid

References

Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 132, 1987.

McLean, W. G. and Nelson, E. W. ``First Moments and Centroids.'' Ch. 9 in Schaum's Outline of Theory and Problems of Engineering Mechanics: Statics and Dynamics, 4th ed. New York: McGraw-Hill, pp. 134-162, 1988.

• Poincaré Formula
• Poincaré-Fuchs-Klein Automorphic Function
• Poincaré Group
• Poincaré-Hopf Index Theorem
• Poincaré Hyperbolic Disk
• Poincaré Manifold
• Poincaré Metric
• Poincaré Separation Theorem
• Poincaré's Holomorphic Lemma
• Poincaré's Lemma
• Poinsot Solid
• Poinsot's Spirals
• Point
• Point at Infinity
• Point Estimator
• Point Groups
• Point-Line Distance--2-D
• Point-Line Distance--3-D
• Point Picking
• Point-Plane Distance
• Point-Point Distance--1-D
• Point-Point Distance--2-D
• Point-Point Distance--3-D
• Point Probability
• Point-Quadratic Distance