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The centroid of an object in -dimensional space is the intersection of all hyperplanes that divide into two parts of equal moment ... Quarter-circular area [2] ...
The second moment of area, also known as area moment of inertia, is a geometrical property of an area which reflects how its points are distributed with respect to an arbitrary axis. The unit of dimension of the second moment of area is length to fourth power, L 4, and should not be confused with the mass moment of inertia.
The centroid is indexed as X(2). Characteristic Property of Centroid at cut-the-knot; Interactive animations showing Centroid of a triangle and Centroid construction with compass and straightedge; Experimentally finding the medians and centroid of a triangle at Dynamic Geometry Sketches, an interactive dynamic geometry sketch using the gravity ...
The "vertex centroid" comes from considering the polygon as being empty but having equal masses at its vertices. The "side centroid" comes from considering the sides to have constant mass per unit length. The usual centre, called just the centroid (centre of area) comes from considering the surface of the polygon as having constant density ...
For a semicircle with a diameter of a + b, the length of its radius is the arithmetic mean of a and b (since the radius is half of the diameter). The geometric mean can be found by dividing the diameter into two segments of lengths a and b, and then connecting their common endpoint to the semicircle with a segment perpendicular to the diameter ...
The SI unit for first moment of area is a cubic metre (m 3). In the American Engineering and Gravitational systems the unit is a cubic foot (ft 3 ) or more commonly inch 3 . The static or statical moment of area , usually denoted by the symbol Q , is a property of a shape that is used to predict its resistance to shear stress .
Torus with minor radius a, major radius b and mass m. About an axis passing through the center and perpendicular to the diameter: (+) [5] About a diameter: (+) [5] Ellipsoid (solid) of semiaxes a, b, and c with mass m
Archimedes introduced the salinon in his Book of Lemmas by applying Book II, Proposition 10 of Euclid's Elements.Archimedes noted that "the area of the figure bounded by the circumferences of all the semicircles [is] equal to the area of the circle on CF as diameter."