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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.
Area rectangle area General triangular area + + [1] ... L = the length of the prism see above for general ... r = the radius of the sphere ...
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 ...
Sphere (shell) of radius r 2 and mass m, with centered spherical cavity of radius r 1. When the cavity radius r 1 = 0, the object is a solid ball (above). When r 1 = r 2, =, and the object is a hollow sphere.
The area A of any triangle is the product of its inradius (the radius of its inscribed circle) and its semiperimeter: A = r s . {\displaystyle A=rs.} The area of a triangle can also be calculated from its semiperimeter and side lengths a, b, c using Heron's formula :
A stadium is a two-dimensional geometric shape constructed of a rectangle with semicircles at a pair of opposite sides. [1] The same shape is known also as a pill shape, [2] discorectangle, [3] obround, [4] [5] or sausage body. [6] The shape is based on a stadium, a place used for athletics and horse racing tracks.
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An arbitrary shape. ρ is the distance to the element dA, with projections x and y on the x and y axes.. The second moment of area for an arbitrary shape R with respect to an arbitrary axis ′ (′ axis is not drawn in the adjacent image; is an axis coplanar with x and y axes and is perpendicular to the line segment) is defined as ′ = where