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The external surface area A of the cap equals r2 only if solid angle of the cone is exactly 1 steradian. Hence, in this figure θ = A/2 and r = 1. The solid angle of a cone with its apex at the apex of the solid angle, and with apex angle 2 θ, is the area of a spherical cap on a unit sphere
By contrast, if a beam's weight is fixed, its cross-sectional dimensions are unconstrained, and increased stiffness is the primary goal, the performance of the beam will depend on Young's modulus divided by either density squared or cubed.
The root-3 rectangle is also called sixton, [6] and its short and longer sides are proportionally equivalent to the side and diameter of a hexagon. [7] Since 2 is the square root of 4, the root-4 rectangle has a proportion 1:2, which means that it is equivalent to two squares side-by-side. [7] The root-5 rectangle is related to the golden ratio ...
In solid mechanics and structural engineering, section modulus is a geometric property of a given cross-section used in the design of beams or flexural members.Other geometric properties used in design include: area for tension and shear, radius of gyration for compression, and second moment of area and polar second moment of area for stiffness.
With the invention of the metric system, based on powers of ten, there was an attempt to replace degrees by decimal "degrees" in France and nearby countries, [note 3] where the number in a right angle is equal to 100 gon with 400 gon in a full circle (1° = 10 ⁄ 9 gon).
The angular diameter, angular size, apparent diameter, or apparent size is an angular separation (in units of angle) describing how large a sphere or circle appears from a given point of view. In the vision sciences , it is called the visual angle , and in optics , it is the angular aperture (of a lens ).
1 kg/cm 2 equals exactly 10 000 kg/m 2. With the pound and inch legally defined as 0.453 592 37 kg and 0.0254 m respectively, it follows that the (mass) pounds per square inch is approximately: 1 lb m /in 2 = 0.453 592 37 kg /(0.0254 m × 0.0254 m) ≈ 703.069 58 kg/m 2
By assuming a form of Coulomb's law in which the Coulomb constant k e is taken as unity, Maxwell then determined that the dimensions of an electrostatic unit of charge were Q = T −1 L 3/2 M 1/2, [15] which, after substituting his M = T −2 L 3 equation for mass, results in charge having the same dimensions as mass, viz. Q = T −2 L 3.