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Effective Radius of a Contact Area between two spheres

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Solid angle (in spherical coordinates)

In geometry, a solid angle is the two-dimensional angle in three-dimensional space that an object subtends at a point. It is a measure of how large the ... more

Gaussian beam ( radius of curvature )

In optics, a Gaussian beam is a beam of electromagnetic radiation whose transverse electric field and intensity (irradiance) distributions are well ... more

Oblate spheroid eccentricity (c<a)

A spheroid, or ellipsoid of revolution is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid ... more

Horizontal Curve - Allowable radius

The allowable radius for a horizontal curve can then be determined by knowing the intended design velocity, the coefficient of friction, and the allowed ... more

Horizontal Curve - Degree of curve

Aside from momentum, when a vehicle makes a turn, two forces are acting upon it. The first is gravity, which pulls the vehicle toward the ground. The ... more

Radial acceleration in circular motion

Uniform circular motion, that is constant speed along a circular path, is an example of a body experiencing acceleration resulting in velocity of a ... more

Half Sphere Mass

A sphere is defined mathematically as the set of points that are all the same distance r from a given point in three-dimensional space. This distance r is ... more

Hyperbolic sector (area)

A hyperbolic sector is a region of the Cartesian plane {(x,y)} bounded by rays from the origin to two points (a, 1/a) and (b, 1/b) and by the hyperbola xy ... more

Relation between the inradius and exradii of a right triangle

Right triangle or right-angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle). The incircle or inscribed circle of ... more

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