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The polar angle is denoted by [,]: it is the angle between the z-axis and the radial vector connecting the origin to the point in question. The azimuthal angle is denoted by φ ∈ [ 0 , 2 π ] {\displaystyle \varphi \in [0,2\pi ]} : it is the angle between the x -axis and the projection of the radial vector onto the xy -plane.
Vectors are defined in cylindrical coordinates by (ρ, φ, z), where . ρ is the length of the vector projected onto the xy-plane,; φ is the angle between the projection of the vector onto the xy-plane (i.e. ρ) and the positive x-axis (0 ≤ φ < 2π),
The distance from the axis may be called the radial distance or radius, while the angular coordinate is sometimes referred to as the angular position or as the azimuth. The radius and the azimuth are together called the polar coordinates , as they correspond to a two-dimensional polar coordinate system in the plane through the point, parallel ...
Roundness is the measure of how closely the shape of an object approaches that of a mathematically perfect circle.Roundness applies in two dimensions, such as the cross sectional circles along a cylindrical object such as a shaft or a cylindrical roller for a bearing.
The radius or radial distance is the Euclidean distance from the origin O to P. The inclination (or polar angle) is the signed angle from the zenith reference direction to the line segment OP. (Elevation may be used as the polar angle instead of inclination; see below.)
t is the radial thickness of the cylinder; l is the axial length of the cylinder. An alternative to hoop stress in describing circumferential stress is wall stress or wall tension (T), which usually is defined as the total circumferential force exerted along the entire radial thickness: [3] = Cylindrical coordinates
As an example, consider the problem of determining the potential of a unit source located at (,,) inside a conducting cylindrical tube (e.g. an empty tin can) which is bounded above and below by the planes = and = and on the sides by the cylinder =. [3]
Note that in the case of the right circular cylinder, the height and the generatrix have the same measure, so the lateral area can also be given by: L = 2 π r g {\displaystyle L=2\pi rg} . The area of the base of a cylinder is the area of a circle (in this case we define that the circle has a radius with measure r {\displaystyle r} ):