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The z-axis is vertical and the x-axis is highlighted in green. The three surfaces intersect at the point P with those coordinates (shown as a black sphere); the Cartesian coordinates of P are roughly (1.0, −1.732, 1.0). Cylindrical coordinate surfaces.
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), z is the regular z-coordinate. (ρ, φ, z) is given in Cartesian coordinates by:
The center of mass of a body with an axis of symmetry and constant density must lie on this axis. Thus, the center of mass of a circular cylinder of constant density has its center of mass on the axis of the cylinder. In the same way, the center of mass of a spherically symmetric body of constant density is at the center of the sphere.
Cylinder sets are often used to define a measure, using the Kolmogorov extension theorem; for example, the measure of a cylinder set of length m might be given by 1/m or by 1/2 m. Cylinder sets may be used to define a metric on the space: for example, one says that two strings are ε-close if a fraction 1−ε of the letters in the strings match.
In the case of a right circular cylinder with a cylindric section that is an ellipse, the eccentricity e of the cylindric section and semi-major axis a of the cylindric section depend on the radius of the cylinder r and the angle α between the secant plane and cylinder axis, in the following way: = , = .
The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object X {\displaystyle X} in n {\displaystyle n} - dimensional space is the intersection of all hyperplanes that divide X {\displaystyle X} into two parts of equal moment about the hyperplane.
A point mass does not have a moment of inertia around its own axis, but using the parallel axis theorem a moment of inertia around a distant axis of rotation is achieved. Two point masses, m 1 and m 2 , with reduced mass μ and separated by a distance x , about an axis passing through the center of mass of the system and perpendicular to the ...
A point plotted with cylindrical coordinates. Consider a cylindrical coordinate system ( ρ , φ , z ), with the z–axis the line around which the incompressible flow is axisymmetrical, φ the azimuthal angle and ρ the distance to the z–axis.