User:Garygo golob/Slovene phonology/sandbox

Angles
Angles are dimensionless physical quantities that have its own units, depending on how many dimensions the unit n-sphere has. For example, when drawing an angle on paper, it defines an arc on a unit circle, which has two dimensions. In two dimensions, the unit is radian. In three dimensions, a solid angle defines a part of a surface of a sphere, and the unit is radian squared or steradian. On fandom sites and among hobbyists, the angles are extended for higher dimensions.

Other dimensionless quantities
There are many other dimensionless quantities that arise due to simply counting something (decays, pedestrians, rotations, particles etc.) or are ratios, coefficients, factors or moduli of other quantities and the dimensions cancel out. Examples include coefficient of friction, shear strain, specific gravity, and phase.

There is a specific relation between units that are measured with radians and those that are not. If radians are not included, that means the number of full rotations is counted, and not the angles. The factor between the two is hence τ = 2π. A common example for this are frequency (f; measured in 1/s) and angular speed (ω; measured in rad/s), and the relation between them is ω = 2πf.

Derivatives and antiderivatives of distance and displacement
In the table are given the derivatives and antiderivatives of displacement (vector) and distance (scalar).

Antiderivatives of placement
Antiderivatives of placement or reciprocals of derivatives of distance bear the prefix pre- and are only scalar: