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The unit of angular frequency is the radian per second (rad/s) but, for discrete-time signals, can also be expressed as radians per sampling interval, which is a dimensionless quantity. Angular frequency is frequency multiplied by 2 π.
This is a list of well-known dimensionless quantities illustrating their variety of forms and applications. The tables also include pure numbers, dimensionless ratios, or dimensionless physical constants; these topics are discussed in the article.
Dimensionless quantities, or quantities of dimension one, [1] are quantities implicitly defined in a manner that prevents their aggregation into units of measurement. [ 2 ] [ 3 ] Typically expressed as ratios that align with another system, these quantities do not necessitate explicitly defined units .
Measure for how the magnetization of material is affected by the application of an external magnetic field H/m L M T −2 I −2: intensive Permittivity: ε s: Measure for how the polarization of a material is affected by the application of an external electric field F/m L −3 M −1 T 4 I 2: intensive Plane angle: θ: Ratio of circular arc ...
A quantity of dimension one is historically known as a dimensionless quantity (a term that is still commonly used); all its dimensional exponents are zero and its dimension symbol is . Such a quantity can be regarded as a derived quantity in the form of the ratio of two quantities of the same dimension.
Replace each of them with a quantity scaled relative to a characteristic unit of measure to be determined; Divide through by the coefficient of the highest order polynomial or derivative term; Choose judiciously the definition of the characteristic unit for each variable so that the coefficients of as many terms as possible become 1;
The Strouhal number gives the vortex shedding frequency resulting from placing an object in a steady flow, so it describes the flow unsteadiness as a result of an instability of the flow downstream of the object. Conversely, the Keulegan–Carpenter number is related to the oscillation frequency of an unsteady flow into which the object is placed.
A meaningful test on the time-variation of G would require comparison with a non-gravitational force to obtain a dimensionless quantity, e.g. through the ratio of the gravitational force to the electrostatic force between two electrons, which in turn is related to the dimensionless fine-structure constant.