# For number of revolutions

as **number of revolutions** or **revolution frequency** *n* or **circulation speed** *f* one calls the quotient, in an educated manner from the number of the circulation or revolutions as counter and the time interval t needed *for it* denominator. The number of revolutions is not of the dimension 1 (“dimensionless”), like it thoseEnding* - number* to assume leaves, it is thus no number, but physical dimension with the dimension 1/Zeit.

The reciprocal value of the number of revolutions results in the duration of a circulation <math> T< /math> :

<math> T= \ frac {1} {n} = \ frac {1} {f}< /math>

Under the angle of rotation <math> \ varphi< /math> one understands the product of the number of circulation *N* ina certain time interval and the angle of a circulation (with a circulation <math> = 2 \ pi </math>): <math> \ varphi = 2 \ pi N< /math>

Over the definition of the angular speed <math> \ omega = \ frac {\ varphi} {t}< /math> and the values for a revolution one receives the rotative frequency (angular velocity) <math> \ to omega< /math> too:

<math> \ omega= {2 \ pi \ cdot n} = {2 \ pi \ f cdot} = \ frac {2 \ pi} {T}< /math> , with the unit <math> [\ omega] = \ frac {1} {s} = \ mathrm {cycles per second} </math> (Hertz).

## unit

SI-UNIT: <math> [n] = [f] = \ frac {1} {s} = \ mathrm {cycles per second}< /math> (Hertz). The special name Hertz for the reciprocal second should not preferably forNumbers of revolutions to be used.

From other legal time units further “ legal units in the measurement” can be formed for numbers of revolutions,

for example: 1 cycles per second = 1 /s = 60/(60 s) = 60/min = 3600/(60 min) = 3600/h = (24 x 3600)/(24 h) = 86400/d.

Those is not standardfurther frequently indication of numbers of revolutions used in* revolutions per minute (rpm)*, because “revolution” or “U” is not unit; in the English linguistic usage RPM *is * to be found *or* r/min.

## examples

of numbers of revolutions in the unit min^{ -1}:

- Globe: approx. 0.000694
- records forLanguage course and. A.: 16
- LP records with 25 cm or 30 cm diameters: about 33
- single record with 17 cm diameters: 45
- shellac records: 78
- marine propellers: 70-150
- main rotor of a helicopter: to 400
- autoengines with no-load operation: approx. 700 to 900 (crankshaft)
- floppy disk drives, depending upon type: to approx. 800
- propellerssport airplane: 2500
- three-phase alternating current synchronous engine at 50 cycles per second of mains voltage: approx. 3000
- non removable disks for personal computers: 3600, 4500, 5400, 7200, 10000, 15000
- maximum permissible engine speed of a gasoline autoengine: approx. 9000 (sport engines as in the F1 to over 20,000)
- propeller piston motors (model airplane): 10,000 to 30,000
- running engine that Formula 1: up to 19,000
- gas turbines: 100,000
- superchargers for combustion engines: 200,000
- turbine-driven dentist drills: up to 5,000,000