# rotational speed

Physical size
Surname rotational speed
Size type frequency
Formula symbol ${\ displaystyle n, \, f _ {\ mathrm {red}}}$
Size and
unit system
unit dimension
SI s −1 T −1
Tachometer in a car (large dial on the right)

The rotational speed (also rotational frequency or rotational frequency ) is a variable which , in the case of - preferably mechanical  - rotational movements, indicates the number of revolutions in a time period based on this time period. It is, for example, an essential feature in the labeling of power s parameters for motors . It is stated in the art usually in revolutions per minute (1 / min), in the physics rather in revolutions per second (1 / s).

The speed is the reciprocal of the cycle time :${\ displaystyle n = {\ frac {1} {T}}}$

The speed variable for rotary movements corresponds to the frequency variable for other periodic processes, e.g. B. Vibrations .

The speed measurement can be done in different ways, such. B. by measuring the cycle time, by comparison with a known stroboscope frequency, by measuring an induction voltage , etc.

## Definition and unity

The speed is defined by the number of revolutions within a selectable time interval based on this time interval ${\ displaystyle \ Delta N}$ ${\ displaystyle \ Delta t}$

${\ displaystyle n = {\ frac {\ Delta N} {\ Delta t}}}$.

The unit of measurement for speed according to the SI system of units is  . Often used and common in mechanical engineering and related fields, it is stated in ( per minute ). The special name rotation (unit symbol r, in German-speaking countries U) is usually used instead of one as a unit in the specification for rotating machines. Correspondingly, the units of revolutions per second (unit symbol in the German-speaking world revolutions per second) or revolutions per minute (unit symbol rpm) are widely used for rotational speed. According to DIN 1301 , this notation is prescribed in legally defined units in business and official transactions, while common units defined in DIN may be used outside legal or official traffic or within this in addition to legal units. The notation in the running text here is min −1 (example: 5700 min −1 ) or 1 / min (whereby the value of the speed must be in the counter, for example 5700 / min). ${\ displaystyle \ mathrm {\ tfrac {1} {s}}}$${\ displaystyle \ mathrm {\ tfrac {1} {min}}}$

The unit Hertz is only to be used for frequency, not for speed. In English usage, rpm or r / min ( revolutions per minute ) or rps ( revolutions per second ) can be found.

The angular velocity also has the unit 1 / s or rad / s, where the unit rad (radian) indicates an angle. It is in accordance with ${\ displaystyle \ omega}$

${\ displaystyle 1 \, \ mathrm {rad} = 1 \, \ mathrm {\ tfrac {m} {m}} = 1 \ ;.}$

Since a full revolution corresponds to an angle 2π, the angular velocity is related to the speed

${\ displaystyle \ omega = 2 \, \ pi \, n \}$

or.

${\ displaystyle \ omega = 2 \, \ pi \, f \ ;.}$

## Examples

Examples of speeds s −1     min −1
Vinyl records (LP) 30 cm in diameter 59 33 13
Audio CD 3.5 to 8 210 to 480
Main rotor of a helicopter to 7 up to 400
Car engines at idle ( crankshaft ) 8.5 to 15 510 to 900
Spin speed washing machine approx. 10 to 30 approx. 600 to 1,800
Two-pole generator for 50 Hz mains voltage (e.g. Europe) 50 3,000
Maximum speed of a diesel engine approx. 90 approx. 5,500 (limited by the ignition delay )
Maximum speed of a gasoline engine 150 to 300 approx. 20,000 (determined by mechanical stress)
Dental drill up to 7,000 up to 400,000
Laser- induced rotation of a calcium carbonate crystal (speed record ) 10,000,000 600,000,000

The specific speed of a turbo machine is used to design turbines.

## literature

• Horst Stöcker: Pocket book of physics . 4th edition, Verlag Harri Deutsch, Frankfurt am Main, 2000, ISBN 3-8171-1628-4
• Ali Farschtschi: Electric machines in theory and practice . 1st edition, VDE-Verlag GmbH, Berlin and Offenbach, 2001, ISBN 3-8007-2563-0

## Individual evidence

1. Almost literally from DIN EN ISO 80000-3: 2013-08 Sizes and Units - Space and Time , Nos. 3–14a and 3–15b
2. The legal units in Germany ( Memento of the original from October 10, 2017 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. . DIN 1301. Physikalisch-Technische Bundesanstalt Braunschweig and Berlin. Accessed April 24, 2018.
3. DIN EN ISO 80000-3: 2013-08, No. 3–15a
4. DIN 1301-2: 1978-02 Units - Commonly used parts and multiples
5. DIN 1301-1: 2010-10 units - unit names, unit symbols
6. Yoshihiko Arita, Michael Mazilu, Kishan Dholakia: Laser-induced rotation and cooling of a trapped microgyroscope in vacuum . In: Nature Communications . August 28, 2013. doi : 10.1038 / ncomms3374 .