# What is the difference between frequency and speed

## rotation speed

The rotation speed (also Rotation frequency or Rotation frequency) is a variable that specifies the frequency of revolutions in the case of - preferably mechanical - rotary movements. For example, it is an essential property when identifying the performance parameters for engines. In technology, the specification is usually made in revolutions per minute (min−1), in physics rather in Revolutions per second (see−1).

The speed is the reciprocal of the period of rotation: \$ n = \ frac 1 T \$

The size rotation speed in the case of rotary movements corresponds to the size frequency in 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 \$ \ Delta N \$ within a selectable time interval \$ \ Delta t \$ based on this time interval

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

The unit of measurement for the speed according to the SI system of units is \$ \ mathrm {\ tfrac1s} \$. Often used and common in mechanical engineering and related fields, the specification in \$ \ mathrm {\ tfrac1 {min}} \$ (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 revolution per second (unit symbol in German-speaking countries rev / s) or revolution per minute (unit symbol rpm) are widespread for rotational speed.[1] According to DIN 1301, this notation is to be avoided with the use of an auxiliary unit. The spelling in the running text 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).

The unit Hertz is only to be used for frequency, not for speed.[2][3] In English usage, rpm or r / min (revolutions per minute) or rps (revolutions per second) to be found.

The Angular velocity\$ \ omega \$ also has the unit 1 / s or rad / s, where the unit rad (radiant) indicates an angle. It is in accordance with[4]

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

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

\$ \ omega = 2 \, \ pi \, n \ \$

or.

\$ \ omega = 2 \, \ pi \, f \ ;. \$

### Examples

Examples of speeds s−1     min−1
Vinyl records (LP) 30 cm in diameter 59 331/3
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)[5]10.000.000600.000.000

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

### literature

• Horst Stocker: Physics paperback. 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 Quantities and units - space and time, Nos. 3-14a and 3-15b
2. ↑ DIN EN ISO 80000-3: 2013-08, No. 3–15a
3. ↑ DIN 1301-2: 1978-02 Units - Commonly used parts and multiples
4. ↑ DIN 1301-1: 2010-10 Units - unit names, unit symbols
5. ↑ 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.