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Revolutions per minute

From Wikipedia, the free encyclopedia
Unit of rotational speed
For other uses, seeRevolutions per minute (disambiguation).
"rpm" redirects here. For other uses, seeRPM (disambiguation).
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Revolutions per minute
A car'stachometer marked in multiples of a thousand rpm
General information
Unit ofRotational speed, rotational frequency
Symbolrpm, r/min
Conversions
1 rpmin ...... is equal to ...
   SI accepted units   1 min−1
   SI units   1/60 Hz = 0.016 Hz
   SI base units   0.016 s−1

Revolutions per minute (abbreviatedrpm,RPM,rev/min,r/min, orr⋅min−1) is a unit ofrotational speed (orrotational frequency) for rotating machines.One revolution perminute is equivalent to1/60hertz.

Standards

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ISO 80000-3:2019 defines aphysical quantity calledrotation (ornumber of revolutions),dimensionless, whoseinstantaneous rate of change is calledrotational frequency (orrate of rotation), with units ofreciprocal seconds (s−1).[1]

A related but distinct quantity for describing rotation isangular frequency (orangular speed, the magnitude ofangular velocity), for which the SI unit is theradian per second (rad/s).

Although they have the samedimensions (reciprocal time) and base unit (s−1), the hertz (Hz) and radians per second (rad/s) are special names used to express two different but proportionalISQ quantities: frequency and angular frequency, respectively. The conversions between a frequencyf and an angular frequencyω areω=2πf,f=ω2π.{\displaystyle \omega =2\pi f,\quad f={\frac {\omega }{2\pi }}.}

Thus a disc rotating at 60 rpm is said to have an angular speed of 2π rad/s and a rotation frequency of 1 Hz.

TheInternational System of Units (SI) does not recognize rpm as a unit. It defines units ofangular frequency andangular velocity as rad s−1, and units offrequency asHz, equal to s−1.

1 rads=12π Hz=602π rpm2π rads=1 Hz=60 rpm2π60 rads=160 Hz=1 rpm{\displaystyle {\begin{array}{rcrcr}1~{\dfrac {\text{rad}}{\text{s}}}&=&{\dfrac {1}{2\pi }}~{\text{Hz}}&=&{\dfrac {60}{2\pi }}~{\text{rpm}}\\2\pi ~{\dfrac {\text{rad}}{\text{s}}}&=&1~{\text{Hz}}&=&60~{\text{rpm}}\\{\dfrac {2\pi }{60}}~{\dfrac {\text{rad}}{\text{s}}}&=&{\dfrac {1}{60}}~{\text{Hz}}&=&1~{\text{rpm}}\end{array}}}

Examples

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  • For a wheel, a pump, or a crank shaft, the number of times that it completes one full cycle in one minute is given the unit revolution per minute. A revolution is one complete period of motion, whether this be circular, reciprocating or some other periodic motion.
  • On many kinds of disc recording media, the rotational speed of the medium under the read head is a standard given in rpm.Phonograph (gramophone) records, for example, typically rotate steadily at16+23,33+13, 45 rpm or 78 rpm (0.28, 0.55, 0.75, or 1.3, respectively, in Hz).
  • Air turbine rotating up to1500000 rpm (25 kHz)
  • Modern air turbinedental drills can rotate at over800000 rpm (13.3 kHz).
  • Thesecond hand of a conventional analog clock rotates at 1 rpm.
  • Audio CD players read their discs at a precise, constant rate (4.3218 Mbit/s of raw physical data for 1.4112 Mbit/s (176.4 KB/s) of usable audio data) and thus must vary the disc's rotational speed from 8 Hz (480 rpm) when reading at the innermost edge to 3.5 Hz (210 rpm) at the outer edge.[2]
  • DVD players also usually read discs at a constant linear rate. The disc's rotational speed varies from 25.5 Hz (1530 rpm) when reading at the innermost edge, to 10.5 Hz (630 rpm) at the outer edge.[2]
  • Awashing machine's drum may rotate at 500 rpm to2763 rpm (8 Hz – 46 Hz) during the spin cycles.
  • Abaseball thrown by aMajor League Baseball pitcher can rotate at over2500 rpm (41.7 Hz); faster rotation yields more movement onbreaking balls.[3]
  • A power-generation turbine (with a two-pole alternator) rotates at 3000 rpm (50 Hz), 3600 rpm (60 Hz), and over 4000 rpm (66+23 Hz)
  • Modernautomobileengines are typically operated around1600 rpm2800 rpm (31 Hz – 48 Hz) when cruising, with a minimum (idle) speed around 750 rpm – 900 rpm (12.5 Hz – 15 Hz), and an upper limit anywhere from 4800 rpm to up to9500 rpm (80 Hz – 158 Hz) for a road car, very rarely reaching up to10000 rpm for certain cars (such as theGMA T.50), or22000 rpm for racing engines such asthose in Formula 1 cars (during the2006 season, with the 2.4 L N/AV8 engine configuration; limited to15000 rpm, with the 1.6 LV6turbo-hybrid engine configuration).[4] The exhaust note ofV8,V10, andV12F1 cars has a much higher pitch than anI4 engine, because each of thecylinders of afour-stroke engine fires once for every two revolutions of thecrankshaft. Thus an eight-cylinder engine turning 300 times per second will have an exhaust note of1200 Hz.
  • Largetwo-stroke slow speeddiesel engines are often used asship engines. Most of them operate below 120 rpm, and some very long stroke engines have a maximum speed of around 80 rpm.
  • A pistonaircraft engine typically rotates at a rate between2500 rpm and10000 rpm (42 Hz – 166 Hz).
  • Computerhard drives typically rotate at7500 rpm10000 rpm (125 Hz – 166 Hz), the most common speeds for theATA orSATA-based drives in consumer models. High-performance drives (used in fileservers and enthusiast-gaming PCs) rotate at10000 rpm15000 rpm (160 Hz – 250 Hz), usually with higher-level SATA,SCSI orFibre Channel interfaces and smaller platters to allow these higher speeds, the reduction in storage capacity and ultimate outer-edge speed paying off in much quicker access time and average transfer speed thanks to the high spin rate. Until recently, lower-end and power-efficient laptop drives could be found with4200 rpm or even3600 rpm spindle speeds (70 Hz or 60 Hz), but these have fallen out of favour due to their lower performance, improvements in energy efficiency in faster models and the takeup ofsolid-state drives for use in slimline and ultraportable laptops. Similar to CD and DVD media, the amount of data that can be stored or read for each turn of the disc is greater at the outer edge than near the spindle; however, hard drives keep a constant rotational speed so the effective data rate is faster at the edge (conventionally, the "start" of the disc, opposite to a CD or DVD).
  • Floppy disc drives typically ran at a constant 300 rpm or occasionally 360 rpm (a relatively slow 5 Hz or 6 Hz) with a constant per-revolution data density, which was simple and inexpensive to implement, though inefficient. Some designs such as those used with older Apple computers (Lisa, early Macintosh, later II's) were more complex and used variable rotational speeds and per-track storage density (at a constant read/record rate) to store more data per disc; for example, between 394 rpm (with 12 sectors per track) and 590 rpm (8 sectors) with Mac's 800 kB double-density drive at a constant 39.4 kB/s (max) – versus 300 rpm, 720 kB and 23 kB/s (max) for double-density drives in other machines.[5]
  • AZippe-type centrifuge for enriching uranium spins at100000 rpm (1666 Hz) or faster.[6]
  • Gas turbine engines rotate at tens of thousands of rpm. JetCat model aircraft turbines are capable of over100000 rpm (1700 Hz) with the fastest reaching165780 rpm (2763 Hz).[7]
  • AFlywheel energy storage system works at60000 rpm500000 rpm (1 kHz – 8.3 kHz) range using a passively magnetic levitated flywheel in a vacuum.[8] The choice of the flywheel material is not the most dense, but the one that pulverises the most safely, at surface speeds about 7 times the speed of sound.
  • A typical 80 mm, 30 CFM computer fan will spin at2600 rpm3000 rpm (43 Hz – 50 Hz) on 12 V DC power.
  • Amillisecond pulsar can have near50000 rpm (833 Hz).
  • Aturbocharger can reach1000000 rpm (16.6 kHz), while100000 rpm250000 rpm (1 kHz – 3 kHz) is common.
  • Asupercharger can spin at speeds between or as high as50000 rpm100000 rpm (833 Hz – 1666 Hz)
  • Molecular microbiology – molecular engines. The rotation rates of bacterialflagella have been measured to be10200 rpm (170 Hz) forSalmonella typhimurium,16200 rpm (270 Hz) forEscherichia coli, and up to500000 rpm (1700 Hz) for polar flagellum ofVibrio alginolyticus, allowing the latter organism to move in simulated natural conditions at a maximum speed of 540 mm/h.[9]
  • The sample inmagic angle spinning, anuclear magnetic resonance technique, typically rotates between300000 and6000000 rpm (5–100 kHz), with experimental instruments reaching speeds as high as12000000 rpm (200 kHz).

See also

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Notes

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References

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  1. ^ISO 80000-3:2019.
  2. ^ab"Physical parameters".DVD Technical Notes. Moving Picture Experts Group (MPEG). 1996-07-21. Archived fromthe original on 2012-02-19. Retrieved2008-05-30.
  3. ^Chichester, Ryan (June 10, 2021)."The Athletic's Eno Sarris talks Spider Tack, Gerrit Cole with Moose & Maggie".WFAN. RetrievedJune 14, 2021 – via MSN.com.
  4. ^"2014 season changes". Formula One. Retrieved2014-08-18.
  5. ^"Double-Density Versus High-Density Disks". Apple. Retrieved2012-05-05.
  6. ^"Slender and Elegant, It Fuels the Bomb". The Electricity Forum. Retrieved2006-09-24.
  7. ^"P60-SE Special Edition". JetCat USA. Archived fromthe original on 2012-04-19. Retrieved2006-07-19.
  8. ^Post, Richard F. (April 1996)."A New Look at an Old Idea: The Electromechanical Battery"(PDF).Science & Technology Review. University of California:12–19.ISSN 1092-3055. Retrieved2008-05-30.
  9. ^Magariyama, Y.; Sugiyama, S.; Muramoto, K.; Maekawa, Y.; Kawagishi, I.; Imae, Y.; Kudo, S. (October 27, 1994)."Very fast flagellar rotation".Nature.371 (6500): 752.Bibcode:1994Natur.371..752M.doi:10.1038/371752b0.PMID 7935835.
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