# Revolutions per minute

Last updated
Revolutions per minute
A car's tachometer marked in multiples of a thousand rpm.
General information
Unit ofRotational speed, rotational frequency
Symbolrpm,r/min
Conversions
1 rpm in ...... 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 (abbreviated rpm, RPM, rev/min, r/min, or r⋅min−1) is a unit of rotational speed (or rotational frequency) for rotating machines. One revolution per minute is equivalent to 1/60 hertz.

## Standards

ISO 80000-3:2019 defines a physical quantity called rotation (or number of revolutions), dimensionless, whose instantaneous rate of change is called rotational frequency (or rate of rotation), with units of reciprocal seconds (s−1). [1]

A related but distinct quantity for describing rotation is angular frequency (or angular speed, the magnitude of angular velocity), for which the SI unit is the radian per second (rad/s).

Although they have the same dimensions (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 proportional ISQ quantities: frequency and angular frequency, respectively. The conversions between a frequency f and an angular frequency ω are:

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

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.

The International System of Units (SI) does not recognize rpm as a unit. It defines units of angular frequency and angular velocity as rad s−1, and units of frequency as Hz, equal to s−1.

## Examples

• 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 at 16+23, 33+13, 45 rpm or 78 rpm (0.28, 0.55, 0.75, or 1.3, respectively, in Hz).
• Modern air turbine dental drills can rotate at up to 800000 rpm (13.3 kHz).
• The second 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]
• A washing machine's drum may rotate at 500 rpm to 2000 rpm (8 Hz – 33 Hz) during the spin cycles.
• A baseball thrown by a Major League Baseball pitcher can rotate at over 2500 rpm (41.7 Hz); faster rotation yields more movement on breaking balls. [3]
• A power-generation turbine (with a two-pole alternator) rotates at 3000 rpm (50 Hz) or 3600 rpm (60 Hz), depending on country – see AC power plugs and sockets.
• Modern automobile engines are typically operated around 2000 rpm3000 rpm (33 Hz – 50 Hz) when cruising, with a minimum (idle) speed around 750 rpm – 900 rpm (12.5 Hz – 15 Hz), and an upper limit anywhere from 4500 rpm to 10000 rpm (75 Hz – 166 Hz) for a road car, very rarely reaching up to 12000 rpm for certain cars (such as the GMA T.50), or 20000 rpm for racing engines such as those in Formula 1 cars (during the 2006 season, with the 2.4 L N/A V8 engine configuration; limited to 15000 rpm, with the 1.6 L V6 turbo-hybrid engine configuration). [4] The exhaust note of V8, V10, and V12 F1 cars has a much higher pitch than an I4 engine, because each of the cylinders of a four-stroke engine fires once for every two revolutions of the crankshaft. Thus an eight-cylinder engine turning 300 times per second will have an exhaust note of 1200 Hz.
• A piston aircraft engine typically rotates at a rate between 2000 rpm and 3000 rpm (33 Hz – 50 Hz).
• Computer hard drives typically rotate at 5400 rpm7200 rpm (90 Hz – 120 Hz), the most common speeds for the ATA or SATA-based drives in consumer models. High-performance drives (used in fileservers and enthusiast-gaming PCs) rotate at 10000 rpm15000 rpm (160 Hz – 250 Hz), usually with higher-level SATA, SCSI or Fibre 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 with 4200 rpm or even 3600 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 of solid-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]
• A Zippe-type centrifuge for enriching uranium spins at 90000 rpm (1500 Hz) or faster. [6]
• Gas turbine engines rotate at tens of thousands of rpm. JetCat model aircraft turbines are capable of over 100000 rpm (1700 Hz) with the fastest reaching 165000 rpm (2750 Hz). [7]
• A Flywheel energy storage system works at 60000 rpm200000 rpm (1 kHz – 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 at 2600 rpm3000 rpm (43 Hz – 50 Hz) on 12 V DC power.
• A millisecond pulsar can have near 50000 rpm (833 Hz).
• A turbocharger can reach 290000 rpm (4.8 kHz), while 80000 rpm200000 rpm (1 kHz – 3 kHz) is common.
• A supercharger can spin at speeds between or as high as 50000 rpm65000 rpm (833 Hz – 1083 Hz)
• Molecular microbiology – molecular engines. The rotation rates of bacterial flagella have been measured to be 10200 rpm (170 Hz) for Salmonella typhimurium , 16200 rpm (270 Hz) for Escherichia coli , and up to 102000 rpm (1700 Hz) for polar flagellum of Vibrio alginolyticus , allowing the latter organism to move in simulated natural conditions at a maximum speed of 540 mm/h. [9]

## Related Research Articles

Disk storage is a general category of storage mechanisms where data is recorded by various electronic, magnetic, optical, or mechanical changes to a surface layer of one or more rotating disks. A disk drive is a device implementing such a storage mechanism. Notable types are the hard disk drive (HDD) containing a non-removable disk, the floppy disk drive (FDD) and its removable floppy disk, and various optical disc drives (ODD) and associated optical disc media.

Frequency, measured in hertz, is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as temporal frequency for clarity and to distinguish it from spatial frequency. Ordinary frequency is related to angular frequency by a factor of 2π. The period is the interval of time between events, so the period is the reciprocal of the frequency: f = 1/T.

The hertz is the unit of frequency in the International System of Units (SI), equivalent to one event per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that one hertz is the reciprocal of one second. It is named after Heinrich Rudolf Hertz (1857–1894), the first person to provide conclusive proof of the existence of electromagnetic waves. Hertz are commonly expressed in multiples: kilohertz (kHz), megahertz (MHz), gigahertz (GHz), terahertz (THz).

In physics and mechanics, torque is the rotational analogue of linear force. It is also referred to as the moment of force. It describes the rate of change of angular momentum that would be imparted to an isolated body.

The angular displacement – also called angle of rotation, rotational displacement, or rotary displacement – of a physical body is the angle through which the body rotates around a centre or axis of rotation. Angular displacement may be signed, indicating the sense of rotation ; it may also be greater than a full turn.

In physics, angular velocity, also known as angular frequency vector, is a pseudovector representation of how the angular position or orientation of an object changes with time, i.e. how quickly an object rotates around an axis of rotation and how fast the axis itself changes direction.

A flywheel is a mechanical device which uses the conservation of angular momentum to store rotational energy; a form of kinetic energy proportional to the product of its moment of inertia and the square of its rotational speed. In particular, assuming the flywheel's moment of inertia is constant then the stored (rotational) energy is directly associated with the square of its rotational speed.

In physics, angular frequency, also called angular speed and angular rate, is a scalar measure of the angle rate or the temporal rate of change of the phase argument of a sinusoidal waveform or sine function . Angular frequency is the magnitude of the pseudovector quantity angular velocity.

Rotational frequency, also known as rotational speed or rate of rotation, is the frequency of rotation of an object around an axis. Its SI unit is the reciprocal seconds (s−1); other common units of measurement include the hertz (Hz), cycles per second (cps), and revolutions per minute (rpm).

One turn is a unit of plane angle measurement equal to  radians, 360 degrees or 400 gradians. Thus it is the angular measure subtended by a complete circle at its center.

A dynamometer or "dyno" for short, is a device for simultaneously measuring the torque and rotational speed (RPM) of an engine, motor or other rotating prime mover so that its instantaneous power may be calculated, and usually displayed by the dynamometer itself as kW or bhp.

In optical storage, constant linear velocity (CLV) is a qualifier for the rated speed of an optical disc drive, and may also be applied to the writing speed of recordable discs. CLV implies that the angular velocity varies during an operation, as contrasted with CAV modes. The concept of constant linear velocity was patented in 1886 by phonograph pioneers Chichester Bell and Charles Tainter.

Rotation around a fixed axis or axial rotation is a special case of rotational motion around an axis of rotation fixed, stationary, or static in three-dimensional space. This type of motion excludes the possibility of the instantaneous axis of rotation changing its orientation and cannot describe such phenomena as wobbling or precession. According to Euler's rotation theorem, simultaneous rotation along a number of stationary axes at the same time is impossible; if two rotations are forced at the same time, a new axis of rotation will result.

A fluid coupling or hydraulic coupling is a hydrodynamic or 'hydrokinetic' device used to transmit rotating mechanical power. It has been used in automobile transmissions as an alternative to a mechanical clutch. It also has widespread application in marine and industrial machine drives, where variable speed operation and controlled start-up without shock loading of the power transmission system is essential.

The radian per second is the unit of angular velocity in the International System of Units (SI). The radian per second is also the SI unit of angular frequency. The radian per second is defined as the angular frequency that results in the angular displacement increasing by one radian every second.

The inverse second or reciprocal second (s−1), also called per second, is a unit defined as the multiplicative inverse of the second. It is applicable for physical quantities of dimension reciprocal time, such as frequency and strain rate.

A permanent magnet synchronous generator is a generator where the excitation field is provided by a permanent magnet instead of a coil. The term synchronous refers here to the fact that the rotor and magnetic field rotate with the same speed, because the magnetic field is generated through a shaft mounted permanent magnet mechanism and current is induced into the stationary armature.

Flywheel energy storage (FES) works by accelerating a rotor (flywheel) to a very high speed and maintaining the energy in the system as rotational energy. When energy is extracted from the system, the flywheel's rotational speed is reduced as a consequence of the principle of conservation of energy; adding energy to the system correspondingly results in an increase in the speed of the flywheel.

The motor size constant and motor velocity constant are values used to describe characteristics of electrical motors.

Tangential speed is the speed of an object undergoing circular motion, i.e., moving along a circular path. A point on the outside edge of a merry-go-round or turntable travels a greater distance in one complete rotation than a point nearer the center. Travelling a greater distance in the same time means a greater speed, and so linear speed is greater on the outer edge of a rotating object than it is closer to the axis. This speed along a circular path is known as tangential speed because the direction of motion is tangent to the circumference of the circle. For circular motion, the terms linear speed and tangential speed are used interchangeably, and both use units of m/s, km/h, and others.

## References

1. "Physical parameters". DVD Technical Notes. Moving Picture Experts Group (MPEG). 1996-07-21. Archived from the original on 2012-02-19. Retrieved 2008-05-30.
2. Chichester, Ryan (June 10, 2021). "The Athletic's Eno Sarris talks Spider Tack, Gerrit Cole with Moose & Maggie". WFAN . Retrieved June 14, 2021 via MSN.com.
3. "2014 season changes". Formula One. Retrieved 2014-08-18.
4. "Double-Density Versus High-Density Disks". Apple. Retrieved 2012-05-05.
5. "Slender and Elegant, It Fuels the Bomb". The Electricity Forum. Retrieved 2006-09-24.
6. "P60-SE Special Edition". JetCat USA. Archived from the original on 2012-04-19. Retrieved 2006-07-19.
7. 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 . Retrieved 2008-05-30.
8. 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:. PMID   7935835.