Revolutions per minute
Encyclopedia
Revolutions per minute (abbreviated rpm, RPM, r/min, or r·min−1) is a measure of the frequency
of a rotation. It annotates the number of full rotations
completed in one minute around a fixed axis
. It is used as a measure of rotational speed
of a mechanical component.
Standards organization
s generally recommend the symbol r/min, which is more consistent with the general use of unit symbols. This is not enforced as an international standard. In French for example, tr/mn is commonly used, and the German
equivalent reads U/min .
(SI), rpm is not a unit. This is because Revolutions is a semantic
annotation
rather than a unit. The annotation is instead done in the subscript of the formula sign if needed. Because of the measured physical quantity
, the formula sign has to be f for (rotational) frequency
and ω or Ω for angular velocity
. The corresponding basic SI unit is s−1 or Hz
. When measuring angular speed, rad·s−1
can also be used as unit.
Even though angular velocity, angular frequency and hertz
all have the dimensions of 1/s, angular velocity and angular frequency are not expressed in hertz, but rather in an appropriate angular unit such as radians per second. Thus a disc rotating at 60 revolutions per minute (rpm) is said to be rotating at either 2π rad/s or 1 Hz, where the former measures the angular velocity and latter reflects the number of complete revolutions per second. The conversion between a frequency f measured in hertz and an angular velocity ω measured in radians per second are:
ω=2*π*f and f=ω/(2*π)
rpm to Hz
2400*2*3.14=15072 rad/min
15072/60=251.2 rad/s
(1800*2*3.14)/60=188.4 rad/s
(3300*2*3.14)/60=345.4 rad/s
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
of a rotation. It annotates the number of full rotations
Turn (geometry)
A turn is an angle equal to a 360° or 2 radians or \tau radians. A turn is also referred to as a revolution or complete rotation or full circle or cycle or rev or rot....
completed in one minute around a fixed axis
Rotation around a fixed axis
Rotation around a fixed axis is a special case of rotational motion. The fixed axis hypothesis exclude the possibility of a moving axis, and cannot describe such phenomena as wobbling or precession. According to Euler's rotation theorem, simultaneous rotation around more than one axis at the same...
. It is used as a measure of rotational speed
Rotational speed
Rotational speed tells how many complete rotations there are per time unit. It is therefore a cyclic frequency, measured in hertz in the SI System...
of a mechanical component.
Standards organization
Standards organization
A standards organization, standards body, standards developing organization , or standards setting organization is any organization whose primary activities are developing, coordinating, promulgating, revising, amending, reissuing, interpreting, or otherwise producing technical standards that are...
s generally recommend the symbol r/min, which is more consistent with the general use of unit symbols. This is not enforced as an international standard. In French for example, tr/mn is commonly used, and the German
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
equivalent reads U/min .
International System of Units
According to the International System of UnitsInternational System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...
(SI), rpm is not a unit. This is because Revolutions is a semantic
Semantics
Semantics is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata....
annotation
Annotation
An annotation is a note that is made while reading any form of text. This may be as simple as underlining or highlighting passages.Annotated bibliographies give descriptions about how each source is useful to an author in constructing a paper or argument...
rather than a unit. The annotation is instead done in the subscript of the formula sign if needed. Because of the measured physical quantity
Physical quantity
A physical quantity is a physical property of a phenomenon, body, or substance, that can be quantified by measurement.-Definition of a physical quantity:Formally, the International Vocabulary of Metrology, 3rd edition defines quantity as:...
, the formula sign has to be f for (rotational) frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
and ω or Ω for angular velocity
Angular velocity
In physics, the angular velocity is a vector quantity which specifies the angular speed of an object and the axis about which the object is rotating. The SI unit of angular velocity is radians per second, although it may be measured in other units such as degrees per second, revolutions per...
. The corresponding basic SI unit is s−1 or Hz
Hertz
The hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications....
. When measuring angular speed, rad·s−1
Radian per second
The radian per second is the SI unit of angular velocity, commonly denoted by the Greek letter ω...
can also be used as unit.
Even though angular velocity, angular frequency and hertz
Hertz
The hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications....
all have the dimensions of 1/s, angular velocity and angular frequency are not expressed in hertz, but rather in an appropriate angular unit such as radians per second. Thus a disc rotating at 60 revolutions per minute (rpm) is said to be rotating at either 2π rad/s or 1 Hz, where the former measures the angular velocity and latter reflects the number of complete revolutions per second. The conversion between a frequency f measured in hertz and an angular velocity ω measured in radians per second are:
ω=2*π*f and f=ω/(2*π)
rpm to Hz
2400*2*3.14=15072 rad/min
15072/60=251.2 rad/s
(1800*2*3.14)/60=188.4 rad/s
(3300*2*3.14)/60=345.4 rad/s
Examples
- On some kinds of disc or tape-like recording media, the rotational speed of the medium under the read head is a standard given in rpm. Gramophone (phonograph) recordsGramophone recordA gramophone record, commonly known as a phonograph record , vinyl record , or colloquially, a record, is an analog sound storage medium consisting of a flat disc with an inscribed, modulated spiral groove...
, for example, typically rotate steadily at , , 45 or 78 rpm . - Modern ultrasonic dental drillDental drillA dental drill is a small, high-speed drill used during dental procedures, usually to remove decay and shape tooth structure prior to the insertion of a filling or crown...
s can rotate at up to 800,000 rpm (13.3 kHz).
- The "second" hand of a conventional analogue clock rotates at 1 rpm.
- Audio CDRed Book (audio CD standard)Red Book is the standard for audio CDs . It is named after one of the Rainbow Books, a series of books that contain the technical specifications for all CD and CD-ROM formats.The first edition of the Red Book was released in 1980 by Philips and Sony; it was adopted by the Digital Audio Disc...
players read their discs at a constant 150 kB/s and thus must vary the disc's rotational speed from around 500 rpm (actually 8 Hz), when reading at the innermost edge, to 200 rpm (actually 3.5 Hz) at the outer edge. CD-ROM drives’ maximum rotational speeds are rated in multiples of this figure, even though they do not hold to constant read speeds when reading from most disc formats. - DVDDVDA DVD is an optical disc storage media format, invented and developed by Philips, Sony, Toshiba, and Panasonic in 1995. DVDs offer higher storage capacity than Compact Discs while having the same dimensions....
players also usually read discs at a constant linear rate. The disc's rotational speed varies from 1530 rpm (actually 25.5 Hz), when reading at the innermost edge, and 630 rpm (actually 10.5 Hz) at the outer edge. DVD drives’ speeds are usually given in multiples of this figure. - A washing machineWashing machineA washing machine is a machine designed to wash laundry, such as clothing, towels and sheets...
's drum may rotate at 500 to 2000 rpm (8–33 Hz) during the spin cycles. - A power generation turbine (with a 2 pole alternator) rotates at 3000 rpm (50 Hz) or 3600 rpm (60 Hz), depending on country - see AC power plugs and sockets.
- AutomobileAutomobileAn automobile, autocar, motor car or car is a wheeled motor vehicle used for transporting passengers, which also carries its own engine or motor...
engineEngineAn engine or motor is a machine designed to convert energy into useful mechanical motion. Heat engines, including internal combustion engines and external combustion engines burn a fuel to create heat which is then used to create motion...
s are usually operated at around 2500 rpm (41 Hz), with the minimum speed usually around 1000 rpm (16 Hz), and the redlineRedlineRedline refers to the maximum engine speed at which an internal combustion engine or traction motor and its components are designed to operate without causing damage to the components themselves or other parts of the engine...
at 6000-10,000 rpm (100–166 Hz). - A piston aircraft engineAircraft engineAn aircraft engine is the component of the propulsion system for an aircraft that generates mechanical power. Aircraft engines are almost always either lightweight piston engines or gas turbines...
typically rotates at a rate between 2000 and 3000 rpm (30–50 Hz). - Computers’ hard drives typically rotate at 5400 or 7200 rpm (90 or 120 Hz)—most commonly with ATA or SATASerial ATASerial ATA is a computer bus interface for connecting host bus adapters to mass storage devices such as hard disk drives and optical drives...
interfaces—and some high-performance drives rotate at 10,000 or 15,000 rpm (160 or 250 Hz)—usually with SATA, SCSISCSISmall Computer System Interface is a set of standards for physically connecting and transferring data between computers and peripheral devices. The SCSI standards define commands, protocols, and electrical and optical interfaces. SCSI is most commonly used for hard disks and tape drives, but it...
or Fibre ChannelFibre ChannelFibre Channel, or FC, is a gigabit-speed network technology primarily used for storage networking. Fibre Channel is standardized in the T11 Technical Committee of the InterNational Committee for Information Technology Standards , an American National Standards Institute –accredited standards...
interfaces. - The engine of a Formula OneFormula OneFormula One, also known as Formula 1 or F1 and referred to officially as the FIA Formula One World Championship, is the highest class of single seater auto racing sanctioned by the Fédération Internationale de l'Automobile . The "formula" designation in the name refers to a set of rules with which...
racing carFormula One carA modern Formula One car is a single-seat, open cockpit, open wheel racing car with substantial front and rear wings, and an engine positioned behind the driver. The regulations governing the cars are unique to the championship...
can reach 18,000 rpm (300 Hz) under some circumstances. The exhaust note of the car has a much higher pitch, 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 1200Hz. - A Zippe-type centrifugeZippe-type centrifugeThe Zippe-type centrifuge is a device designed to collect Uranium-235. It was developed in the Soviet Union by a team of 60 Austrian and German scientists captured after World War II, working in detention...
for enriching uranium spins at 90,000 rpm (1,500 Hz) or faster. - Gas turbineGas turbineA gas turbine, also called a combustion turbine, is a type of internal combustion engine. It has an upstream rotating compressor coupled to a downstream turbine, and a combustion chamber in-between....
engines rotate at tens of thousands of rpm. JetCat model aircraft turbines are capable of over 100,000 rpm (1,700 Hz) with the fastest reaching 165,000 rpm (2,750 Hz). - An electromechanical battery (EMB) works at 60,000–200,000 rpm (1–3 kHz) range using a passively magnetic levitated flywheel in vacuum. 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 turbochargerTurbochargerA turbocharger, or turbo , from the Greek "τύρβη" is a centrifugal compressor powered by a turbine that is driven by an engine's exhaust gases. Its benefit lies with the compressor increasing the mass of air entering the engine , thereby resulting in greater performance...
can reach 290,000 rpm (4,800 Hz), while 80,000–200,000 rpm (1–3 kHz) is common.
See also
- Orders of magnitude (angular velocity)Orders of magnitude (angular velocity)This page is a progressive and labeled list of the SI angular velocity orders of magnitude, with certain examples appended to some list objects.-External links:**...
- Constant linear velocityConstant linear velocityIn optical storage, constant linear velocity 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...
, or CLV, used when referring to the speed of audio CDs - Constant angular velocityConstant angular velocityIn optical storage, constant angular velocity is a qualifier for the rated speed of an optical disc drive, and may also be applied to the writing speed of recordable discs...
, or CAV, used when referring to the speed of gramophone (phonograph) records - Turn (geometry)Turn (geometry)A turn is an angle equal to a 360° or 2 radians or \tau radians. A turn is also referred to as a revolution or complete rotation or full circle or cycle or rev or rot....