Revolutions per minute

Revolutions per minute (abbreviated rpm, RPM, r/min, or r·min⁻¹) is a unit of frequency of rotation: 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 organizations 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 (tours par minute) is commonly used, and the German unit reads U/min (Umdrehungen pro Minute) or 1/min (= 1 min^-1).

The corresponding unit in the International System of Units (SI) is hertz (symbol Hz) or s^-1 (1/second). Revolutions per minute is converted to hertz through division by 60. Conversion from hertz to RPM is by multiplication with 60.

1 rpm = 1/min = 1/(60s) = 1/60 Hertz = 16.667 mHz

Another related unit is the SI unit for angular velocity, radian per second (rad·s⁻¹):

1 RPM = 2π rad·min⁻¹ = 2π/60 rad·s⁻¹ ≈ 0.10471976 rad·s⁻¹

Formula

A formula for calculating the RPM of a rotating object may be written as

where υ is the linear velocity of a point in the rotating object (in units of distance/minute) and C refers to the circumference of the circle that this measuring point performs around the axis of rotation.

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 r/min. Gramophone (phonograph) records, for example, typically rotate steadily at 16+²⁄₃, 33+¹⁄₃, 45 or 78 r/min (⁵⁄₁₈, ⁵⁄₉, ³⁄₄, or 1.3 Hz respectively).
• Modern ultrasonic dental drills can rotate at up to 800,000 r/min (13.3 kHz).
• The "second" hand of a conventional analogue clock rotates at 1 r/min.
• Audio CD players read their discs at a constant 150 kB/s and thus must vary the disc's rotational speed from around 500 r/min (actually 8 Hz), when reading at the innermost edge, to 200 r/min (actually 3.5 Hz) at the outer edge.^[1] 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.
• DVD players also usually read discs at a constant linear rate. The disc's rotational speed varies from 1530 r/min (actually 25.5 Hz), when reading at the innermost edge, and 630 r/min (actually 10.5 Hz) at the outer edge.^[1] DVD drives’ speeds are usually given in multiples of this figure.
• A washing machine's drum may rotate at 500 to 2000 r/min (8–33 Hz) during the spin cycles.
• A power generation turbine rotates at 3000 r/min (50 hz) or 3600 r/min (60 Hz), depending on country - see AC power plugs and sockets.
• Automobile engines are usually operated at 2500 r/min (41 Hz), with the minimum speed usually around 1000 r/min (16 Hz), and the redline at 6000-10,000 r/min (100-166 Hz).
• A piston aircraft engine typically rotates at a rate between 2000 and 3000 r/min (30–50 Hz).
• Computers’ hard drives typically rotate at 5400 or 7200 r/min (90 or 120 Hz)—most commonly with ATA or SATA interfaces—and some high-performance drives rotate at 10,000 or 15,000 r/min (160 or 250 Hz)—usually with SATA, SCSI or Fibre Channel interfaces.
• The engine of a Formula One racing car can reach 19,000 r/min (320 Hz) under some circumstances.^[2]
• A Zippe-type centrifuge for enriching uranium spins at 90,000 r/min (1,500 Hz) or faster.^[3]
• Gas turbine engines rotate at tens of thousands of r/min. JetCat model aircraft turbines are capable of over 100,000 r/min (1,700 Hz) with the fastest reaching 165,000 r/min (2,750 Hz).^[4]
• An electromechanical battery (EMB) works at 60,000–200,000 r/min (1–3 kHz) range using a passively magnetic levitated flywheel in vacuum.^[5] 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 turbocharger can reach 290,000 r/min (4,800 Hz), while 80,000–200,000 r/min (1–3 kHz) is common.
• a bullet fired from an M16A2 rifle, using a 5.56x45mm NATO rifle cartridge, spins at ~315,000 r/min.

See also

• Orders of magnitude (angular velocity)
• Constant linear velocity, or CLV, used when referring to the speed of audio CDs
• Constant angular velocity, or CAV, used when referring to the speed of gramophone (phonograph) records
• Turn (geometry)

References