# Revolutions per minute

(Redirected from Rpm)

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 turns 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 equivalent reads U/min (Umdrehungen pro Minute).

## International System of Units

According to the International System of Units (SI), rpm is not a unit. This is because the Revolution 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.

1 rad·s−1 = 60/2π rpm = c.9.55 rpm = 1/2π Hz.

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:

$\omega = 2 \pi f\,\,\!$ and $\,\,f = \frac {\omega} {2 \pi}\text{.}\,\!$

## Examples

• On many kinds of disc recording media, the rotational speed of the medium under the read head is a standard given in rpm. Gramophone (phonograph) records, for example, typically rotate steadily at 16 23, 33 13, 45 or 78 rpm (518, 59, 34, or 1.3 Hz respectively).
• Modern ultrasonic dental drills can rotate at up to 800,000 rpm (13.3 kHz).
• The "second" hand of a conventional analogue clock rotates at 1 rpm.
• Audio CD players read their discs at a precise, constant rate (4.12335 mbit/sec of raw physical data for 1.4112 mbit/sec (172.2KB/s) of usable audio data) and thus must vary the disc's rotational speed from around 480 rpm (actually 8 Hz), when reading at the innermost edge, to 210 rpm (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. A plain figure, e.g. "8x" denotes a continual read speed and variable spin speed up to eight times the original maximum (64 Hz, 3840 RPM); one noted as e.g. "32x max" denotes a constant spin speed at thirty-two times the original minimum (112 Hz, 6720 RPM) and a variable read speed which may be as low as 14x at the point where a 1x drive would spin at 480 RPM, only reaching a true 32x in the regions which would have required 210 RPM. By holding the RPM constant, a greater maximum read speed can be achieved for the same maximum RPM (an "8x" drive becomes an "18x max"; drives commonly offer 40, 48 or 52x maximum speeds when problems of vibration and discs disintegrating due to centrifugal forces would otherwise limit them to less than 24x / 11000 RPM) when there is no need for it to remain fixed across the whole disc. As more linear space is available per rotation at the outer edges, and late-1970s technology imposed quite coarse limits on the minimum size of the physical data structures, keeping a constant RPM would have been wasteful of disc area and demanded larger discs, lower audio quality, shorter running time, or a combination of all three. Despite the additional complexity of continually adjusting the rotational speed, it is a worthwhile tradeoff to improve data density.
• DVD 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.[1] PC DVD drives’ speeds are, like CD drives, usually given in multiples of this figure, either as an overall multiplier (e.g. in slower 4x drives which may spin at up to 6120 RPM when reading data near the spindle), or a maximum based on peak read speed (e.g. "16x max" for a model that spins up to 10080 RPM across the whole disc). The overall multipliers are lower than for CDs, as "single speed" DVD already spins approximately 3x faster than CD but is subject to similar limits on maximum RPM. The remainder of the difference in data transfer speed (1385 vs 150 KB/sec for data (DVD has no mode equivalent to CDDA), or a little more than 9x) comes from increased linear storage density and a slight improvement in error-correction efficiency. The same limits are also seen in Blu-ray drives and media, where the basic spin rate is higher still (similar to 4x CD) and the fastest typical PC drives operate at "12x max" (5x minimum) BD speed; almost 52 MB/sec, over 350x basic CDROM speed, but still no higher physical spin speed than the 10~12,000 RPM of 48~52x Max CDROMs.
• A washing machine'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.
• Modern Automobile engines are typically operated around 2000–3000 rpm (33–50 Hz) when cruising, with a minimum (idle) speed around 750–900 rpm (12.5–15 Hz), and an upper limit anywhere from 4500 to 10,000 rpm (75–166 Hz) for a road car or nearly 20,000 rpm for racing engines such as those in Formula 1 cars (currently limited to 18,000 rpm).[2] The exhaust note of V8 F1 cars have 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 and 3000 rpm (30–50 Hz).
• Computers’ hard drives typically rotate at 5400 or 7200 rpm (90 or 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 10,000 or 15,000 rpm (160 or 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 "eco" laptop drives could be found with 4200 or even 3600 RPM spindle speeds (70 and 60 Hz) but these have fallen out of favour due to their lower performance, improvements in energy efficiency amongst faster models, and the takeup of solid-state drives for use in slimline and "ultra portable" machines. 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 RPM, so the effective data rate is faster at the edge (conventionally, the "start" of the disc, opposite to CD/DVD).
• Floppy disc drives typically ran at a constant 300 or occasionally 360 RPM (a relatively slow 5 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 RPM 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/track) and 590 RPM (8 sectors) with the Mac's 800 KB double-density drive at a constant 39.4 KB/sec (max) – vs 300 RPM, 720 KB and 23 KB/sec (max) for double-density drives in other machines.[3]
• A Zippe-type centrifuge for enriching uranium spins at 90,000 rpm (1,500 Hz) or faster.[4]
• Gas turbine 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).[5]
• A Flywheel energy storage system works at 60,000–200,000 rpm (1–3 kHz) range using a passively magnetic levitated flywheel in vacuum.[6] 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 rpm (4,800 Hz), while 80,000–200,000 rpm (1–3 kHz) is common.