## Dr. Ahmed G. Abo-Khalil

Electrical Engineering Department

## Revolutions/ min

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 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 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:

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

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