Revolutions per minute explained

Revolutions per minute
Quantity:Rotational speed, rotational frequency
Symbol:rpm
Symbol2:r/min
Units1:SI accepted units
Inunits1:1 min−1
Units2:SI units
Inunits2: Hz = 0.01 Hz
Units3:SI base units
Inunits3:0.01 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 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 and an angular frequency are:

\omega=2\pif,    f=

\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.

\begin{align} 1~&rad
s

&&=&

1
2\pi

~&Hz&&=&

60
2\pi

~&rpm\\ 2\pi~&

rad
s

&&=&1~&Hz&&=&60~&rpm\\

2\pi~&
60
rad
s

&&=&

1
60

~&Hz&&=&1~&rpm \end{align}

Examples

See also

Notes and References

  1. https://www.iso.org/obp/ui/#iso:std:iso:80000:-3:ed-2:v1:en ISO 80000-3:2019
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