Revolution per minute

Tachometer with flight time indicator of a Flugzeugbau Samburo M ChildhoodD. Use as a symbol "min"^-1».

A GA16-DE motor tachometer from a Nissan Sunny N14 marking the cutting speed of injection. It uses as a "r/min" symbol.

Instrument panel of a Mazda Cosmo (3rd generation, produced between the years 1981 and 1989). It uses as a symbol of the "rpm" spin regime.

Instrument board of an Alfa Romeo Giulietta (2010). It indicates the speed of the engine as "Giri x 1000", in Italian.

A revolution per minute is a unit of frequency that is also used to express angular speed. In this context, the number of rotations completed each minute by a revolving body is indicated.

Sometimes the term rate of rotation is used to refer to the speed of rotation expressed in revolutions per minute and not to be confused with the angular velocity expressed in radians per second.

Symbolization

To express a value in revolutions per minute, this unit is symbolized as min^-1 or r/min, although they are also used Traditionally used symbols that have not been fixed by standardization institutions such as rpm, RPM. Although units of measurement are normally represented by symbols and not abbreviations, the abbreviation r also exists. p. m. to represent this unit.

In other languages it is possible to find other symbols such as «tr/min», from the French «tours par minute»; "U/min", from the German "Umdrehungen pro Minute"; or "giri/min", from the Italian "giri per minute".

Relationship with other units

According to the International Bureau of Weights and Measures, rpm is not a unit consistent with the International System of Units (SI), so it is advisable to substitute it or represent such values together with the equivalents expressed in units consistent with the SI such as min^-1, Hz, or rad/s. This is because the term "revolutions" in "rpm" or "r/min" is a semantic notation, rather than a unit of measure.

Frequency (f)

The International System of Units (SI) unit of frequency is the hertz (Hz). When expressing frequency values, in the same way that a hertz is not identified with a cycle per second, revolutions are not expressed as a unit.

1min− − 1=1min=160s=160Hz{displaystyle {rm {1 min^{-1}={frac {1}{min}}={frac {1}{60 s}}}={frac {1}{1}{60}}}}} Hz?

Angular velocity (rad/s)

Although angular velocity, angular frequency, and frequency have the dimensions of 1/s (hertz or Hz), angular velocity and angular frequency are not expressed in hertz, but rather in an appropriate unit for a ratio between angle and time. Thus, the SI unit of angular velocity is the radian per second. However, the radian is a dimensionless unit, and one revolution or one complete turn is equal to 2π radians.

1rpm=1rmin=2π π rad60s=π π 30⋅ ⋅ rads≈ ≈ 0,10471976rads{displaystyle {rm {1 rpm=1{frac {r}{min}}}={frac {frac {2pi rad}{60 s}}}={frac {pi }{cdot {frac {rad}{s}}{approx 0,10471976 {frac {rad}{s}}}}}}}}}}}}}}

Relationship between frequency and angular velocity

The relationship between a frequency

f[chuckles]Hz]=ω ω [chuckles]rad/s]2π π [chuckles]rad]{displaystyle f[mathrm {Hz} ]={frac {omega [mathrm {rad/s}}}{2pi [mathrm {rad}}}}}}}}}}}}

or else

ω ω =2π π ⋅ ⋅ f{displaystyle omega =2pi cdot f}

Turn regime of an electric machine

The nominal rotation regime of a synchronous electric machine and the synchronism regime of an asynchronous machine can be calculated in revolutions per minute by the following formula:

n[chuckles]min− − 1]=60[chuckles]smin]⋅ ⋅ f[chuckles]Hz]p=120[chuckles]smin]⋅ ⋅ f[chuckles]Hz]P{displaystyle nleft {mathrm {min} ^{-1}right]=60left[{frac {s}{mathrm {min}}{right}{cdot {f}{mathrm {Hz}}{p}}}}{120left[s}{cfrat}{m} {bright} {bright} {bright}}}} {bright}{m} {bright}} {bright} {bright} {bright} {bright} {bright} {bright} {bright} {bright} {bright} {bright} {bright} {bright} {bright} {bright} {bright} {bright} {bright}} {bright} {bright} {bright} {bright} {bright} {bright} {bright} {bright} {bright} {bright} {bright} {bright} {bright} {bright}{bright} {bright} {

where f is the frequency of the electric current (in Europe 50 Hz and in America 60 Hz), p are pairs of poles and P is the number of poles (p=P/2).