The radian per second (symbol: rad⋅s
−1 or rad/s) is the unit of
angular velocity in the
International System of Units (SI). The
radian per second is also the SI unit of
angular frequency, commonly denoted by the Greek letter ''ω'' (omega). The radian per second is defined as the angular frequency that results in the
angular displacement increasing by one
radian every
second.
The angular frequency of one radian per second corresponds to a
frequency of 1/(2)
hertz (Hz), or cycles per second. This is because one cycle of rotation corresponds to an angular rotation of one
turn (360
degrees), which equals 2 radians. Since the radian is a
dimensionless unit in the
SI, the radian per second is dimensionally equivalent to the hertz—both are defined as s
−1. One radian per second also corresponds to about 9.55
revolutions per minute
Revolutions per minute (abbreviated rpm, RPM, rev/min, r/min, or with the notation min−1) is a unit of rotational speed or rotational frequency for rotating machines.
Standards
ISO 80000-3:2019 defines a unit of rotation as the dimensio ...
.
:
Coherent units
A use of the unit radian per second is in calculation of the power transmitted by a shaft. In the
International System of Quantities (SI) and the
International System of Units, widely used in
physics and
engineering, the power ''p'' is equal to the rotational speed ''ω'' multiplied by the
torque ''τ'' applied to the shaft: . When
coherent units are used for these quantities, which are respectively the
watt, the radian per second, and the
newton-metre, and thus , no numerical factor needed when performing the numerical calculation. When the units are not coherent (e.g.
horsepower,
turn/min, and
pound-foot), an additional factor will generally be necessary.
See also
*
Cycle per second
*
Normalized frequency (digital signal processing)
*
Order of magnitude (angular velocity)
References
SI derived units
Units of angular velocity
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