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| {{infobox unit
| | The author is known as Irwin. Managing people has been his working day occupation for a whilst. What I love performing is to gather badges but I've been using on new issues lately. South Dakota is her beginning location but she needs to move because of her family members.<br><br>Here is my web blog; [http://wixothek.com/blog/557 http://wixothek.com/blog/557] |
| | image = [[Image:AngularFrequency.gif]]
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| | caption = Angular frequency [[omega|ω]] (in radians per second), is larger than frequency [[nu (letter)|ν]] (in cycles per second, also called[[Hertz|Hz]]), by a factor of 2π, because 2π rad/s = 1 Hz.
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| | standard = [[SI derived unit]]
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| | quantity = [[Rotational speed]]
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| | symbol = {{gaps|rad|/|s}}
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| | symbol2 = {{gaps|rad|•|s<sup>−1</sup>}}
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| }}
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| The '''radian per second''' (symbol: '''rad·s<sup>−1</sup>''' or '''rad/s''') is the [[SI]] unit of [[rotational speed]] ([[angular velocity]]), commonly denoted by the Greek letter ω (omega). The radian per second is also the unit of [[angular frequency]]. | |
| The radian per second is defined as the change in the [[orientation (rigid body)|orientation]] of an object, in [[radian]]s, every [[second]].
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| :{| class="wikitable"
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| |-
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| ! Angular frequency ''ω''
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| ! (Ordinary) [[frequency]] <math>\nu = \omega/{2\pi}</math>
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| |-
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| || 2π radians per second || exactly 1 [[hertz]] (Hz)
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| |-
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| || 1 radian per second || approximately 0.159155 Hz
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| |-
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| || 1 radian per second|| approximately 57.29578 degrees per second
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| |-
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| || 1 radian per second|| approximately 9.5493 [[revolutions per minute]] (rpm)
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| || 0.1047 radian per second|| approximately 1 rpm
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| |}
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| Note that because the radian is a [[dimensionless unit]], the radian per second is dimensionally equivalent to the hertz—both are defined as one s<sup>−1</sup>. This means that great care must be taken to avoid confusing angular frequency ''ω'' and frequency ''ν''.
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| One of the important uses of the ''unit radian per second'' is in calculation of the power transmitted by a shaft. In the [[International System of Units|International System]], widely used in [[physics]] and [[engineering]], the power, p, delivered to the shaft is given by the product of ω (in radians per second) times the [[torque]], τ, in [[newton-meter]]s applied to the shaft. Thus, p = ω • τ, and the unit is the [[watt]], with no numerical coefficient needed.
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| In other systems, the calculation is somewhat more complicated, because if one multiplies angular velocity in [[revolutions per minute]] (r.p.m.) times the torque in [[pound-foot (torque)|pound-feet]], then a multiplicative constant is needed to give the result in [[horsepower]].
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| 1 rad/s = 60/2π rpm exactly = 9.55 rpm approx.
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| 1 rad/s = 1/2π Hz exactly = 0.159 Hz approx.
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| ==See also==
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| *[[Order of magnitude (angular velocity)]]
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| *[[Cycle per second]]
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| *[[Normalized frequency (digital signal processing)|Normalized frequency]]
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| ==External links==
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| *[http://online.unitconverterpro.com/unit-conversion/convert-alpha/velocity---angular.html UnitConverterPro.com online angular velocity conversion]
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| [[Category:SI derived units]]
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| [[Category:Units of frequency]]
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| {{physics-stub}}
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The author is known as Irwin. Managing people has been his working day occupation for a whilst. What I love performing is to gather badges but I've been using on new issues lately. South Dakota is her beginning location but she needs to move because of her family members.
Here is my web blog; http://wixothek.com/blog/557