Inverse second: Difference between revisions

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{{Short description|Unit of frequency}}

The '''inverse second''', '''reciprocal second''', or '''per second''' (s⁻¹) is a unit of [[frequency]], defined as the [[multiplicative inverse]] of the [[second]] (a unit of time). It is [[dimensional analysis|dimensionally]] equivalent to:

{{Infobox unit

* [[Hertz]] (the SI unit for [[cycles per second]])

| name = inverse second

* [[Becquerel]]s (the SI unit for aperiodic or stochastic ''[[radioactivity|radionuclide]]'' events per second)

| image =

It also provides the [[denominator]] for [[temporal rate]]s, such as that of [[angular frequency]] in [[radians per second]].

| caption =

| symbol = s⁻¹

| standard = [[SI]]

| quantity = [[frequency]]

| units1 = [[SI units]]

| inunits1 = {{val|1|ul=Hz}}

}}

The '''inverse second''', or '''reciprocal second''', or ('''per second''' (s⁻¹'''), also called '''''per second''''', is a [[unit of [[frequencymeasurement|unit]], defined as the [[multiplicative inverse]] of the [[second]] (a unit of [[time]]). It is applicable for [[dimensionalphysical analysisquantities]] of [[dimension (physics)|dimensionallydimension]] equivalent'''reciprocal to:time''', such as [[frequency]] and [[strain rate]].

It is [[dimensional analysis|dimensionally]] equivalent to:

==See also==

* [[hertz]] (Hz), historically known as [[cycles per second]] – the SI unit for [[frequency]] and [[rotational frequency]]

*[[:Category:Units of frequency]]

* [[Becquerelbecquerel]]s (Bq) – the SI unit for the rate of occurrence of aperiodic or stochastic ''[[radioactivity|radionuclide]]'' events per second)

*[[Aperiodic frequency]]

* [[baud]] (Bd) – the unit for [[symbol rate]] over a communication link

* [[bit per second]] (bit/s) – the unit of bit rate

*''However, the special names and symbols above for s⁻¹ are recommend for clarity.{{efn|"The SI unit of frequency is given as the hertz, implying the unit cycles per second; the SI unit of angular velocity is given as the radian per second; and the SI unit of activity is designated the becquerel, implying the unit counts per second. Although it would be formally correct to write all three of these units as the reciprocal second, the use of the different names emphasises the different nature of the quantities concerned."'' <ref>{{cite web |url=http://www.bipm.org/en/publications/si-brochure/section2-2-2.html |title=Units with special names and symbols; units that incorporate special names and symbols }}</ref>}}{{efn|"(d) The hertz is used only for periodic phenomena, and the becquerel (Bq) is used only for stochastic processes in activity referred to a radionuclide."<ref>{{cite web |url=http://www.bipm.org/en/publications/si-brochure/section2-2.html#section2-2-2 |title=BIPM – Table 3 |publisher=[[BIPM]] |access-date=2012-10-24}}</ref>}}

Reciprocal second should not be confused with [[radian per second]] (rad⋅s⁻¹), the SI unit for [[angular frequency]] and [[angular velocity]]. As the [[radian]] is a [[dimensionless unit]], radian per second is dimensionally consistent with reciprocal second. However, they are used for different [[kind of quantity|kinds of quantity]], frequency and angular frequency, whose numerical value differs by 2{{pi}}.

==References==

*''"The SI unit of frequency is given as the hertz, implying the unit cycles per second; the SI unit of angular velocity is given as the radian per second; and the SI unit of activity is designated the becquerel, implying the unit counts per second. Although it would be formally correct to write all three of these units as the reciprocal second, the use of the different names emphasises the different nature of the quantities concerned."'' {{cite web |url=http://www.bipm.org/en/publications/si-brochure/section2-2-2.html |title=Units with special names and symbols; units that incorporate special names and symbols }}

The '''inverse minute''' or '''reciprocal minute''' ('''min⁻¹'''), also called '''''per minute''''', is 60⁻¹ s⁻¹, as 1&nbsp;min = 60&nbsp;s; it is used in quantities of type "[[countable quantity|counts]] per minute", such as:

*''"(d) The hertz is used only for periodic phenomena, and the becquerel (Bq) is used only for stochastic processes in activity referred to a radionuclide."'' {{cite web |url=http://www.bipm.org/en/publications/si-brochure/section2-2.html#section2-2-2 |title=BIPM - Table 3 |publisher=[[BIPM]] |accessdate=2012-10-24}}

* [[Actions per minute]]

* [[Beats per minute]]

* [[Counts per minute]]

* [[Revolutions per minute]] (rpm)

* [[Words per minute]]

Inverse square second (s⁻²) is involved in the units of linear [[acceleration]], [[angular acceleration]], and [[rotational acceleration]].

== See also ==

*[[:Category:{{main category|Units of frequency]]}}

* [[Aperiodic frequency]]

* [[Inverse metre]]

* [[Reciprocal length]]

* [[Unit of time]]

== Notes ==

{{notelist}}

== References ==

{{reflist}}

[[Category:Units of frequency]]