This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: "Radian per second" – news · newspapers · books · scholar · JSTOR (June 2020) (Learn how and when to remove this template message)

Radian per second | |
---|---|

General information | |

Unit system | SI derived unit |

Unit of | rotational speed |

Symbol | rad/s or rad⋅s^{−1} |

The **radian per second** (symbol: **rad⋅s ^{−1}** or

The angular frequency of one radian per second is equivalent to an *ordinary frequency* of 1/(2π) hertz, or cycles per second. This is because one cycle of a rotating object is an angular rotation of one turn (360 degrees), which equals 2π 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 is also equivalent to about 9.55 revolutions per minute.

Angular frequency *ω*(Ordinary) frequency 2π radians per second exactly 1 hertz (Hz) 1 radian per second approximately 0.159155 Hz 1 radian per second approximately 57.29578 degrees per second 1 radian per second approximately 9.5493 revolutions per minute (rpm) 0.1047 radians per second approximately 1 rpm

A use of the *unit radian per second* is in calculation of the power transmitted by a shaft. In the International System of Units, widely used in physics and engineering, the power *p* is equal to the rotational speed *ω* (in radians per second) multiplied by the torque *τ* applied to the shaft, in newton-metres. Thus, *p* = *ω* ⋅ *τ*, and the unit is the watt, with no numerical coefficient needed. In other systems, an additional factor may be necessary. For example, if one multiplies angular velocity in revolutions per minute (rpm) by the torque in pound-feet, then a factor is needed to convert the result to units of horsepower.