Radian per second
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| radian per second | |
|---|---|
angular speed | |
| Symbol | rad/s, rad⋅s−1 |
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 (symbol ω, omega). The radian per second is defined as the angular frequency that results in the angular displacement increasing by one radian every second.[1]
Relation to other units
A
Since the radian is a
One radian per second also corresponds to about 9.55
Quantity correspondence Angular frequency Frequency 2π rad/s 1 Hz 1 rad/s ≈ 0.159155 Hz 1 rad/s ≈ 9.5493 rpm 0.1047 rad/s ≈ 1 rpm
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 angular speed ω multiplied by the torque τ applied to the shaft: p = ω ⋅ τ. When coherent units are used for these quantities, which are respectively the watt, the radian per second, and the newton-metre, and thus W = rad/s × N·m, 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)
- Radian per metre
References
- ^ "6.1: Rotation Angle and Angular Velocity". College Physics. OpenStax. Retrieved 20 January 2024.
- ^ "radians per second :: unit". conversion.org. Retrieved 28 January 2024.
- ^ "Metric Conversion: Language Resources". Macquarie Dictionary. Macquarie Dictionary Publishers. Archived from the original on 29 February 2016. Retrieved 27 January 2024 – via National Library of Australia.
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