Radian per second
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radian per second | |
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General information | |
Unit system | SI |
Unit of | 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
Relation to other units
[edit]A frequency of one hertz (1 Hz), or one cycle per second (1 cps), corresponds to an angular frequency of 2
Since the radian is a dimensionless unit in the SI, the radian per second is dimensionally equivalent to the hertz—both can be expressed as reciprocal seconds, s−1. So, context is necessary to specify which kind of quantity is being expressed, angular frequency or ordinary frequency.
One radian per second also corresponds to about 9.55 revolutions per minute (rpm).[3] Degrees per second may also be defined, based on degree of arc, where 1 degree per second (°/s) is equivalent to
Quantity correspondence Angular frequency Frequency 2 π rad/s1 Hz 1 rad/s ≈ 0.159155 Hz 1 rad/s ≈ 9.5493 rpm 0.1047 rad/s ≈ 1 rpm
Coherent units
[edit]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
See also
[edit]- Cycle per second
- Normalized frequency (digital signal processing)
- Order of magnitude (angular velocity)
- Radian per metre
References
[edit]- ^ "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.