Velocity To Radians Per Second

SI unit of angular velocity or athwart frequency

Radian per 2nd
Athwart frequency ω (in radians per 2d), is smaller than frequency ν (in cycles per 2nd, as well called Hz), by a cistron of 2π, because 1 rad/s corresponds to 2π Hz.
General information
Unit system	SI
Unit of	rotational speed
Symbol	rad/south or rad⋅due south⁻¹

The radian per second (symbol: rad⋅s⁻¹ or rad/s) is the unit of measurement of angular velocity in the International System of Units (SI), unremarkably denoted by the Greek alphabetic character ω (omega). The radian per 2d is also the SI unit of athwart frequency. The radian per 2d is defined as the change in the orientation of an object, in radians, every second.

The athwart frequency of one radian per 2d is equivalent to an ordinary frequency of 1/(2 $π$ ) hertz, or cycles per 2d. This is because one bicycle of a rotating object is an angular rotation of ane plow (360 degrees), which equals ii $π$ 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 due south⁻¹.

Ane radian per second is too equivalent to virtually ix.55 revolutions per minute.

Angular frequency ω	(Ordinary) frequency $\nu =\omega /{two\pi }$
2π radians per second	exactly 1 hertz (Hz)
ane radian per second	approximately 0.159155 Hz
i radian per second	approximately 57.29578 degrees per second
1 radian per 2nd	approximately nine.5493 revolutions per minute (rpm)
0.1047 radians per second	approximately i rpm

A use of the unit radian per second is in adding of the ability transmitted past a shaft. In the International System of Units, widely used in physics and engineering, the ability p is equal to the rotational speed ω (in radians per 2nd) 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 case, if one multiplies athwart velocity in revolutions per minute (rpm) past the torque in pound-feet, then a factor is needed to convert the result to units of horsepower.