Radian per second
The radian per second is the SI unit of angular velocity, commonly denoted by the Greek letter ω. The radian per second is also the unit of angular frequency.
The radian per second is defined as the change in the orientation of an object, in radians, every second.
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. This may lead to confusion between the quantities angular frequency ω and frequency ν.
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 multiplied by the torque τ applied to the shaft, in newton-meters. Thus,, 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 by the torque in pound-feet, then a factor is needed to convert the result to units of horsepower.
An angular frequency,, corresponds to an ordinary frequency,, which corresponds to a frequency of rotation of. In other words 6 radians is about 360 degrees.
