Rotational frequency

Rotational speed (sometimes called speed of revolution) indicates, for example, how fast a motor is running. Rotational speed is equivalent to angular speed, but with different units. Rotational speed tells how many complete rotations (i.e. revolutions or cycles) there are per time unit. It is therefore a cyclic frequency, measured in hertz (revolutions per second) in the SI System. The units revolutions per minute (rpm or 1/min) are more common in everyday life. Angular speed, however, tells the change in angle per time unit, which is measured in radians per second in the SI system. Since there are 2π radians per cycle, or 360 degrees per cycle, we can convert angular speed to rotational speed by:

\omega _{cyc}=\omega _{rad}/2\pi \,

and

\omega _{cyc}=\omega _{ang}/360\,

where

$\omega _{cyc}\,$ is rotational speed (cycles per second)
$\omega _{rad}\,$ is angular speed (radians per second)
$\omega _{ang}\,$ is angular speed (degrees per second)

For example, a stepper motor might turn exactly one complete revolution each second. Its angular speed is 360 degrees per second (360°/s), or 2π radians per second (2π rad/s), while the rotational speed is 60 rpm.

Rotational speed is not to be confused with tangential speed, despite some relation between the two concepts. Imagine a rotating merry-go-round. No matter how close or far you stand from the axis of rotation, your rotational speed will remain constant. However, your tangential speed does not remain constant. If you stand two meters from the axis of rotation, your tangential speed will be double the amount if you were standing only one meter from the axis of rotation.

See also