Rotational frequency

Related quantities

Tangential speed v (Latin letter v), rotational frequency \nu, and radial distance r, are related by the following equation: \begin{align} v &= 2\pi r\nu \ v &= r\omega. \end{align}

An algebraic rearrangement of this equation allows us to solve for rotational frequency: \begin{align} \nu &= v/2\pi r \ \omega &= v/r. \end{align}

Thus, the tangential speed will be directly proportional to r when all parts of a system simultaneously have the same \omega, as for a wheel, disk, or rigid wand. The direct proportionality of v to r is not valid for the planets, because the planets have different rotational frequencies.

Regression analysis

Rotational frequency can measure, for example, how fast a motor is running. Rotational speed is sometimes used to mean angular frequency rather than the quantity defined in this article. Angular frequency gives the change in angle per time unit, which is given with the unit radian per second in the SI system. Since 2π radians or 360 degrees correspond to a cycle, we can convert angular frequency to rotational frequency by \nu = \omega/2\pi , where

• \nu, is rotational frequency, with unit cycles per second
• \omega, is angular frequency, with unit radian per second or degree per second

For example, a stepper motor might rotate exactly once per second so that its angular frequency is 360 degrees per second (360°/s), or 2π radians per second (2π rad/s), while the rotational frequency is 60 rpm.

Rotational frequency is not to be confused with tangential speed, despite some relation between the two concepts. Imagine a merry-go-round with a constant rate of rotation. No matter how close to or far from the axis of rotation you stand, your rotational frequency 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.

Notes

References

References

1. (2019). "ISO 80000-3:2019 Quantities and units — Part 3: Space and time". [[International Organization for Standardization]].
2. "Rotational Quantities".
3. {{SIbrochure9th
4. (2020-03-04). "The NIST Guide for the Use of the International System of Units, Special Publication 811". [[National Institute of Standards and Technology]].