World Library  
Flag as Inappropriate
Email this Article

Rotational speed

Article Id: WHEBN0000813086
Reproduction Date:

Title: Rotational speed  
Author: World Heritage Encyclopedia
Language: English
Subject: Revolutions per minute, Radian per second, Classical mechanics, Torque, Angular velocity
Collection: Physical Quantities, Temporal Rates
Publisher: World Heritage Encyclopedia

Rotational speed

Rotational speed
Common symbols
ω (omega)
SI unit hertz
Derivations from
other quantities
ω = v / 2πr

Rotational speed (or speed of revolution) of an object rotating around an axis is the number of turns of the object divided by time, specified as revolutions per minute (rpm), revolutions per second (rev/s), or radians per second (rad/s). Rotational speed is equal to the angular velocity ω (or Ω) divided by 2π.[1]

The symbol for rotational speed is \omega_{cyc}(the Greek lowercase letter "omega").

When proper units are used for tangential speed v, rotational speed \omega_{cyc}, and radial distance r, the direct proportion of v to both r and ω becomes the exact equation:[2]

v = 2\pi r\omega_{cyc}
v = r\omega_{rad}

An algebraic rearrangement of this equation allows us to solve for rotational speed:

\omega_{cyc} = v/2\pi r
\omega_{rad} = v/r

Thus, the tangential speed will be directly proportional to r when all parts of a system simultaneously have the same ω, as for a wheel, disk, or rigid wand. It is important to note that the direct proportionality of v to r is not valid for the planets, because the planets have different rotational speeds (ω).

Rotational speed can measure, for example, how fast a motor is running. Rotational speed and angular speed are sometimes used as synonyms, but typically they are measured with a different unit. 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\,


\omega_{cyc} = \omega_{deg}/360\,


  • \omega_{cyc}\, is rotational speed in cycles per second
  • \omega_{rad}\, is angular speed in radians per second
  • \omega_{deg}\, is angular speed in 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


  1. ^ Atkins, Tony; Escudier, Marcel (2013). A Dictionary of Mechanical Engineering. Oxford University Press.  
  2. ^
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.