 #jsDisabledContent { display:none; } My Account |  Register |  Help Flag as Inappropriate This article will be permanently flagged as inappropriate and made unaccessible to everyone. Are you certain this article is inappropriate?          Excessive Violence          Sexual Content          Political / Social Email this Article Email Address:

# Rotational speed

Article Id: WHEBN0000813086
Reproduction Date:

 Title: Rotational speed Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### 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.

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:

v = 2\pi r\omega_{cyc}

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

\omega_{cyc} = v/2\pi 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:

and

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

where

• \omega_{cyc}\, is rotational speed in cycles per second