How To Find Rotor Speed

This article is well-nigh the scalar quantity. For the vector quantity, see Rotational velocity.

Rotational speed
Common symbols	ω (omega)
SI unit	rad/south
Derivations from other quantities	ω = 5 / r
Dimension	${\displaystyle {\mathsf {T}}^{-ane}}$

Rotational speed (besides known as speed of revolution or charge per unit of rotation), of an object rotating around an axis is the number of turns of the object divided by time, specified equally revolutions per infinitesimal (rpm), cycles per 2d (cps), radians per second (rad/southward), etc.^[i]

The symbol for rotational speed is ${\displaystyle \omega _{\text{cyc}}}$ ^{[ citation needed ]}(the Greek lowercase letter "omega").

Tangential speed five, rotational speed ${\displaystyle \omega _{\text{cyc}}}$ , and radial distance r, are related by the following equation:^[2]

${\displaystyle 5=ii\pi r\omega _{\text{cyc}}}$

${\displaystyle v=r\omega _{\text{rad}}}$

An algebraic rearrangement of this equation allows u.s.a. to solve for rotational speed:

${\displaystyle \omega _{\text{cyc}}=v/ii\pi r}$

${\displaystyle \omega _{\text{rad}}=five/r}$

Thus, the tangential speed will exist directly proportional to r when all parts of a system simultaneously have the same ω, as for a bicycle, deejay, or rigid wand. The direct proportionality of v to r is not valid for the planets, because the planets have different rotational speeds (ω).

Rotational speed tin can measure, for example, how fast a motor is running. Rotational speed and angular speed are sometimes used as synonyms, simply typically they are measured with a different unit. Angular speed, however, tells the alter in angle per fourth dimension unit, which is measured in radians per 2nd in the SI organization. Since there are 2π radians per cycle, or 360 degrees per bike, we tin convert angular speed to rotational speed by

${\displaystyle \omega _{\text{cyc}}=\omega _{\text{rad}}/ii\pi \,}$

and

${\displaystyle \omega _{\text{cyc}}=\omega _{\text{deg}}/360\,}$

where

For instance, a stepper motor might plough exactly one complete revolution each second. Its athwart speed is 360 degrees per second (360°/s), or 2π radians per 2d (2π rad/s), while the rotational speed is threescore rpm.

Rotational speed is non to exist confused with tangential speed, despite some relation between the two concepts. Imagine a rotating merry-go-round. No matter how close or far y'all stand from the centrality of rotation, your rotational speed will remain constant. However, your tangential speed does non remain constant. If you lot stand 2 meters from the centrality of rotation, your tangential speed will exist double the amount if you were standing only one meter from the centrality of rotation.

See also [edit]

• Athwart velocity
• Compressor map
• Orders of magnitude (angular velocity)
• Revolutions per minute
• Rotation period

References [edit]

1. ^ Atkins, Tony; Escudier, Marcel (2013). A Dictionary of Mechanical Engineering. Oxford University Press. ISBN9780199587438.
2. ^ "Rotational Quantities".

Source: https://en.wikipedia.org/wiki/Rotational_speed

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