Length
18542
223017854
2008-07-02T05:26:23Z
SJP
2716074
Reverted edits by [[Special:Contributions/210.87.251.48|210.87.251.48]] to last version by SJP (using [[WP:HG|Huggle]])
{{Unreferenced|date=August 2007}}
{{otheruses-word}}
{{Wiktionarypar3|length|width|breadth}}
'''Length''' is the long [[dimension]] of any object. The length of a thing is the distance between its ends, its linear extent as measured from end to end. This may be distinguished from [[height]], which is vertical extent, and '''width''' or '''breadth''', which are the distance from side to side, measuring across the object at right angles to the length. In the physical sciences and engineering, the word "length" is typically used synonymously with "[[distance]]", with symbol <math>l</math> or <math>L</math>.
Length is a measure of one dimension, whereas [[area]] is a measure of two dimensions (length squared) and [[volume]] is a measure of three [[dimensions]] (length cubed). In most systems of measurement, length is a [[fundamental unit]], from which other units are derived.
== Units of length ==
In the physical sciences and engineering, when one speaks of "units of length", the word "length" is synonymous with "[[distance]]". There are several [[Units of measurement|units]] that are used to [[Measurement|measure]] length. Units of length may be based on lengths of human body parts, the distance travelled in a number of paces, the distance between landmarks or places on the Earth, or arbitrarily on the length of some fixed object.
In the [[International System of Units]] (SI), the [[SI base unit|basic unit]] of length is the ''[[metre]]'' and is now defined in terms of the [[speed of light]]. The ''[[centimetre]]'' and the ''[[kilometre]]'', derived from the metre, are also commonly used units. In [[U.S. customary units]], English or [[Imperial system of units]], commonly used units of length are the ''[[inch]]'', the ''[[foot (unit of length)|foot]]'', the ''[[yard]]'', and the ''[[mile]]''.
Units used to denote distances in the vastness of space, as in [[astronomy]], are much longer than those typically used on Earth and include the ''[[astronomical unit]]'', the ''[[light-year]]'', and the ''[[parsec]]''.
Units used to denote microscopically small distances, as in [[chemistry]], include the ''micron'' and the ''[[ångström]]''.
== Length of moving rods ==
{{context|section}}
While the length of a resting rod can be measured by direct comparison with a measuring rod, this comparison cannot be performed while the rod is moving. In this case we define its moving length as the distance between its two endpoints at a given instance.
If the [[world line]]s of the two endpoints of the rod expressed in the coordinates of an <math> R \,</math> inertial reference frame are
::<math>\mathbf x_1(t) = (t,x_1(t),y_1(t),z_1(t))\, </math>
and
::<math>\mathbf x_2(t) = (t,x_2(t),y_2(t),z_2(t))\, </math> ,
then the length of the rod in this reference frame at the <math>t \,</math> instance is
::<math>l_R(t) = \sqrt{ \left(x_2(t)-x_1(t)\right)^2 + \left(y_2(t)-y_1(t)\right)^2 + \left(z_2(t)-z_1(t)\right)^2 }.</math>
Since in [[special relativity]] the relation of [[Relativity of simultaneity|simultaneity]] depends on the chosen frame of reference, the length of moving rods also depends.
== See also ==
*[[Distance]]
*[[Dimension]]
*[[Orders of magnitude (length)]]
* [http://www.howround.com/ How round is your circle?] Contains a chapter giving the history of length and angle measurement.
*[[Smoot]]
[[Category:Length|Length]]
[[ar:طول]]
[[zh-min-nan:Tn̂g-té]]
[[be-x-old:Даўжыня]]
[[ca:Longitud (física)]]
[[cs:Délka]]
[[cy:Hyd]]
[[da:Længde]]
[[de:Längenmaß]]
[[et:Pikkus]]
[[el:Μήκος]]
[[eo:Longo]]
[[fr:Longueur]]
[[ko:길이]]
[[hr:Duljina]]
[[ia:Longitude]]
[[is:Lengd]]
[[it:Lunghezza]]
[[he:אורך]]
[[la:Longitudo]]
[[lv:Garums]]
[[hu:Hossz]]
[[ms:Panjang]]
[[nl:Lengte (meetkunde)]]
[[ja:長さ]]
[[no:Lengde]]
[[pt:Comprimento]]
[[ro:Lungime]]
[[qu:Karu kay]]
[[ru:Длина]]
[[sq:Gjatësia]]
[[simple:Length]]
[[sl:Dolžina]]
[[sr:Дужина]]
[[fi:Pituus]]
[[sv:Längd]]
[[ta:நீளம்]]
[[th:มาตราวัดความยาว]]
[[vi:Chiều dài]]
[[tr:Uzunluk birimleri]]
[[uk:Довжина]]
[[yi:לענג]]
[[zh:长度]]