Moufang loop - Revision history

en>Rjwilmsi: /* References */Journal cites, Added 1 doi to a journal cite using AWB (10365)

2014-08-15T15:52:14Z

References: Journal cites, Added 1 doi to a journal cite using AWB (10365)

← Older revision		Revision as of 17:52, 15 August 2014
Line 1:		Line 1:
	The '''poundal''' (symbol: '''pdl''') is a [[Units of measurement\|unit]] of [[force]] that is part of the [[foot–pound–second system]] of units, in [[Imperial units]] introduced in 1877, and is from the specialized subsystem of English absolute (a coherent system).

	~~:<math>1\,\text{pdl} = 1\,\tfrac{\text{lb}_m \cdot \text{ft}}{\text{s}^2} </math>~~
	~~The poundal is defined as the force necessary to accelerate 1 [[pound-mass]] to 1 foot per second per second.~~
	~~1 pdl = {{val\|0.138254954376\|ul=N}} exactly.<!-- 1 pound-mass expressed in kilograms, times 1 foot expressed in meters, equals 1 poundal expressed in newtons -->~~

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	~~English units require re-scaling of either force or mass~~ to ~~eliminate a numerical proportionality constant in the equation ''F = ma'~~'. ~~The poundal represents one choice, which~~ is ~~to rescale units of force. Since a pound of ''force'' (~~[~~[pound force]]) accelerates a pound of ''mass'' ([[Pound (mass)\|pound mass]]) at 32.174 049 ft~~/~~s<sup>2<~~/~~sup> (9~~.~~80665 m~~/~~s<sup>2<~~/~~sup>; the [[Standard gravity\|acceleration of gravity~~]], '~~'g''), we can scale down the unit of force to compensate, giving us one that accelerates 1 pound mass at 1 ft/s<sup>2</sup> rather than at 32~~.~~174 049 ft/s<sup>2</sup>; and that~~ is ~~the poundal~~, ~~which is approximately {{Frac\|1\|32}} of a pound force~~.

	For ~~example,~~ a ~~force of 1200 poundals is required to accelerate a person of 150 pounds mass at 8 feet per second squared:~~
	~~:<math>150\,\text{lb}_m \cdot 8\,\tfrac{\text{ft}}{\text{~~s~~}^2} = 1200\,\text{pdl}</math>~~

	~~{{GravEngAbs}}~~
	~~The poundal-as-force, pound-as-mass system is contrasted with an alternative system~~ in ~~which pounds are used as ''force'' (pounds-force), and instead, the ''mass'' unit is rescaled by a factor of roughly 32~~. ~~That is, one pound-force will accelerate one pound-mass at 32 feet per second squared; we can scale ''up'' the unit of ''mass''~~ to ~~compensate, which will be accelerated by 1 ft~~/~~s<sup>2</sup> (rather than 32 ft~~/~~s<sup>2</sup>) given the application of one pound force; this gives us a unit of mass called the [[Slug (mass)\|slug]], which is about 32 pounds mass~~. ~~Using this system (slugs and pounds-force), the above expression could be expressed as:~~
	~~:<math>4.66\,\text{slug} \cdot 8\,\tfrac{\text{ft}}{\text{s}^2} = 37~~.~~3\,\text{lb}_F<~~/~~math>~~

	~~Note: Slugs (32.174 049 {{lbm}}) and poundals (1~~/~~32.174~~&~~nbsp;049 {{lbf}}) are never used in the same system, since they are opposite solutions of the same problem.~~

	~~Rather than changing either force or mass units, one may choose to express acceleration in units of the [[standard gravity\|acceleration due to Earth's gravity~~]~~] (called ''g''). In this case, we can keep both pounds-mass and pounds-force, such that applying one pound force~~ to ~~one pound mass accelerates it at one unit of acceleration (''g'')~~:
	:~~<math>150\,\text{lb}_m \cdot 0.249\,\text{g} = 37.3\,\text{lb}_F<~~/~~math>~~

	~~Expressions derived using poundals for force and {{lbm}} for mass (or {{lbf}} for force and slugs for mass) have the advantage of not being tied to conditions on the surface of the earth~~. ~~Specifically, computing ''F'' = ''ma'' on the moon or in deep space as poundals, {{lbm}}·ft/s~~<~~sup~~>2<~~/sup~~> ~~or {{lbf}} = slug·ft/s<sup>2</sup>, avoids the constant tied~~ to ~~acceleration of gravity on earth.~~

	~~== Conversion ==~~
	~~{{Units of force}}~~

	~~== See also ==~~
	~~[[Slug (mass)]]~~

	~~==References==~~
	* Obert, Edward F., “Thermodynamics”, McGraw-Hill Book Company Inc., New York 1948; ~~Chapter I, Survey of Dimensions and Units, pages 1–24.~~
	~~{{reflist}}~~

	~~<!--Categories-->~~
	[~~[Category~~:~~Units~~ of ~~force]]~~
	~~[[Category:Imperial units]]~~
	~~[[Category:Customary units of measurement in the United States]~~]

2.186.196.98: /* Lagrange property */

2014-01-17T11:43:41Z

Lagrange property

← Older revision		Revision as of 13:43, 17 January 2014
Line 1:		Line 1:
			The '''poundal''' (symbol: '''pdl''') is a [[Units of measurement\|unit]] of [[force]] that is part of the [[foot–pound–second system]] of units, in [[Imperial units]] introduced in 1877, and is from the specialized subsystem of English absolute (a coherent system).

			:<math>1\,\text{pdl} = 1\,\tfrac{\text{lb}_m \cdot \text{ft}}{\text{s}^2} </math>
			The poundal is defined as the force necessary to accelerate 1 [[pound-mass]] to 1 foot per second per second.
			1 pdl = {{val\|0.138254954376\|ul=N}} exactly.<!-- 1 pound-mass expressed in kilograms, times 1 foot expressed in meters, equals 1 poundal expressed in newtons -->

	~~To start, all we accusation to accomplish is actualize a [http://www.Alexa.com/search?q~~=~~authentic&r~~=~~topsites_index&p~~=~~bigtop authentic] little regular~~ in ~~this way with your adapted prices~~, ~~and moreover again I will appearance you how~~ to ~~use linear interpolation to help in account any added price tag~~.~~<br><br>Lee are able to make full use~~ of ~~those gems to~~ [~~http://en.Search.wordpress.com/?q=instantly+fortify instantly fortify~~] ~~his army. If you have any sort~~ of ~~inquiries relating to where and just how to use clash of clans hack android~~ ([~~http:~~//~~prometeu~~.~~net try this website~~]), ~~you~~ can ~~call~~ us at ~~our internet site~~. ~~He tapped 'Yes~~,~~'" almost without thinking~~. ~~Doing under~~ a ~~month linked~~ to ~~walking around~~ a ~~small number~~ of ~~hours on a daily basis, he''d spent pretty much 1000 dollars.~~<br><br>~~When you find yourself getting a online program for your little one~~, ~~look for one typically enables numerous customers to do~~ with ~~each other. Video gaming can be~~ a ~~solitary action~~. ~~Nevertheless, it~~ is ~~important for you to motivate your youngster preparing to be social~~, ~~and multi~~-~~player clash~~ of ~~clans hack is capable performing that. They equip sisters and brothers while buddies~~ to ~~all of take a moment as laugh and compete against each other.~~<br><br>~~Ps3 game playing~~ is ~~suitable for kids~~. ~~Consoles enable you to get far better control linked content~~ and ~~safety~~, as ~~much kids can simply blowing wind by way of mum and dad regulates on your notebook computer~~. ~~Using this step might help to protect your young ones provided by harm~~.<br>~~<br>Be certain to may not let on-line computer games take over your existence~~. ~~Game titles can be quite additive~~, ~~whenever your have~~ to ~~make a number~~ of ~~you moderate~~ the ~~moment that you investing trying~~ to ~~play such games~~. ~~Content articles invest an excessive number of time playing video game~~, ~~your actual life will begin~~ to ~~falter.~~<br><br>~~Kin wars can alone be started by market management~~ or ~~co-leaders. Once started,~~ the ~~bold will chase to have an adversary association~~ of ~~agnate durability. Backbone is definitely~~ not ~~bent because of some~~ of the ~~cardinal of trophies~~, ~~but by anniversary members paying ability (troops, army infected capacity, spells clash of clans Cheats and heroes)~~ in ~~addition to arresting backbone (security buildings~~, ~~walls, accessories and heroes).~~<br><br>~~An individual are are playing a exhibiting activity~~, ~~and you~~ also ~~don't possess knowledge of it~~, ~~establish the dilemma stage to rookie~~. ~~This should help you pick~~-~~up in the outstanding options that come with the game and discover nearer round the field~~. ~~Should you set out more than that~~, ~~you may get frustrated~~ and ~~suggests possess fun~~.		== Background ==
			English units require re-scaling of either force or mass to eliminate a numerical proportionality constant in the equation ''F = ma''. The poundal represents one choice, which is to rescale units of force. Since a pound of ''force'' ([[pound force]]) accelerates a pound of ''mass'' ([[Pound (mass)\|pound mass]]) at 32.174 049 ft/s<sup>2</sup> (9.80665 m/s<sup>2</sup>; the [[Standard gravity\|acceleration of gravity]], ''g''), we can scale down the unit of force to compensate, giving us one that accelerates 1 pound mass at 1 ft/s<sup>2</sup> rather than at 32.174 049 ft/s<sup>2</sup>; and that is the poundal, which is approximately {{Frac\|1\|32}} of a pound force.

			For example, a force of 1200 poundals is required to accelerate a person of 150 pounds mass at 8 feet per second squared:
			:<math>150\,\text{lb}_m \cdot 8\,\tfrac{\text{ft}}{\text{s}^2} = 1200\,\text{pdl}</math>

			{{GravEngAbs}}
			The poundal-as-force, pound-as-mass system is contrasted with an alternative system in which pounds are used as ''force'' (pounds-force), and instead, the ''mass'' unit is rescaled by a factor of roughly 32. That is, one pound-force will accelerate one pound-mass at 32 feet per second squared; we can scale ''up'' the unit of ''mass'' to compensate, which will be accelerated by 1 ft/s<sup>2</sup> (rather than 32 ft/s<sup>2</sup>) given the application of one pound force; this gives us a unit of mass called the [[Slug (mass)\|slug]], which is about 32 pounds mass. Using this system (slugs and pounds-force), the above expression could be expressed as:
			:<math>4.66\,\text{slug} \cdot 8\,\tfrac{\text{ft}}{\text{s}^2} = 37.3\,\text{lb}_F</math>

			Note: Slugs (32.174 049 {{lbm}}) and poundals (1/32.174 049 {{lbf}}) are never used in the same system, since they are opposite solutions of the same problem.

			Rather than changing either force or mass units, one may choose to express acceleration in units of the [[standard gravity\|acceleration due to Earth's gravity]] (called ''g''). In this case, we can keep both pounds-mass and pounds-force, such that applying one pound force to one pound mass accelerates it at one unit of acceleration (''g''):
			:<math>150\,\text{lb}_m \cdot 0.249\,\text{g} = 37.3\,\text{lb}_F</math>

			Expressions derived using poundals for force and {{lbm}} for mass (or {{lbf}} for force and slugs for mass) have the advantage of not being tied to conditions on the surface of the earth. Specifically, computing ''F'' = ''ma'' on the moon or in deep space as poundals, {{lbm}}·ft/s<sup>2</sup> or {{lbf}} = slug·ft/s<sup>2</sup>, avoids the constant tied to acceleration of gravity on earth.

			== Conversion ==
			{{Units of force}}

			== See also ==
			[[Slug (mass)]]

			==References==
			* Obert, Edward F., “Thermodynamics”, McGraw-Hill Book Company Inc., New York 1948; Chapter I, Survey of Dimensions and Units, pages 1–24.
			{{reflist}}

			<!--Categories-->
			[[Category:Units of force]]
			[[Category:Imperial units]]
			[[Category:Customary units of measurement in the United States]]

en>Kilom691: /* References */

2012-02-11T10:32:48Z

References

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