748:
idea to justify our analysis. A formula might be right in situation A, and if it is, then it should be right for any consistent system of units. But why should that rightness tell me anything about situation B? Why should a theory of arbitrary human unit choices lead to a theory that can deduce the speed of a ship from it's scale model? Certainly, two coordinate systems that can be used to describe a game of chess can also be used to describe a game of checkers, but we don't expect to be able to deduce winning strategies of one based on the other just by a coordinate transformation. I subscribe to the school of Sonin (2001) and Tolman (1917) that the root of dimensional analysis needs to be with the observation that some physical quantities behave additively -- the whole is the sum of the parts. So, if we break a fly brick in two, the weight of the original brick is equal to the sum of the weights of the two pieces. I believe this was part of Tolman's motivation for defining the concepts of extensive and intensive quantities which are core to thermodynamic theory -- once we have empirically identified extensive quantities, we have a first-principles justification for rescalings like ship-speed extrapolation.
393:
641:
change if the base units were to change in size. This is the essence of the subject as originally considered by
Fourier in his analysis of heat equations. Bridgman says (paraphrasing here) that dimensional analysis has something of the character of an analysis of an analysis. This is the correct view - it is a meta-analysis of the original analysis, asking what must change if the sizes of the base units were to change. And this meta-analysis leads to conclusions about the forms the equations are allowed to take. Simply tracking and converting dimensions and units does not really capture the essence of the subject at all.
169:
159:
135:
31:
544:
383:
362:
278:
257:
89:
64:
473:
288:
22:
807:
Work and energy have the same dimensionality ( ) as do torque and energy (ie: the amount of energy applied in the form of torque does work to increase rotational kinetic energy), so mightn't
Knowledge (XXG) need a better example of two quantities with the same dimensions but which are fundamentally
747:
It is mentioned above that dimensional analysis is a meta-analysis of the relations between quantities, and how they should be related if we change the units we use to measure them. But for me, this puts the cart before the horse. Before we get to the mathematics, we need some empirical, scientific
640:
Even the top-level paragraph introducing this article is somewhat misleading, in my opinion. The essence of dimensional analysis is not really tracking the units and dimensions of quantities in a calculation. This is much too narrow in scope. It has more to do with considering how a calculation must
613:
It is an interesting fact that
Bridgman works primarily with value equations in his seminal reference, yet reaches all the important results just the same. But Bridgman is not mentioned (although he is listed as a reference). Also Bridgman's theorem should be introduced and discussed somewhere - it
606:
I think there is too much emphasis in the article on this relatively routine topic. It would be of great interest to show that the method of algebraic substitution (e.g. 1 yd <= 3 ft) yields equivalent results to the factor-label method. The more important principle is that quantities and units
711:
I am faily new to the idea of dimensional analysis. I will soon be teaching a class for nursing students using diemsional analysis to calculate medication dosages. I guess I thought there might be more information regarding the use of diensional analysis in healthcare. I am so new to this process
511:
is
Knowledge (XXG)'s entry, as of September 2010, and which dismisses the insertion of a dimensioned quantity into the argument of a transcendental function on the basis of the Taylor expansion of these functions (20). The Knowledge (XXG) article argues that the Taylor expansion of transcendental
666:
This article, I think, mixes 'unit conversion' with what I would call dimensional analysis; specifically resolving a physical situation to M L T N etc. I think it needs splitting into two - I'm not
Knowledge (XXG) savvy enough to do it - but it is a poor article at prrsent
607:
are subject to the rules of algebra, including substitution and cancellation, i.e. quantity calculus. Quantity calculus needs to be mentioned as a pre-requisite topic and referenced near the top of this article, and not just mentioned as a related area at the bottom.
770:"Even when two physical quantities have identical dimensions, it may nevertheless be meaningless to compare or add them. For example, although torque and energy share the dimension T−2L2M, they are fundamentally different physical quantities."
35:
854:
629:
What you say makes sense. The sections on the factor-label method could be trimmed down to a fraction of its current content. At present, it reads a bit like an example sheet for a junior school class.
239:
674:
864:
844:
904:
859:
614:
is the only important theorem of dimensional analysis, besides
Buckingham's pi theorem. In his book he proves his theorem first, then uses that result to prove the pi theorem.
909:
524:
449:
344:
839:
884:
874:
334:
229:
899:
439:
191:
889:
849:
310:
727:
What you're looking for can be found in the
Conversion of units page-I'll go make sure that's been properly linked/referenced in the article.
392:
869:
610:
In order to explain this adequately, likely the topic of quantity equations must be introduced, and perhaps contrasted with value equations.
215:
512:
functions leads to terms of different dimensions that cannot be added or subtracted (rule 1), and hence, the argument cannot be dimensioned.
415:
182:
140:
95:
69:
879:
812:
561:
557:
678:
492:"Can One Take the Logarithm or the Sine of a Dimensioned Quantity or a Unit? Dimensional Analysis Involving Transcendental Functions"
301:
262:
894:
406:
367:
834:
44:
293:
591:
481:
570:
753:
50:
816:
732:
670:
100:
74:
646:
619:
749:
697:
414:
on
Knowledge (XXG). If you would like to participate, please visit the project page, where you can join
309:
on
Knowledge (XXG). If you would like to participate, please visit the project page, where you can join
190:
on
Knowledge (XXG). If you would like to participate, please visit the project page, where you can join
168:
712:
that I really dont even know what to ask. I was looking for help but did not find it in this article.
642:
615:
21:
689:
728:
717:
656:
Agreed. If you (or others) are feeling energetic, a complete rewrite would not be a bad idea. —
576:
518:
174:
158:
134:
657:
631:
221:
693:
572:
543:
398:
828:
713:
277:
256:
574:
491:
382:
361:
187:
820:
757:
736:
721:
701:
682:
660:
650:
634:
623:
88:
63:
472:
388:
283:
164:
306:
287:
411:
490:
Cherif F. Matta, Lou Massa, Anna V. Gubskaya, and Eva Knoll (2011).
577:
537:
467:
224:
in the banner shell. Please resolve this conflict if possible.
220:
This article has been given a rating which conflicts with the
15:
855:
Knowledge (XXG) level-5 vital articles in Physical sciences
410:, a collaborative effort to improve the coverage of
305:, a collaborative effort to improve the coverage of
186:, a collaborative effort to improve the coverage of
845:
Knowledge (XXG) vital articles in Physical sciences
773:In light of the Work-Kinetic Theory for Rotation:
688:I went ahead and moved the offending section into
865:B-Class articles with conflicting quality ratings
509:that nevertheless reaches the correct conclusion
98:, a project which is currently considered to be
910:Knowledge (XXG) pages referenced by the press
585:This page has archives. Sections older than
8:
523:: CS1 maint: multiple names: authors list (
905:C-Class physics articles of High-importance
860:C-Class vital articles in Physical sciences
668:
356:
251:
129:
58:
358:
253:
200:Knowledge (XXG):WikiProject Mathematics
131:
110:Knowledge (XXG):WikiProject Measurement
60:
19:
840:Knowledge (XXG) level-5 vital articles
707:Dimensional analysis use in healthcare
595:when more than 4 sections are present.
516:
675:2A00:23C4:1594:E600:D52:B352:BBAD:C28
319:Knowledge (XXG):WikiProject Economics
7:
404:This article is within the scope of
299:This article is within the scope of
180:This article is within the scope of
94:This article is within the scope of
424:Knowledge (XXG):WikiProject Physics
49:It is of interest to the following
222:project-independent quality rating
14:
885:Low-importance Economics articles
875:Mid-priority mathematics articles
589:may be automatically archived by
482:mentioned by a media organization
900:High-importance physics articles
542:
507:An example of a flawed argument
471:
391:
381:
360:
286:
276:
255:
203:Template:WikiProject Mathematics
167:
157:
133:
113:Template:WikiProject Measurement
87:
62:
29:
20:
444:This article has been rated as
339:This article has been rated as
234:This article has been rated as
890:WikiProject Economics articles
850:C-Class level-5 vital articles
758:18:40, 11 September 2023 (UTC)
322:Template:WikiProject Economics
1:
496:Journal of Chemical Education
418:and see a list of open tasks.
313:and see a list of open tasks.
294:Business and economics portal
194:and see a list of open tasks.
870:B-Class mathematics articles
821:00:06, 20 January 2024 (UTC)
683:16:03, 29 January 2021 (UTC)
427:Template:WikiProject Physics
702:00:33, 29 August 2022 (UTC)
926:
880:C-Class Economics articles
450:project's importance scale
345:project's importance scale
767:The article text states:
722:20:38, 5 March 2023 (UTC)
661:16:24, 27 July 2020 (UTC)
651:15:10, 27 July 2020 (UTC)
635:13:02, 23 July 2020 (UTC)
624:03:09, 23 July 2020 (UTC)
443:
376:
338:
271:
233:
219:
152:
82:
57:
895:C-Class physics articles
763:A better example needed?
737:16:54, 29 May 2023 (UTC)
240:project's priority scale
602:The Factor-Label Method
183:WikiProject Mathematics
96:WikiProject Measurement
835:C-Class vital articles
592:Lowercase sigmabot III
480:This article has been
302:WikiProject Economics
43:on Knowledge (XXG)'s
36:level-5 vital article
743:Extensive quantities
206:mathematics articles
116:Measurement articles
690:Conversion of units
407:WikiProject Physics
325:Economics articles
175:Mathematics portal
45:content assessment
808:not comparable?
685:
673:comment added by
599:
598:
536:
535:
464:
463:
460:
459:
456:
455:
355:
354:
351:
350:
250:
249:
246:
245:
128:
127:
124:
123:
917:
594:
578:
546:
538:
528:
522:
514:
504:
502:
475:
468:
432:
431:
430:physics articles
428:
425:
422:
401:
396:
395:
385:
378:
377:
372:
364:
357:
327:
326:
323:
320:
317:
296:
291:
290:
280:
273:
272:
267:
259:
252:
208:
207:
204:
201:
198:
177:
172:
171:
161:
154:
153:
148:
145:
137:
130:
118:
117:
114:
111:
108:
91:
84:
83:
78:
66:
59:
42:
33:
32:
25:
24:
16:
925:
924:
920:
919:
918:
916:
915:
914:
825:
824:
765:
745:
709:
604:
590:
579:
573:
551:
532:
531:
515:
500:
498:
489:
485:
446:High-importance
429:
426:
423:
420:
419:
397:
390:
371:High‑importance
370:
324:
321:
318:
315:
314:
292:
285:
265:
205:
202:
199:
196:
195:
173:
166:
146:
143:
115:
112:
109:
106:
105:
72:
40:
30:
12:
11:
5:
923:
921:
913:
912:
907:
902:
897:
892:
887:
882:
877:
872:
867:
862:
857:
852:
847:
842:
837:
827:
826:
764:
761:
750:Uscitizenjason
744:
741:
740:
739:
708:
705:
664:
663:
638:
637:
603:
600:
597:
596:
584:
581:
580:
575:
571:
569:
566:
565:
553:
552:
547:
541:
534:
533:
530:
529:
486:
479:
478:
476:
462:
461:
458:
457:
454:
453:
442:
436:
435:
433:
416:the discussion
403:
402:
399:Physics portal
386:
374:
373:
365:
353:
352:
349:
348:
341:Low-importance
337:
331:
330:
328:
311:the discussion
298:
297:
281:
269:
268:
266:Low‑importance
260:
248:
247:
244:
243:
232:
226:
225:
218:
212:
211:
209:
192:the discussion
179:
178:
162:
150:
149:
138:
126:
125:
122:
121:
119:
92:
80:
79:
67:
55:
54:
48:
26:
13:
10:
9:
6:
4:
3:
2:
922:
911:
908:
906:
903:
901:
898:
896:
893:
891:
888:
886:
883:
881:
878:
876:
873:
871:
868:
866:
863:
861:
858:
856:
853:
851:
848:
846:
843:
841:
838:
836:
833:
832:
830:
823:
822:
818:
814:
813:76.30.103.137
809:
805:
803:
799:
795:
791:
787:
784:
782:
778:
774:
771:
768:
762:
760:
759:
755:
751:
742:
738:
734:
730:
729:Quantivariate
726:
725:
724:
723:
719:
715:
706:
704:
703:
699:
695:
691:
686:
684:
680:
676:
672:
662:
659:
655:
654:
653:
652:
648:
644:
636:
633:
628:
627:
626:
625:
621:
617:
611:
608:
601:
593:
588:
583:
582:
568:
567:
564:
563:
559:
555:
554:
550:
545:
540:
539:
526:
520:
513:
510:
497:
493:
488:
487:
483:
477:
474:
470:
469:
466:
451:
447:
441:
438:
437:
434:
417:
413:
409:
408:
400:
394:
389:
387:
384:
380:
379:
375:
369:
366:
363:
359:
346:
342:
336:
333:
332:
329:
312:
308:
304:
303:
295:
289:
284:
282:
279:
275:
274:
270:
264:
261:
258:
254:
241:
237:
231:
228:
227:
223:
217:
214:
213:
210:
193:
189:
185:
184:
176:
170:
165:
163:
160:
156:
155:
151:
142:
139:
136:
132:
120:
103:
102:
97:
93:
90:
86:
85:
81:
76:
71:
68:
65:
61:
56:
52:
46:
38:
37:
27:
23:
18:
17:
810:
806:
801:
797:
793:
789:
788:
785:
780:
776:
775:
772:
769:
766:
746:
710:
687:
669:— Preceding
665:
639:
612:
609:
605:
586:
556:
548:
508:
506:
499:. Retrieved
495:
465:
445:
405:
340:
300:
236:Mid-priority
235:
181:
147:Mid‑priority
99:
51:WikiProjects
34:
779:torque = Δ
694:fgnievinski
197:Mathematics
188:mathematics
141:Mathematics
107:Measurement
70:Measurement
829:Categories
783:rotation
643:Antiskid56
616:Antiskid56
519:cite news
316:Economics
307:Economics
263:Economics
39:is rated
798:dω / dt
786:where:
714:MbrsnLyf
671:unsigned
549:Archives
658:Quondum
632:Quondum
587:90 days
448:on the
421:Physics
412:Physics
368:Physics
343:on the
238:on the
144:B‑class
101:defunct
75:defunct
41:C-class
501:23 May
47:scale.
28:This
817:talk
811:~~
796:rot
792:=∫
754:talk
733:talk
718:talk
698:talk
679:talk
647:talk
620:talk
525:link
503:2016
440:High
781:KE_
335:Low
230:Mid
831::
819:)
804:
802:dθ
800:⋅
794:I_
777:W_
756:)
735:)
720:)
700:)
692:.
681:)
649:)
622:)
560:,
521:}}
517:{{
505:.
494:.
815:(
790:W
752:(
731:(
716:(
696:(
677:(
645:(
630:—
618:(
562:2
558:1
527:)
484::
452:.
347:.
242:.
216:B
104:.
77:)
73:(
53::
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
