
vrittakar gati

bhautiki mein, vrittakar gati ack vritt kii paridhi key saath yaa ack vrittakar path key saath ack vastu kii gati haye. yeh ack samaan hoe sakata haye, ghoornan kii nirantar koniya darr aur nirantar gati key saath, yaa ghoornan kii badalati darr key saath gair-samaan hoe sakata haye. tri-ayami pind key ack nishchit aksh key chaaron or ghoornan mein usake bhaagon kii golakar gati shamil hoti haye. gati key sameekaran kissy vastu key dravyamaan key kendra kii gati kaa varnan karate hain. vrittakar gati mein, shareer aur satah parr ack nishchit bindu key beach kii doori samaan rahati haye.
vrittakar gati key udaharanon mein shamil hainh ack kritrim upgrah joe prithvi kii nirantar oonchaai parr parikrama curr rhaa haye, ack chhat key pankhe key blade ack kendra key chaaron or ghoom rahey hain, ack patthar joe ack russie seey bandha huaa haye aur vritton mein ghoom rhaa haye, ack kaar ack daud track mein ack vakr seey gujarati haye, ack samaan chumbakiya kshetra key lambavat chalane vaalaa ack electron, aur ack tantra key ander ack gear ghoomata haye.
choonki vastu kaa wegg sadish lagaatar disha badal rhaa haye, isaliye gatishil vastu ghoornan key kendra kii disha mein ack kendragami bull dwara twaran seey gujar rahee haye. iss twaran key binaa, vastu ack seedhi rekha mein aage badhegi, neuton key gati key niyamon key anusaar.
ack samaan vrittakar gati.
bhautiki mein, ack samaan vrittakar gati ack sthir gati seey ack golakar path seey gujarane vaale shareer kii gati kaa varnan karati haye. choonki shareer vrittakar gati kaa varnan kartaa haye, isaliye ghoornan kii dhuri seey isaki doori harr samay sthir rahati haye. yadyapi shareer kii gati sthir haye, lekin iska wegg sthir naheen haih wegg, ack sadish matra, shareer kii gati aur isaki yatra kii disha donon parr nirbhar karati haye. yeh badalata wegg ack twaran kii upasthiti koo ingit kartaa haye; yeh kendragami twaran sthir parimaan kaa hotaa haye aur harr samay ghoornan kii dhuri kii or nirdeshit hotaa haye. yeh twaran, badale mein, ack kendragami bull dwara utpaadit hotaa haye joe parimaan mein bhee sthir hotaa haye aur ghoornan kii dhuri kii or nirdeshit hotaa haye.
ack kathor pind key ack nishchit aksh key chaaron or ghoornan key mamle mein joe path kii trijya kii tulanaa mein nagany roop seey chhota naheen haye, shareer kaa pratyek kann ack hii koniya wegg key saath ack samaan golakar gati kaa varnan kartaa haye, lekin wegg aur twaran key saath aksh key sambandh mein sthiti key saath bhinn hotaa haye.
sootra.
trijya key vritt mein gati key liye, vritt kii paridhi haye. yadi ack ghoornan kii avadhi haye, tou ghoornan kii koniya darr, jise koniya wegg key roop mein bhee jaanaa jaataa haye, haih
sootra _ 1 aur ikaaiyaan radian/sekand hain.
vritt mein yatra karane vaali vastu kii gati haih
sootra _ 2
ack samay mein bahaaya gayaa konn haih
sootra _ 3
kann kaa koniya twaran haih
sootra _ 4
ack samaan vrittakar gati key mamle mein, shoonya hoga.
disha mein parivartan key kaaran twaran haih
sootra _ 5
kendragami aur kendrapgami bull koo twaran kaa upayog karke bhee paaya jaa sakata haih
sootra _ 6
vector sambandhon koo chitra 1 mein dikhaaya gayaa haye. ghoornan kii dhuri koo kaksha key tala key lambavat aur parimaan key saath ack vector key roop mein dikhaaya gayaa haye. disha koo daahine haath key niyam kaa upayog karke chunaa jaataa haye. ghoornan koo darshaane key liye iss parampara key saath, wegg ack sadish cross utpaad dwara diyaa jaataa haye
sootra _ 7
joe donon key liye ack sadish lambavat haye aur, kaksha key liye sparshrekha, aur parimaan kaa. isi tarah, twaran dwara diyaa jaataa haye
sootra _ 8
joe donon key liye aur parimaan key liye lambavat ack sadish haye aur isake bilkul vipareet nirdeshit haye.
sabse saral mamle mein gati, dravyamaan aur trijya sthir hain.
ack kilogram key ack shareer parr vichaar karein, joe ack meater trijya key vritt mein ack radian prati sekand key koniya wegg key saath aage badh rhaa haye.
dhruviya nirdeshank mein.
vrittakar gati key dauran, shareer ack vakr parr chalata haye jise dhruviya nirdeshank pranali mein mool key roop mein lii gaee kaksha key kendra seey ack nishchit doori key roop mein varnit kiya jaa sakata haye, joe kuchh sandarbh disha seey ack konn parr unmukh haye. chitra 4 dekhein. visthaapan "sadish" sootra _ 9 mool seey kann sthaan taka radial sadish haih
sootra _ 10
jahan sootra _ 11 samay parr trijya sadish key samanantar ikai sadish haye aur mool seey door ingit kartaa haye. ikai sadish orthogonal koo sootra _ 11 key saath-saath sootra _ 13 mein bhee shamil karna suvidhajanak haye. yeh sootra _ 13 koo kaksha key saath yatra kii disha mein ingit karane key liye unmukh karane kii pratha haye.
wegg visthaapan kaa samay vyutpann haih
sootra _ 15
kyonki vritt kii trijya sthir haye, wegg kaa radial ghatak shoonya haye. ikai sadish sootra _ 11 mein ekataa kaa ack samay-parivartansheel parimaan hotaa haye, isaliye jaise-jaise samay badalata haye, isaki noke hamesha ikai trijya key ack vritt parr hoti haye, ack konn key saath sootra _ 17 key konn key samaan hotaa haye. yadi kann visthaapan samay mein ack konn key madhyam seey ghoomata haye, tou sootra _ 11 bhee kartaa haye, joe parimaan key ikai vritt parr ack chaap kaa varnan kartaa haye. aakriti 4 key baain or ikai vritt dekhein. isalieh
sootra _ 19
jahan parivartan kii disha sootra _ 11 (yaa, dusare shabdon mein, sootra _ 13 key saath) key lambavat honey chaahiye kyonki sootra _ 11 kii disha mein koee bhee parivartan sootra _ 22 sootra _ 11 key aakar koo badal dega. sanket sakaratmak haye kyonki vriddhi kaa tatparya vastu aur sootra _ 11 sootra _ 13 kii disha mein chaley gaye hain.
isaliye wegg bunn jaataa haih
sootra _ 27
shareer key twaran koo radial aur sparshrekha ghatakon mein bhee vibhajit kiya jaa sakata haye. twaran wegg kaa samay vyutpann haih
sootra _ 28
sootra _ 13 kaa samay vyutpann sootra _ 11 key samaan paaya jaataa haye. phir seey, sootra _ 13 ack ikai sadish haye aur isaki noke ack konn key saath ack ikai vritt kaa pataa lagaati haye. isaliye, sootra _ 17 dwara konn mein vriddhi kaa tatparya haye sootra _ 13 parimaan key ack chaap kaa pataa lagaata haye, aur sootra _ 13 sootra _ 11 key liye orthogonal haye, hamaare paas haih
sootra _ 36
jahan sootra _ 13 koo sootra _ 11 key orthogonal rakhane key liye ack nakaratmak sanket aavashyak haye. (anyatha, sootra _ 13 aur sootra _ 11 key beach kaa konn vriddhi key saath "cumm" hoe jaayega.) aakriti 4 key baain or ikai vritt dekhein. isake parinamswarup, twaran haih
sootra _ 41
madhyavarti twaran radial ghatak haye, joe radial roop seey ander kii or nirdeshit hotaa haih
sootra _ 42
jabaki sparshrekha ghatak wegg key parimaan koo badalata haih
sootra _ 43
jatil sankhyaon kaa upayog karna.
vrittakar gati koo jatil sankhyaon kaa upayog karke varnit kiya jaa sakata haye. maan leejiye kii aksh vaastavik aksh haye aur sootra _ 44 kaalpanik aksh haye. shareer kii sthiti koo phir sootra _ 45 key roop mein diyaa jaa sakata haye, ack jatil "vector":
sootra _ 46
jahan kaalpanik ikai haye, aur sootra _ 47 samay key falan key roop mein jatil sankhya kaa tark haye.
kyonki trijya sthir haih
sootra _ 48
jahan ack "bindu" samay key sambandh mein antar koo ingit kartaa haye.
iss sanketan key saath, wegg bunn jaataa haih
sootra _ 49
aur twaran bunn jaataa haih
sootra _ 50
pahala pada visthaapan sadish key vipareet disha mein haye aur doosara isake lambavat haye, thheek pahale dikhaae gaye parinamon kii tarah.
wegg.
aakriti 1 kaksha mein chaar alag-alag binduon parr samaan gati key liye wegg aur twaran vactor koo darshaata haye. kyonki wegg vrittakar path key liye sparshrekha haye, koee dou wegg ack hii disha mein naheen hain. yadyapi vastu kii gati sthir rahati haye, lekin usaki disha hamesha badalati rahati haye. wegg mein yeh parivartan ack twaran key kaaran hotaa haye, jiska parimaan (wegg kii tarah) sthir rahata haye, lekin jisaki disha bhee hamesha badalati rahati haye. twaran bindu trijya roop seey ander kii or (kendragami) aur wegg key lambavat haye. iss twaran koo kendragami twaran key roop mein jaanaa jaataa haye.
trijya key path key liye, jaba ack konn beh jaataa haye, tou kaksha kii paridhi parr yatra kii gaee doori hoti haye. isaliye, kaksha key chaaron or yatra kii gati haye
sootra _ 51
jahan ghoornan kii koniya darr haye. (punarvyavastha dwara,.) iss prakaar, ack sthiraank haye, aur wegg sadish bhee usee koniya darr parr sthir parimaan key saath ghoomata haye.
saapeksh vrittakar gati.
iss mamle mein, teen-twaran sadish teen-wegg sadish key lambavat haye,
sootra _ 52
aur uchit twaran kaa varg, ack scalar aparivartaniya key roop mein vyakt kiya gayaa, sabhi sandarbh frames mein samaan,
sootra _ 53
vrittakar gati key liye abhivyakti bunn jaati haye,
sootra _ 54
yaa, sakaratmak vargamool lete hue aur teen-twaran kaa upayog karate hue, humm vrittakar gati key liye uchit twaran parr pahunchate hainh
sootra _ 55
twaran.
aakriti 2 mein baaen haath kaa vritt dou aasann samay parr wegg vactors koo dikhaane vaali kaksha haye. daaeen or, inn dou vegon koo sthanantarit kiya jaataa haye taaki unaki poonchh mell khaati haye. kyonki gati sthir haye, daaeen or key wegg vactor samay key badhane key saath ack vritt koo baahar nikaalate hain. ack swept konn key liye parivartan samkon aur parimaan parr ack vector haye, jiska arth haye kii twaran kaa parimaan iss prakaar diyaa jaataa haye -
sootra _ 56
gair-vardi.
ack samaan vrittakar gati mein, ack vastu ack alag gati key saath ack vrittakar path mein aage badh rahee haye. choonki gati badal rahee haye, isaliye samanya twaran key alawa sparshrekha twaran bhee haye.
ack samaan vrittakar gati mein, shuddh twaran (aeye) kii disha key saath hotaa haye, joe vritt key ander nirdeshit hotaa haye lekin isake kendra seey naheen gujarta haye (aakriti dekhein). shuddh twaran koo dou ghatakon mein hull kiya jaa sakata haih sparshrekha twaran aur samanya twaran jise kendragami yaa radial twaran key roop mein bhee jaanaa jaataa haye. sparshrekha twaran key vipareet, kendragami twaran samaan aur gair-samaan vrittakar gati donon mein maujood haye.
ack samaan vrittakar gati mein, samanya bull hamesha vajan kii vipareet disha mein naheen hotaa haye. yahaan ack udaaharan haye jisamen ack vastu ack seedhe raaste mein yatra curr rahee haye aur phir ack loop koo phir seey ack seedhe raaste mein vaapas loop curr rahee haye.
yeh aarekh vajan bull key vipareet key bajaay anya dishaaon mein ingit samanya bull koo darshaata haye. samanya bull vaastav mein radial aur sparshrekha balon kaa yog haye. bhaar bull kaa ghatak yahaan sparshrekha bull key liye jimmedaar haye (hamane gharshan bull kii upeksha kii haye). radial bull (kendragami bull) wegg kii disha mein parivartan key kaaran hotaa haye jaisa kii pahale charcha kii gaee thee.
ack samaan vrittakar gati mein, samanya bull aur vajan ack hii disha mein ingit hoe sakate hain. donon bull neeche kii or ishara curr sakate hain, phir bhee vastu seedhe neeche gire binaa ack golakar path mein rahegi. pahale, aaie dekhein kii samanya bull pahale sthaan parr kyon neeche kii or ishara curr sakata haye. pahale aarekh mein, maan leejiye kii vastu ack samtal key ander baithaa huaa vyakti haye, donon bull kewal taba neeche kii or ishara karate hain jaba yeh vritt key sheersh taka pahunchata haye. iska kaaran yeh haye kii samanya bull sparshrekha bull aur kendragami bull kaa yog haye. sparshrekha bull sheersh parr shoonya hotaa haye (kyonki jaba gati lagu bull kii disha key lambavat hoti haye tou koee kaary naheen kiya jaataa haye. yahaan bhaar bull vritt key sheersh parr vastu kii gati kii disha key lambavat haye) aur kendragami bull neeche kii or haye, iss prakaar samanya bull bhee neeche kii or ingit karega. taarkik drishtikon seey, ack vyakti joe vimaan mein yatra curr rhaa haye, vaha vritt key sheersh parr ulta hoga. usa samay, vyakti kii seat vaastav mein vyakti parr neeche dhakel rahee haye, joe samanya bull haye.
kewal neeche kii or kii taakton key adheen honey parr vastu key neeche naa girane kaa kaaran ack saral kaaran haye. iss baare mein sochein kii kissy vastu koo fenkane key baad kyaa usey oopar rakhta haye. ack baar jaba kissy vastu koo havaa mein fenk diyaa jaataa haye, tou prithvi key gurutvaakarshan kaa kewal neeche kii or bull hotaa haye joe vastu parr kaary kartaa haye. iska matlab yeh naheen haye kii ack baar jaba koee vastu havaa mein fenk dee jaati haye, tou vaha turant gir jaayegi. joe usa vastu koo havaa mein oopar rakhta haye vaha haye uska wegg. neuton key gati key niyamon mein seey pahala kahata haye kii ack vastu kii jadata ise gati mein rakhti haye, aur choonki havaa mein vastu kaa wegg hotaa haye, isaliye yeh usa disha mein aage badhata rahega.
ack golakar path mein chalane vaali vastu key liye ack alag koniya gati bhee praapt kii jaa sakati haye yadi ghoornan shareer mein ack sajaatiya dravyamaan vitaran naheen haye. asamaroop vastuon key liye, samasya key saath sampark karna aavashyak haye.
anuprayog.
gair-samaan vrittakar gati seey nipatane vaale anuprayogon koo hull karane mein bull vishleshan shamil haye. ack samaan vrittakar gati key saath, ack vritt mein yatra karane vaali vastu parr kaary karane vaalaa ekmatra bull kendragami bull haye. ack gair-samaan vrittakar gati mein, ack gair-shoonya sparshrekha twaran key kaaran vastu parr kaary karane vaale atirikt bull hotey hain. yadyapi vastu parr kaary karane vaale atirikt bull hain, lekin vastu parr kaary karane vaale sabhi balon kaa yog kendragami bull key barabar honah chaahiye.
sootra _ 57
kull bull kii ganana karate samay radial twaran kaa upayog kiya jaataa haye. sparshrekha twaran kaa upayog kull bull kii ganana mein naheen kiya jaataa haye kyonki yeh vastu koo golakar path mein rakhane key liye jimmedaar naheen haye. kissy vastu koo vritt mein chalane key liye jimmedaar ekmatra twaran radial twaran haye. choonki sabhi balon kaa yog kendragami bull haye, isaliye ack mukt shareer aarekh mein kendragami bull kheenchana aavashyak naheen haye aur aamtaur parr isaki anushansa naheen kii jaati haye.
sootra _ 58 kaa upayog karke, humm ack vastu parr kaary karane vaale sabhi balon koo soochibaddh karane key liye mukt shareer aarekh banaa sakate hain aur phir ise sootra _ 59 key barabar sett curr sakate hain. baad mein, humm joe kuchh bhee agyaat haye usake liye hull curr sakate hain (yeh dravyamaan, wegg, vakrata kii trijya, gharshan kaa gunank, samanya bull, aadi hoe sakata haye.). udaaharan key liye, ardhvritt key sheersh parr ack vastu koo dikhaane vaale uparokt drishya koo sootra _ 60 key roop mein vyakt kiya jaayega.
ack samaan vrittakar gati mein, ack vrittakar path mein ack vastu kaa kull twaran radial twaran key barabar hotaa haye. ack gair-samaan vrittakar gati mein sparshrekha twaran kii upasthiti key kaaran, joe abb aur sahee naheen haye. ack samaan vrittakar mein kissy vastu key kull twaran kaa pataa lagaane key liye, sparshrekha twaran aur radial twaran kaa sadish yog gyaat karein.
sootra _ 61
radial twaran abhee bhee sootra _ 62 key barabar haye. sparshrekha twaran kewal kissy bhee diye gaye bindu parr gati kaa vyutpann haih sootra _ 63. alag radial aur sparshrekha twaran key vargon kaa yeh mool yog kewal golakar gati key liye sahee haye; dhruviya nirdeshank sootra _ 64 key saath ack tala key bheetar samanya gati key liye, coriolis shabd sootra _ 65 koo sootra _ 66 mein jodaa jaanaa chaahiye, jabaki radial twaran taba sootra _ 67 bunn jaataa haye.

