(формат)Тарг
.pdfPaBeHcTBa (11) BbipaMaiOT ycJIOBIUI paBHOBeciHI B aHaJIIITHqeCKoil
qx>pMe: O.ll.R pasHooecu.R npocmpaHCm8eHrtot1 cucmeMbl cxoO.RU{UXCfl cUA Heo6xoouMo u aocmamottHo, ttmo6bt cyM.Mbl npoetet{ut1 amux cu.11 rta
ayro U3 mpex KOOpouHamHblX ocetl 6bl.llU paBHbl HY/110.
EcJIH Bee p,eHCTBYIOI.IJ.IIe Ha TeJIO CXO,!I,HI.IJ.IIeCll CIIJibl JleMaT B O,n:HOH
nJiocKoCTH, TO OHH o6pa3yiOT n.110cteyro cucmeMy cxooflU{UXCfl cu.11. B cJiy-
qae ITJIOCKOH CIICTeMbl CXOJI:lli.IJ.IIXCll CIIJI noJiyqiiM, OlleBIIJI:HO, TOJibKO ,n:Ba ycJioBIIH paBHoBecrrH:
'1:.Fkx = 0, '1:.Fky = 0. |
(12) |
3. Teo p eM a o T p ex c II .ria x. Dpii pernemm |
3a,n:aq CTilTIIKII |
HHor,n:a y,n:o6Ho nOJib30BaTbCH cJie,n:yiOrn.eii TeopeMoii: ec.11u meepooe me-
.llO 1-laXOOUmCfl 8 paBHOBeCUU no(} (}et1cm8UeM mpex Henapa.ll,1e.llbHblX CU.Il,
.lle:JICaU{UX 8 OOHOU n.llOCKOCmu, rno /lUHUU aeucm8Ufl arnux CU/l nepeceteaIOmCfl 8 ooHot1 motttee.
)l,Tlll Jl:OKa3aTeJibCTBa TeopeMbi paCCMOTpllM CHaqaJia Kaime-HII6y,n:b
,n:Be H3 ,n:eiiCTBYIOI.IJ.llX Ha TeJio cnJI, HarrpHMep F1 n F 2 • TaK KaK rro ycJioBHHM TeopeMbl 3TH CllJlbl JieMaT B O,n:HOH ITJIOCKOCTII ll He napaJIJieJibHbi, TO nx JIIIHHH ,n:eiicTBHll nepeceKaiOTCH B neKoTopoii ToqKe A flpHliOMHM CHJihl F1 H F 2 B 3Toii TOl!Ke II 3aMeHHM nx paBHo,n:eiiCTByiOrn.eii
R. Tor,n:a Ha TeJIO 6y,n:yT ,n:eiicTBOBaTb ,n:Be CHJibi: CIIJia R n cnJia F3 , npHJIOMeHHall B KaiWii-To TOl!Ke B TeJia. Eom TeJio rrpn 3TOM Haxo,n:HTCH B paBHOBeCHH, TO CHJibi R H Fa .ll:OJI:lKHbl 6biTb HanpaBJieHbl ITO O,n:HOif npHMOH, T. e. B,n:OJib AB. CJie,n:oBaTeJibHO, JIHHHH ,n:eiicTBHll CHJibi F 3
TOMe npoxo,n:HT qepe3 TOliKY A, liTO n Tpe6oBaJIOCb ,n:oKa3aTb. 06paTHall TeopeMa MeCTa He IIMeeT, T. e. eCJIH JIHHHH p,eiiCTBHH Tpex
CHJI nepeceKaiOTCH B OJI:HOH TO'IKe, TO TeJIO no,n: p,eiiCTBlleM 3THX CHl! MOMeT ll He HaXOJI:HTbC<! B paBHOBeCHH; CJie,l(OBaTeJibHO, TeOpeMa BbipaLIWeT TOJlbKO He06XOOUMOe yC,TIOBHe paBHOBeCHH TeJia ilO,!I, p,eiiCTBHeM TpeX CIIJI.
Pnc. 22 Pnc.
npm.,tep. PaCCMOTpHM 6pyc AB, 3aKpenJJeHHhlll B TO'!KeA rnapHHpOM H ormparoru.niicH Ha Bhictyn D (pnc. 23). Ha 9TOT 6pyc iJ.elktayiOT tpn CHJJhi'cnJJa TH}KeCTH P,
peaKUHSI Nv Bhictyna n peaKUHH RA rnapHnpa. TaK KaK 6pyc HaXOil.HTCH B paaHoaecnn, TO JJHHHH ,~~;elkTBHH 9THX CHJJ iJ.OJI)KHbl nepeceKaThCS! B OiJ.HOH TO'!Ke.JlHHHH iJ.eHCTBHll cnJJ P n ND H3BeCTHhl H OHH nepeceKaiOTCH B TO'!KeK. CJJe,~~;oBaTeJJhHO, JJHHHH .ll.eii-
CTBHH rrpHJJo)KeHHoii B TO'!KeA peaKUHH RA TO)Ke .1\0JJ)KHa npoiitn qepea TO'IKYK, T. e. iJ.OJJ)KHa 6biTh HanpaBJJena BiJ.OJJh npHMoii AK. TeopeMa o tpex CHJJax no:iBOJJHJJa a 9TOM c,'ly'laeonpeiJ.eJJHTh sapaHee HeHsaectHoe HanpaaJJeHne peaKUHH rnapHnpa A.
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§ 5. nPOEKI(Hjl CHJlbl HA OCb H HA nJJOCKOCTb.
AHAJIHTHI.JECKI-Jfi cnOC06 3A,l1.AHH»
U CJIO)I(EHH» CHJl
AHaJIHTHIIeCKnft MeTo,n perneHHH sa.n.aq cTaTHKH OCHOBhiBaeTCfl Ha IIOHflTHH 0 rrpoeKUIIH CHJihi Ha OCb. llpoeKt.fUH. CU/lbl (KaK ll JII060ro .n.py-
roro BeKTopa) fta ocb ecmb a.llce6pattt1,ecKaJl Be.llUttuH.a, pa81-taJl npou3ee-
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fnasa III
MOMEHT CHJlbl OTHOCHTEJibHO l.(EHTPA. nAPA CHJI
§ 8. MOMEHT CHJibl OTHOCHTEJihHO 1..\EHTPA (HJIH T0'1KH)
BBe)l,eM BaJKHOe nOHllTIIe 0 MOMeHTe CIIJibl OTHOCIITeJibHO TOlfKH.
ToliKY. OTHOCiiTeJibHO KOTOporr oepeTCll MOMeHT' Ha3&IBa!OT l{eHmpoM MO.MeHma, a MOMeHT CIIJibl OTHOCIITe.'lbHO~nOH TOl!KII- MOMeHmO.M om-
flOCUtneAbHO l.{eHmpa. EcJIII no,!!. ,!l.eii:cTBIIeM npiiJioJKeHHOH CIIJibl TeJIO
31
MO:lKeT COBeplliaTb BpalllgHHe BOKpyr HeKOTOpOH TOIJ:KH, TO MOMeHT CHJibl OTHOCHTeJihHO <noii roqKH 6y,rr._er xapaKrepH30BaTb spar.u.areJihHhlH 3cp- 'IJeKTCHJlbl.
PaccMoTpHM CHJIY F, npHJIOMeHHyiO K reJiy B roqKe A (pHc. 31). 113 HeKoroporo II.eHTpa 0 onycrnM nepneH)J.HKYJIHp Ha JIHHH!O ,11.eil:crBHH
B CHJibi F; )J.JIHHY h ~noro |
nepneH)J.HKYJIHpa Ha- |
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3biBa!OT nJlei.£OM CUAbl F |
OTHOCHTeJibHO |
II.eHTpa |
0. MoMeHT cHJibi OTHOCHTeJibHO ueHrpa 0 onpe,11.e- |
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JmercH: 1) MO,nyJieM MOMeHTa, paBHbiM npOH3Be- |
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)J.eHH!O Fh; 2) noJIOMeHneM B npocrpaHcrBe |
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nJiocKocrn OAB («nJIOCKOCTH noBopora»), npo- |
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XO)J.HIIJ.eli qepe3 II.eHrp 0 |
II CHJiy F; 3) |
HanpaB- |
JieHHeM nOBOpora B 3TOH |
nJIOCKOCTH. |
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l13 reOMeTpllH ll3BeCTHO, qro TIOJIOMeHHe TIJIOC-
Pnc. 31 |
KOCTH B npocrpaHCTBe onpe)J.eJIHeTCH HanpaBJie- |
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HlleM HOpMaJIH (neprreH)I.HKyJHrpa) K 3TOH TIJIOC- |
KOCTH. TaKHM o6pa30M, MOMeHT CllJibl OTHOCHTeJibHO II.eHTpa xapaKrepuayeTCH He TOJibKO ero tJ:llCJIOBbiM 3HaqeuHeM, HO ll uanpaBJieHHeM B npoCTpaHCTBe, T. e. HBJIHeTCH BeJIHqllHOH BeKTOpHOH.
BBe)J.eM cJie)J.yiOr.u.ee onpe)J.eJJeune: MOJ.teHmoM CUAbt F omHocumeAblio
l{elimpa 0 Hasbt8aemc5l npu.llo:J/CelilibtU 8 u,eHmpe 0 8eKmop m0 (F), Mooy.llb KomopO<!O paeeli npouseeiJeNUIO MoiJyAfl F CUAbt Ha ee nAel.£0 h u IWmopblU NanpaeAeli nepnmiJwcyARplio nAOCKocmu, npoxoiJR~eu t£epe3 lfelimp 0 u cu.11y, 8 my cmopoHy, omKyiJa cu.11a 8UiJHa cmpeMflUtet1cJL noeepHymb me.11o 80Kpye 4e11mpa 0 npomue xoaa iiaeoeou cmpe1lKU (pHc,
31).
lmo(F)!=Fh=2nJI. t:.,_OAB. |
(13) |
DocJie)I.HHii pe3yJihrar cJie.n.yer H3 roro, liTO nJI. 6.0AB=AB ·h/2=
=Fh/2. l13MepHeTCll MOMeHT CllJibi B Hb!OTOH-Merpax (H •M). |
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Hati)J.eM <flopMyJiy, BbipaMaiOIIJ.YIO BeKrop mo (F). )JJill |
3T0f0 |
pac- |
CMOTpHM BeKropuoe npon3Be)J.eHne OA X F BeKropoB OA II |
F. ITo on· |
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pe,11.eneHHIO *, |
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lOA xFI = 2 nJI. 6 OAB= Imo (F) I· |
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HarrpaBJieH BeKrop OA X F nepneH)J.HKYJIHpHo ITJIOCKOCTH |
OAB |
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B ry cropouy, orKy)J.a Kparqafirnee coBMemeune OA c F (ecJIH nx orJio-
MHTh OT |
O)J.HOH |
TO'IKH) Bll)J.HO npOHCXO)J.HIIJ.llM npOTHB XO)J.a qacOBOH |
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crpeJIKH, |
T. e. raK Me, KaK |
seKrop m0 (F). CJie)J.oBareJihHO, BeKropbi |
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OA X F n |
m0 (F) |
coBrra)J.aiOT |
H rro MO)J.YJIIO, II no uanpaBJieHHIO, II, KaK |
* BeKTOpHbiM npOH3Be)l;eHH€M axliBeKTOpOB aH bHa3b!BaeTCH BeKTOp C, paBHhlli DO MOiJ.YJIIO UJIOII(8iJ.H napaJJJieJJOfpaMMa, ITOCTpOeHHOfO H8 BeKTOpaX all b, ll HanpaBJieHHbllf nepneHiJ.llKYJJHpHo ITJIOCKOCTH 3TllX BeKTOpOB B TY CTOpOHy, OTKy)l;a KpaTqafiiiiee COBMe!I(eHHe a C b BlliJ.HO npoHCXOiJ.HII(llM llpOTHB XOiJ.a qacOBOii CTpeJJKll. MoiJ.yJib 0 onpeiJ.eJisreTcsr e!I(e paBeHcTBoM c=ab sin a, r,11;e a - yroJJ Me)KJI:y BeKTOpaMH aH b.
ECJIH aeKTOphl a H b napaJIJJeJibHhl, TO aXb=O.
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nerKo Bn.n;eT&, no pa3MepHOCTH, T. e. BbipaJKaiOT o.n;Hy H TY JKe BeJiwmHy. Orc10.n;a
(14)
r.n;e r-OA - pa.n;Hyc-BeKTOp TO'IKH A, npose.n;eHHblii H3 ueHTpa 0.
TaKHM o6pa3oM, MOMelim CU.Ilbt F omHocumeAbHO t{eHmpa 0 paseH
BeKnwpliOMY npou38eoeHU10 paouyca-eeKmopa r= OA' npooeoeHHOZO U3 ijeHmpa 0 6 motfXy A, zoe npu.llO:J!CeHa CU.Ila, Ha caMy CU.Ily. 3-roT pe3yJib-
TaT MOJKeT CJIYJKHTb .n,pyrHM onpe,l!gJieHHeM llOHllTHll 0 MOMeHTe CIIJibl OTHOCHTeJibHO UeHTpa.
0rMeTHM CJie.n;yiOil\He CBOHCTBa MOMeHTa CIJ:Jibi: 1) MOMeHT CHJibi OTHOCIJ:TeJibHO UeHTpa He H3MeHlleTCll npH nepeHOCe TO'IKH npHJIOJKeHHll CHJibi B)l,OJib ee JIHHHH )J;eHCTBHll; 2) MOMeHT CHJibl OTHOCHTeJibHO UeHTpa
0 paBeH HYJIIO HJIH KOf)l,a CHJia paBHa HyJIIO, HJIH KOr.n;a JIHHllll .n;eikTBIHI CHJibi npoxo.n;HT qepe3 uenTp 0 (nJJeqo paBHO HYJIIO).
§ 9. nAPA CliJI. MOMEHT nAPbl
flapou CU/l * Ha3bl6aemCfl cucmeMa oeyx paBHblX no ,uooyAto, napa.llM/lbHblX u HanpasAeHiiblX e npomueonoAO:J/CHbte cmopOHbl cu.11, iJeii- cmey/O~ux .Ha a6co.ll/Omrw meepooe me.llo (pnc. 32, a). CIJ:cTeMa CHJI F,
f',o6pa3YIOI.UHX napy, OlleBH)l,HO, He HaXO)J;HTCll B paBHOBeCHll (3TH CllJihl He HanpaBJieHbl B)J;OJib O)J;HOH npHMOii). B TO JKe BpeMll napa CHJI He HMeeT paBHO)l,eHCTBYIOI.UeH, nOCKOJihKy, KaK 6y.n;eT )J;OKa3aHO, paB-
Ho.n;eiicTBYIOIUall .mo6oii |
cnCTeMbi CHJI pasHa ee r JiaBHoMy BeKropy R, |
T. e. cyMMe 3THX CHJI, |
a )];Jill naphl R =F+F' =0. Do3TOMY cBoiicTBa |
naphl ..crrJI, KaK oco6oii Mepbi MexaHnqecKoro B3aHMo.n;eiicTBHH TeJI, )J;OJIJKHbl 6biTb paCC'viOTpeHbl OT)J;eJibHO.
DJiocKOCTh, npoxOAHI.Uall qepes JIHHHH AeiicTBHH naphi crrJI, Ha3bl• BaeTCll n.llOCKOCmbto aeucmeUfl napbl. PaCCTOllHHe d MeJK)J;y JIHHHllMH )l,eH-
CTBHll CHJI napbi Ha3b!BaeTCll n.lletWM napbt. ,UeikTBHe napbi CHJI Ha |
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TBep,ll,Oe TeJIO CBO)J;HTCll K HeKOTOpOMY Bpai.UaTeJibHOMY 3<\XlleKTy, KOTO- |
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pb!H xapaKTepu3yeTCll BeJIHl!HHOH, Ha3hiBaeMOH MOMelimOM napbt. 3-for |
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MOMeHT onpe)l,eJilleTcll: |
1) ero Mo.n;yJieM, paBHbiM npOH3Be)l,eHHIO Fd; |
2) nOJIOJKemreM B npocTpaHCTBe llJIOCKOCTH )l,eHCTBHll napbi; 3) HanpaB- |
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JieHHeM noBopoTa napbi |
B 3TOii nJIOCKOCTH. TaKHM o6pasoM, KaK rr |
MO'vleHT CHJibl OTHOCHTeJibHO UeHTpa, ;;)TO BeJIHl!HHa BeKTOpHall. BBe.n;eM CJie.n;yiOI.Uee Onpe.n;eJieHHe: MOMeHmOM napbt CU/l Ha:Jb{f]{letnCJl
eeKmop m (rrJirr M), MOoyAb KOmopozo paeeH npoU38eoeHuto Mooy.llfl ooHou
U3 CU/l napbt Ha ee n.11etto U KOmOpbtU HanpasAeH nepneliOUKy.llflpHO nAOCKOCmu oeucmeufl napbt e my cmopoHy, omKyoa napa euoHa cmpeMR-~erlcfl
noeepfiYmb me.11o npomue xoaa ttacooou cmpeAKU (pHc.
3aMeTHM ei.Ue, qTo raK KaK nJieqo CHJibi F OTHOCHTeJihHO TO'IJUI A
paBHo d, a TIJIOCKOCTb, npoxo.n;HI.Uall qepes TO'IKYA H cnJiy F, coBnq.n;aer
* Teopmo nap paspa6oTaJI nsaecTHbiH ¢paHuyscKHH yqeHbiHMexaHHK n reoMeTp JI. IlyaHCO (1777-1859).
2 N• 2173 |
33 |
C llJIOCKOCTb!O" ~eHCTBIIll napbl, TO OJI:HOBpeMeHHO m=mA (f) =AB XF.
Ho B OTJIH'!HeOT MOMeHTa CHJibl BeKTOp m, Kai< 6y,n:eT noKa3aHO HHMe, MOJKeT 6b!Tb npHJI.OMeH B JII060H TO'IKe(TaKOH BeKTOp Ha3biBaeTCH 6oiJHbtM). l13MepHeTCR MOMeHT napb!, KaK II MOMeHT CHJihl, B HbiOTOHMetpax.
DoKa:>KeM, 'ITO MOMeHTY napbi MO:lKHO ,ll.aTh ,n:pyroe BblpaJKeHHe:
MoMenm napbt paeeH cyMMe MoMeHmoe omHocumeAbHO A106oco u,eHmpa 0
CUA, o6pa3y/OUI;UX napy, T. e. |
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m=m0 (F)+m0 (F'). |
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Ll.JIH ,n:OKa3aTeJibCTBa npoBe,n:eM H3 npOii3BOJibHOH |
TO'IKH 0 |
(prrc. |
33) |
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pa,n:rrycbi-BeKTOpbl rA -OA II rs=OB. Tor,n:a corJiaCHO |
¢opMyJie |
(14), |
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F |
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PlfC. 32 |
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PlfC. |
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yt:~Tll e~e. 'ITO F' =_:p, noJiyTirrM m0 (F) =~X F, |
m0 (fi) =~XF' = |
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=-~XF II, CJie,n:osaTeJibHO, |
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mo (F)+ nto (F') = rrB-rA) X F = AB X F. |
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TaK KaK |
AB X F=m, TO cnpaBe,n:JIIIBOCTb paBeHCTBa |
(15) |
,n:oKasaHa. |
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0rcro,n:a, |
B 'IaCTHOCTH, CJie,n:yeT yme |
OTMelleHHblll |
BbUIIe pesyJihTaT: |
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m=ABxF=mA (F) |
HJIH m=mB(F'), |
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(15') |
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T. e. trro MoMeHm napbt paeeH MO}rt,enmy oiJnou U3 ee cuA omHocume/lbHO tnOttiCU npuAO:»ceHllJl iJpycoU CU/lbl.
D~b!
m=Fd. |
(15") |
EcJin npnHHTh, 'ITO ,n:eiicTBHe napbl crrJI Ha TBep,n:oe TeJio (ee spamaTeJibHhlii 3$¢€KT) TIOJIHOCTblO onpe,n:eJIHeTCR 3HalleHHeM CYMMbl Mo-
MeHTO~ CHJI napbl OTHOCIITeJibHO JIJOOOrO UeHTpa 0, TO H3 cpopMyJibl
(15) CJie,n:yer, 'ITOiJee napbt CUA, UMeiOU{ue oiJuHaKOBbte MOMeHmbl,
6W/.eHtnHbl, T. e. OKa3b!BaiOT Ha TeJIO OJI:HHaKOBOe MexaHH'leCKOe,n:eiiCTBlle. l1Ha'le3TO 03Hal!aeT, liTO ,n:Be napbl CHJI, He3aBHCIIMO OT TOrO, r,n:e KaJK,ll.a.5l H3 HIIX pacnOJIO:lKeHa B ,n:aHHOH nJIOCKOCTII (IIJIII B napaJIJieJihHb!X nJIOCKOCTRX) II 'leMypaBHbl B OT,n:eJibHOCTII Mo,n:yJIII HX CIIJI II HX llJiel!II, eCJIH llX MOMeHTbi IIMeiOT O,n:HO II TO me 3HalleHIIe m, OY.ll:YT 3KBH-
BaJifHTHb!. TaK KaK Bbi6op ueHTpa 0 npoHSBOJieH, TO BeKTop m MomHo Cl!IITaTb npHJIOMeHHbiM B JIIOOOH TO 'IKe, T. e. ~TO BeKTOp CBOOO,ll.HbiH.
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B .n;aJibHefuneM oy.n;eM OObil!HO Ha qepTeJKe BMeCTO napbi II300p.a)KaTb fJOJIHOCTb!O ee xapaKTepnsyiOW.llH BeKTOp m. Dpn 310M Mo;zi.YJib m
onpe.n;eJIHeT |
MOJI.YJib MOMeHTa napbi [cpopMyJia (15")1, a HanpaBJieHHe |
m |
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onpe,!l;eJIHeT |
nJIOCKOCTb .n;eiicTBHH napbi |
ll HanpaBJieHIIe nOBOpOTa |
B |
<:HOll llJIOCKOCTll. |
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113 cpopMyJibi (15) CJie.n;yeT ~W.e, liTO |
eCJIH Ha TeJIO .n;efiCTByeT Hec- |
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KOJibKO nap C MOMeHTaMH mb m2, ... , mn, TO cyMMa MOMeHTOB BCeX cRJI, o6pasyrorn.IIx 3TH naph1, OTHOCIITeJibHO JII06oro ueHTpa 6y.n;eT paB- a.a m1+m 2+ . . .+mn, a CJie.n;oBaTeJibHO, BCH COBOKynHOCTb 3THX nap 3KBHBaJieHTHa o.n;Hoii nape c MOMeHTOM M ="2.mlt. EfroT pesyJihTaT BbipiDKaeT TeopeMy o cJio:memm nap.
fJJasa IV
flPHBEAEHHE ClfCTEMbl CHJI K I..(EHTPY. YCJIOBH» PABHOBECH»
§ 11. TEOPEMA 0 OAPAJIJ1EJ1bHOM nEPEHOCE CHJ1bl
PaBHO,n:eiieTBYIOill,all eneTeMbl eXOll,llllJ.llXell eHJI Henoepe,n:eTBeHHO Haxo,n:nTell e noMOill,b!O 3aKOHa napaJIJieJiorpaMMa enJI. Ol!eBIIll,HO, qTQ aHaJIOfHl!HY!O 3all,ally MO.IKHO 6y,n:eT peiiiHTb H ll,Jill npOH3BOJibHOii el1CTeMhl eHJI, eeJIH HaUTH ll,Jill HHX MeTOll,, n03BOJill!OIII.HH nepeHeenr Bee eHJJbl B Oll,HY TO'IKY. TaKOH MeTOll, ,n:aeT eJie,n:yiOIII.all TeopeMa: CU/ly, npUAO-
~eflflYJO K a6CO/l/OmflO meepdoMy meAy, MOa/CflO, He U3.Mefl.R5l OKG3bi8GeMOZO
a) |
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i)pyzy10 |
mot.{,KY |
meAa, |
npu- |
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6ae/lAA |
npu |
amoM |
napy c |
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MOMeflmOJt, |
paBflblM |
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my nepeHOCUMOU CU/lbl om- |
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nyeTb Ha TBep,n:oe TeJio ,n:eiieTByeT enJia F'npHJIO.IKeHHall B TOl!Ke A (pile. 37, a). ,UeiiCTBHe ~noli eHJibl He ll3MeHlleTell, eeJIH B JI!060H TOqKe
B TeJia npnJIOJKHTh ,n:Be ypaBHOBeiiieHHbie enJibi F' n F", TaKne, 'ITO
F' =F, F" =-F. iloJiyqeHHall eneTeMa Tpex enJI rr npe,n:eTaBJilleT eo6oii
eHJIY F', paBHYIO F, Ho npHJIO.IKeHHYIO B TOl!Ke B, n napy F, F" C MOMeHTOll;l
(U~)
37
iloGJie.n;Hee paBeHCTBO cJie.n;yeT H3 cpopMyJibl (15'). TaKHM o6pa3oM, TeopeMa .n;oKa3aHa. Pe3yJibTaT, .n;aBaeMbiii TeopeMoii, MOMHO ern.e H306pa3HTb TaK, KaK 3TO noKa3aHo Ha pnc. 37, 6 (cHJIY F Ha 3TOM pncyHKe Ha,Zto Cl!HTaTb oT6poweHHoii). PaccMoTpHM npHMepbi, HJIJIIOCTpHpyiOrn.He TeopeMy.
npHMep 1. ~ho6bi y,n:ep»<aTb B paBHOBeCHH o,n:nopo,n:HblH 6pyc AB AJIHHOH 2a H B~COM p, na,n:o npHJIOJKHTb B ero cepeiJ.HHe C HanpaBJieHHyiO BBepx CHJIY Q, ITO MO,n:yJIIO panny10 p (pHC. 38, a). CorJiaCHO ,n:oKa3aHHOH TeopeMe CHJiy Q MOJKHO 3aMeHHTb CHJIOH Q', npHJIOJKeHHOH K KOHUy A 6pyca, II napoil: C MOMeHTOM, MO,n:yJib KOTOporo m=Qa,
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EcJIH nJieqo aroil: rrapbi |
yMeHbiiiHTb |
iJ.O BeJIH'IHHblh (puc. 38, 6), TO o6pa3YIOIUHe ee |
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CHJibl F, F, HaiJ.O yaeJIH'IHTbTaK, 'IT06hl6brJio Fh=Qa. CJie.n;oaareJibHO, 'IT06bly,n:ep-
lKIITIY 6pyc 3a ero Koneu A, na.n:o KpoMe cn,'lblQ' rrpHJIOJKHTb e!Ue rrapy F, F'. 3ror pe3yJibTaT, BblTeKaiOIUllif H3 ,!IOKa33HHOil: TeopeMbi, Henocpe,llCTBeHHO «OIUyiUaeT» pyKa qeJioBeKa, y.n:epJKnaaiOIUaH 6pyc 3a ero cepeiJ.HHY (pnc. 38, a) HJIH sa Koneu (pHc. 38, 6).
npHMep 2. Ha 6apa6an 1 pa.n:ayca r naMoranbi B npornaono.'lOJKHbiXnanpaBJie-
HHHX ,!llle HHTH, K KOHUaM KoropbiX npaKJia,n:biBaiOT cHJibl F n F'=-F (pnc. 39); Ha 6apa6aH 2 TOrD JK.e p3,ll.Hyca H3MOTaHa O,II;H3 HHTb, K KOTOpOil: IIpHKJia)lbiBaiOT CHJiy,
paanyro 2F. Paccr.IOTpHM, '!eM6y.n:yr OTJIH'I3TbCH,n:eiicTBHH 9THX CHJI.
Ha 6apa6an 1 .n:eil:crayer TOJibKO napa CHJI F, F' c |
MoMenroM, qncJienno paBHbiM |
2Fr, apaiUaiOIUaH t5apa6an. CnJiy, .n:eiicrayiOIUYIO na |
6apa6an 2, MOJKHO saMeHHTb |
cnnoii 2F'= 2F, npHJioJKennoil: K ocn 6apa6ana, n napoil: 2F; 2F". B pesyJihTaTe naxo,n.nM, 'ITOua 9TOT 6apa6an .n:eiicrByiOT: l) napa c 'IHCJiennoTaKHM JKe, KaK n B nep-
BOM CJiy'!ae,MOMeHTOM 2Fr, BpaiUaiOIUaH 6apa6aH, H 2) CHJia 2F', OK33biB310IU3H ,ll.aBJieHHe na ocb 6apa6ana.
HTaK, o6a 6apa6ana 6yil.YT apa!UaTbCl! Oil.HHaKoao. Ho rrpu 9TOM ocb aroporo 6apa6ana HcnbiTbiBaer .n:aaJienne, paanoe 2F, a OCb nepaoro 6apa6ana HHKaKoro .n:aaJieHHH He HCllb!TbiBaeT,
§ 12. nPHBE)J.EHHE CHCTEMbt CHJ1 K J(AHHOMY l(EHTPY
PeiiiHM Tenepb 3a,n;aqy o npHBe,n;eHHH npoH3BOJibHGH cHcTeMhi clfJI K ,n;aHHOMY ueHTpy, T. e. 0 33MeHe ,n;aHHOH CHCTeMbl CHJI ,n;pyroii, eii 3KBHBaJieHTHOH, HO 3H3l!HTeJibHO OOJiee npocTOH, a HMeHHO COCTOll!UeH, KaK
Mbi YBH)J;HM, TOJibKO H3 O)J;HOll CHJibl |
H napb!. |
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Ha TBep.n;oe TeJio .n;eiiCTBYeT npOH3BOJibH3ll CHCTeMa CHJI Flo |
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Fn (pHc. 40, a). Bbi6epeM |
KaKyiO-HH6y.n;b TO'IKY0 3a ueHTp |
IB