§ 117. 3AKOH COXPAHEHM.SI fJIABHoro MOMEHTA
I(OJIHI.JECTB ,ll.BH)I(EHHSI
J13 TeopeMbl MOMeHTOB MOLKHO TIOJiyqHTb TaKHe CJie}l.CTBll5I.
I. flyCTb cyMMa MOMeHTOB OTHOCllTeJibHO rreHTpa 0 BCeX BHelliHllX cnJI, }l.eficTBYIOlllllX Ha cncTeMy, paBHa HYJIIO
'2.m 0 (F'k)=O.
Tor,'I.a H3 ypaBHeHim (35) cm;n.yeT, qTo npll3TOM J(0 =const. TaKHM o6pa30M, ecAu cyJIHta MO.M.eHmae omnocumellbHO oannoe-o u,enmpa ecex npuAO'JICCHHblX K CUcmeMe 8HCUlHUX CUA paeHa HYAIO, mo 2Aa8HblU MOMeHm KaAwtecme aeu'JICeHUR cucmeMbt omnocumeJ!bHO Bmoco u,enmpa 6yaem ttucAeHHa u no nanpael!eHu/0 nocmoRnen. OpnJioLKeHne noro pe3yJibTaTa K cJiyqaiO }l.BHLKeHHH nJiaHeThr ohiJIO paccMoTpeHo B § 86.
2. flycTb BHelliHllC CHJihi, .n.e:fiCTBYIOIU;He Ha CllCTeMy, TaKOBbi, qTO cyMMa HX MOMeHTOB OTHOCHTeJihHO HeKOTOpofi HeTIO)l.BllLKHOll OCll Oz pasHa nymo
'2.mz(Fk) =0.
Tor.n;a 1!3 ypaBHeHnii (36) cJie,n;yeT, qTo npn 3TOM Kz=const. TaKHM o6pa30M, ecAU cyMMa MOMeHmoe ecex aeiicmey10wpx na cucmeMy enemnux cuA omnocumeAbHO KaKaii-nu6yob ocu paena HYJ!to, mo cAaeHbtii MOMenm KaAuttecme oeu'JICeHUfl cucmeMbt omnocumeAbHO Bmoii ocu 6yaem eeAuttuHou nocmORHHOU.
3TH pe3yJihTaThi BblpaLKalOT COOOH 3a1WH CaxpaHCHUfl cJ!afJHOcO AW·
.M.eHma KOJ!uttecme aeu'JICeHufl cucmeAtbt. 113 Hnx cJie}l.yeT, qTo BHyTpemnre CllJibl II3MeHllTb r JiaBHblll MOMeHT KOJillqecTB )J;BllllieHHfl CllCTeMbi He MoryT.
C JI y q a if B p a lll a 10 lll e fi c H c n c T eM hi. PaccMoTpnM CllCTeMy, BpalllalOIU;YIOCfl BOKpyr HeTIO)J;BllLKHOH (HJill npOXO)J;Hlllell qepe3 ueHTP Mace) ocn z. Tor.n;a no cpopMyJie (32) Kz=J zW. EcJIH B 3TOM cJiy-
qae 'Smz(Fk)=O, TO
J zW=COTISf.
0TCIO,'I.a npllXO)l.llM K CJie,n;yiOIU;llM Bb!BO)J;aM:
a) eCJill CllCTeMa HCU3Atefl5leMa (aoCOJIIOTHO TBep}l.Oe T~JIO), TO J z=
=const n, CJie}l.oBaTeJibHO, w=const, T. e. TBep}l.oe TeJio, 3aKpenJieHHoe Ha OCII, BpalllaeTCfl B 3TOM CJiyqae C IIOCTOHHHOH yrJIOBOll CKOpOCThiO; 6) eCJill CllCTeMa U3MCH5leMa, TO TIO}l. .n.eifCTBHeM BHyTpeHHllX (HJIU BHeUIHHX) CHJI OT,ll.eJibHb!e ee TOqKll MOryT y}l.aJif!ThCH OT OCH, qTO Bhl3biBaeT yseJinqeHHe J n HJIH npn6mnKaThCH K ocn, qTo npnBe}l.eT K yMeHbllleHHIO J z• Ho TIOCKOJibKY J zW=const, TO npn yBeJIHqeHHll MO·
MeHTa HHepUMH yrJIOBa11 CKOpOCTb CHCTeMbl 6y,n;eT yMeHhiiiaTbCH, a
nprr yMeHhiiieHrrH MOMeHTa HHepuHrryseJirrqrrsaThCH. TaKnM o6pa30M, .n:eiicTBHeM BHyTpeHHHX CHJI MO)KHO H3MeHHTb yrJIOBYIO CKOpOCTb CHCTeMbl, T8K KaK DOCTOHHCTBO K z He 03HaqaeT B005UJ,e DOCTOl'!HCTBaW.
PactMOTPHM |
HeKOTOphle npHMepbl. |
a) 0 ll hi T hi |
C D JI a T ljJ 0 p M 0 H )K y K 0 B C K 0 r 0. ,[{Jill ,::(eMOHCTpaUHH |
SaKOHa CoxpaHeHHll MOMeHTa KOJIHIJeCTB ,l(BmKeHHll y.u;o6HO IIOJib30BaThCll llpOCTiiM
llpH6opOM, Ha3b1Ba€Mb!M «llJiaT!jJOpMOH )I\yKOBCKOrD». 3To KpyrJiall rOp1130HT8JibHaH I!JiaT!jlOpMa Ha mapHKOBb!X OIIOpHb!X llO,l(lllHllHHK3X, KOTOpall MO:lKeT C ~!aJ!biM TpeHHeM BpaJJJ;aThCll BOKpyr BepTI!Ka.zibHOll OCH Z. )J.JIH qeJioBeKa, CTOl!JJJ;ero Ha TaKOH
nJiaT!jlopMe, :E mz(F'k)= 0 H, CJie.u;oaaTeJibHO, J zro=const. EcJIH IJeJioBcK, pa3se.u;ll pyKil B CTOpOHbl, COOOJJJ;HT ce6e TOJIIJKOM BpaJJJ;~HHe BOKpyr BepTHKaJib!IOH OCH, a 3a-
TeM OllYCTHT pyKH, TO BeJ!HlJUHa J z yMeHblllaeTCll H, CJie/I.OBaTeJibHO, yrJIOBall CKQpOCTb spam:eHml B03pac'i'eTTaKI:!M. cnoco6oM )'BeJIMIJeHHllyrJioaml: cKopocTH m~~tpcOKO IIOJih3YIOTCH B OWieTe, llpH Dpbi>KKaX B B03.!lyXe (caJibTO) H T. ll.
)laJiee, IJeJIOBeK, CTOHJJJ;HM Ha nJiaT!jl.opMe H€llOJl.BH:lKHO (Kz=0), MO:lKeT llOBepHYThCll B mo6y10 cTopoHy:, apamall BhiT!IHYTYIO ropnsoHTaJibHo PYKY B nporrrsono-
JIO:lKHOM |
HanpaaJieHHH. |
YrJIOB&ll |
CKOpOCTb IJeJIOBeKa npH STOM 6y.u;eT T&KOH, 'lTOObl |
B cyMMe |
BeJIH'lllHa Kz |
cHCTeMhl |
ocraJiacb paaHoii HYJIIO. |
6) p |
a C K a lJ H B a II 1'1 e |
K a lJ e J1 e H. ,UasJieHHeM HOf (CHJ13 BHyTpeHHllH) |
qe,10BeK, CTOllW:HH Ha K8lJ€JillX, paCK3IJ8Tb llX He MO:lKeT. Ci!.€JI8Th STO MO)!(HO CJie/l.yiO- |
lliHM o6pa3oM. Kor)la KaiJeJIH HaXO/I.llTCll B JieBoM aepxHeM noJio:lKeHHH A0 , 'leJioBeK |
npHce.aaeT. llpn npoxol!K/I.eHMH qepes sepTHii8Jih oH 61rcrpo Bblnp!!MJilleTcll. Tor.aa |
M8CCbi llpH6JIH:lKaiOTCll K OCR BpaJJJ;eHH!I Z, BeJIHIJHHa J z yMeHblllaeTCll ll yrJIOBall CKQ- |
pOCTb (I) CKa'IKOMB03p3CT&eT. 3TO yBeJIHIJe!lHe (J;) npHBO)lHT B KOHelJHOM CIJeTe K TOMy, |
'ITO KaiJeJIH no.u;HHMYTC11 Bhillle HaiJaJibHoro ypoBHll A0 • B rrpasoM |
sepxHeM noJio- |
:lKeHHH, Korna ro=O, IJeJioBeK OIIHTh rrpnce).laeT M lz yaeJiniJHBaeTcll, |
HO w ocraeTCll |
paBHOH HYJIIO; npH |
npOXO:lKJl.eHHll qepe3 BepTHKaJib Oil CHOBa Bb!IIpllMJil!eTCll 1:1 |
T• .1{. |
B pesyJihTaTe pa3Maxn Ka'leJieH 6ynyr aospacTaTh. |
napa- |
llpollCXOil,llJJJ;He |
Tipll STOM BbiHY:lK/leHHble KOJI€C3Hllll KaiJeJieii: Ha3biB<HOTCll |
J.tempu'leCKUJ.tU, TaK KaK OHII COBeplliiiiOTCli He DO,Il /l.eHCTBHeM nepnOJl.HlJ€CKH M€Hll10llleHcl! CHJ!bl (CM. § 96), a BCJle)lCTBHe nepHO)lll'leCKOfOH3MeHellHll napaMeTpOB CHCTe-
J..Ibl: ee MOMeHTII HHepll,HH |
li I!OJIO:lKeliHll |
ll€HTpa Tll:lKecTH. |
B) p e a K T H B II bl ll |
M 0 M e II T B H H T a. ECJill pacCM&TpHBaTb Kopnyc Bep• |
TOJieTa (m.tecre c naurareJieM), ero BHHT n |
ortipachlBaeMyiO Macey aoanyxa Kak: a,u,Hy |
CllCTeMy, TO CH.1bl B3aHMO)leHcTBllll Me:lKJl.Y |
)lBHraTeJieM H BHHTOM ll Me:lK,I\y BliHTOM |
H B03JlYlliHOH Cpe)lOH 0YilYT ,!\Jill 9TOH CllCTeMb! BHyTpeHHHMH H He MOfYT H3MeHHTb ee cyMMapHbii1 MOMeHT KOJJHIJecTB ,i;BH:lKeHHll, paBHhlll Jl.O nycKa JJ;BHfaTeJill HYJIIO.
DOSTOMY Kopnyc aeprOJieTa )IOJI:lKeH na'laTh spaw:aTbCli B cropoay, npornBOITOJIOJKHyiO HanpaBJieHHIO Bpam,eHH!I BllHTa H 803/lYIIIHOH cpe)lbl. )leii:CTBYIOJJJ;llH npH 9TOM Ha BepToJieT BpaJJJ;aiOJJJ;llH MOMeHT Ha3hiBaiOT peaKmUB!iblM MOMeHTOl\1. 4To6hi npe)lOTBpaTHTb peaKTHBHOe BpaJJJ;eHHe Koprryca O)(JWBHHTOBOrD BepTOJieTa, Ha ero XBOCTOBOK <JaCTH ycTaHaBJIHBaiOT COOTBeTCTBYlOJJJ:HH pyJieBoii: BHHT. Y MHOfOBHHTOBOfO BepTOJieTa BHHTbl ,l(eJiaiOT BpaJJJ;aiOJJJ;HMHCll B pa3Hble CTOpOHbl.
llOi!BJIEmHe peaKTllBHOfO MOMeHTII MO:lKHO llCllOJib30BaTh )lJill SKCIIepHMei!TaJihHOrD orrpe)leJieHHll BpaJJJ;aiOJJJ;ero MOMeHTa aBHaiJ;HOIIHOfO /lBHraTeJI!I, TIIK KIIK STH MOM€HTbl paBHbl .u;pyr .u;pyry DO MO)I.yJIIO, a peaKTllBHbiH MOMeHT MO:lKHO H3MepHTh, ycTaHOBHB )lBHraTeJib C Bpalli8KllliHMCll BHBTOM Ha COOTBeTCTBYIOW,llX BeCaX.
fJiasa XXV
TEOPEMA OB H3MEHEHHH
KHHETHlJECKOfl 3HEPfHH CHCTEMbl
§ 121. KHHETJP.JECKMI 3HEPfiUI CHCTEMbl
I(unemut.tectwii 31iep2Ueii cucmeJrtbl nasbleaemcst ctWAstpliast eeAut.tuna
T, paertafl cy.MAte KUrtemUt-tecKux artepcutl ecex motteK cucmeJrtbt:
KmreTHtJ:ecKaH 3HeprHH HBJIHeTcH xapaKTepHCTHKoil H rroCTyrraTeJihRoro, H Bpalll,aTeJibHOfO )l.BHJKeHHH CHCTeMbi. f JiaBHOe or.TJJiqHe BeJIH'l:H- Hbl T oT BBe)l.eHHbiX paHee xapaKTepHcTHK QH Ro cocToHT B TOM, qTO KHHeTHtJ:eCKaH 3HepmH HBJIHeTCH BCJIH'l:HHOHCKaJIHpHOll H rrpHTOM cy- I.!J,eCTBeHHO ITOJlO)f{HTeJibHOil. Tio3TOMY oHa ne 3aDHCHT OT HanpaBJieHHii: )l.BH.tKeHHH tJ:aCTefi CHCTeMbl H He XapaKTepmyeT H3MeHeHHH 3THX HanpaBJieHHH.
OTMeTHM elll,e cJie)l.yiOw,ee BalliHoe oocTOHTeJibCTBO. BHyTpeHHHe
CHJibl )l.CHCTBYIOT Ha qacTH CHCTeMbl ITO B3aHMHO rrpOTI1BOITOJIO.IKHbiM HanpaBJICHllHM. Tio ~noli npHqHHe OHH, KaK Mbi Bll)J,CJI!l, lie H3:-ACI!HIOT BCK-
TOpHbiX xapaKTepHCTHK QH K0 . Ho ecJIH rro)J. )J.eiicTBHeM BHyTpeHHHX CHJI OYL\YT H3MCHHTbC5l MOJl.YJIH CKOpOCTeH TO'l:eKCHCTCMbl, TO rrpH 3TOM 6y.n.eT H3MeHHTbCH H BeJIHqHHa T. C.Jie)J.OBaTeJihHO, KHHeTHtJ:ecKaH 3Hep-
(J) -
rmr cucTeMbi oTJJH'IaeTcHOT BeJilPHIH Q H Ko eme n TeM, qTo Ha ee H3Me-
HeHHe BJJHHeT ,n;eifcTBHe H BHeiiiHHX, H BHyTpeHHHX CHJJ.
£CJJH CHCTeMa COCTOHT H3 H€CKOJibKHX TeJI, TO ee KHHeTUtieCKaH
3HeprHH paBHa CYMMe KHHeTuqeCKHX 3Hepri1H 3TUX TeJJ.
Haf:i,n;eM cpopMyJJhi ,n;JIH BbJqHcJJeHHH KHHeTnqecKoii 3HeprHH TeJia B pa3Hb!X CJJyqaHX ,!l;BU:>KeHHH.
1. fl 0 C T y I1 a T e JJ b H 0 e .li. B H :1K e H H e. B 3TOM CJJyqae BCe
TOqKH TeJJa ,!J;BH:IKYTCH C 0,/J;HHaKOBb!MU CKOpOCTHMH, paBHb!MH CKOpOCTH
ueHTpa Mace. CJJe,n;oBaTeJJbHo, ~JJH |
mo6oif ToqKn vk =Vc n |
lflopMyJJa |
(41) ,n;aeT |
|
|
HJJH |
|
|
T noCT = |
Mvi:;;2. |
(42) |
TaKHM o6pa3oM, KttHemu'leCKafl :mepzufl meAa npu nocmynameAbHOM oeu:J~CeHuu pasHa noAoeuHe npouseeaeHufl MacCbl meAa Ha Keaapam cKopocmu tteHmpa Mace.
2. B p a m a T e JJ h H o e ,n; B H :>K e H n e. EcJJn TeJJo apamaeTCH BOKpyr KaKOH-HH6y,n;h OCU Qz (eM. puc. 295), TO CKOpOCTh moOOH ero TOqKU V11.=ffihk, r,n;e hh- paCCTOHHHe TOqKu OT OCU BpameHHH, a
yrJJOBaH CKOpOCTb TeJJa. fiO,!l;CTaBJIHH 3TO 3HaqeHHe B cpopMyJJy (41) H Bb!HOCH o6mne MHOlliHTeJJU 3a CK06KU, I10JJyqHM
T ep = 'Lmkffi2 hf/2 = (Smkh'k) ffi 2 /2.
BeJinqnHa, cToHmaH B cKo6KaX, npe,n;CTaBJJHeT co6of:i MOMeHT HHep-
uun TeJJa OTHOCHTeJJbHO OCH Z. TaKUM o6pa30M, OKOHqaTeJJbHO Hafi,n;eM
T. e. KUHemw-tecKaft :mepcuft meAa npu epaw.ameAbHO.M aeu:J~CeHuu pasHa noAoeuHe npouseeoeHufl MOMeHma uHept{uu meAa omHocume.AbHO ocu epaw.eHufl Ha Keaapam eco yZAoeou cKopocmu.
3. fl JJ 0 C K 0 I1 a p a Jl Jl e JJ b H 0 e ,!J; B H )K e H U e *. fipH 3TOM ,!J;BH:~KeHHH CKOpOCTU BCeX TOqeK TeJJa B Ka:>K,!l;b!H MOMeHT BpeMeHH pac-
npe,n;eJJeHbl TaK, KaK ecJJH 6bJ TeJJO Bpaii.J.aJJOCb BOKpyr OCll, nepneH)I,H- KYJJHpHOH nJJocKocTn ,!J;BH:~KeHHH n rrpoxo,n;Hmef:i qepe3 MrHoBeHHblii
ueHTP |
cKopoCTef:i |
P (puc. 303). CJJe,n;oBaTeJihHO, no cpopMyJJe (43) |
|
|
T ll:'!OCK = Jpffi2 ;2, |
(43') |
r,n;e J p |
- MOMeHT |
HH€pi.J.HH TeJia OTHOCHTeJJhHO |
Ha3BaHHOH BbJ!lle OCH; |
(J) - yrJIOBaH CKOpOCTb TeJJa.
BeJJnqHHa J p B cpopMyJJe (43') 6y.n;eT rrepeMeHHoil, TaK KaK noJJo.meHHe I.J.eHTpa p rrpH ,!l;BH:>KeHHU TeJJa BCe BpeMH MeHHeTCH. BBe,n;eM BMeCTO
J p I10CTOHHHhtH MOMeHT HHepi.I.HH J c OTHOCHTeJJbHO OCU, npOXO)I,Hmeii qepe3 I.J.eHTp MaCC C TeJJa. flo TeopeMe fl:oifreHCa (eM. § 103) J p=J c+
+Md2 , r,u:e d=PC. Tio,n;CTaBHM 3TO Bbipa:>KeHHe ,!J;JJH J p B (43'). YtiHThl-
* 3TOT cJiyiJaH MO)KeT 6h!Tb TIOJiyiJell KaK IJaCTHblil H3 paCCMOTpeHIJOfO B CJie)zy.l()o meM nyHKTe o6111.e1o cJiyiJall .U.BH)KeHHll TBep.n:oro reJia.
BaH, tfl'OTOtJKa p - MrHOBeHHhJH ueHTp CKOpOCTeH H, CJie,n;oBaTeJihHO,
wd=ro ·PC=Vc, r,n;e Vc - CKOpOCTh |
ueHTpa Mace C, |
OKOHtJaTeJibHO |
naii,n;eM |
+ J cuP/2. |
(44) |
T nJioc~< = MvV2 |
CJie,!J;OBaTeJihHO, npu nAOCKOnapaA-1eAbHO.M aeuJ/CeHUU KUHemutteCKafl rmepeUR tne/la pa8Ha 8Hepeuu nocmyname/lbflOCJO 8euJ/CeflltR CO CKOpOCmbiO l{ellmpa M.aGC, CAOJ/CeHHOa C KUHemU'1£CKOa 3Hepeuea epawpmellbfl020 8euJJCeHUR eoKpye t~enmpa Atacc.
PHC. 303 |
:c |
PHc. 304 |
4 *. 0 6 rn. u i1 |
c .r1 y tt a i1 ,IJ; a 11 )!{ e H 11 H. EcJJH aw6paTh |
ueHTp Mace C TeJia B KatteCTBe nomoca (pHc. 304), TO ,n,amKeHHe TeJJa B OOlll.eM CJiyttae oy,n;eT CJJaraThCH !13 llOCTynaTeJihHOfO CO CKOpOCTbiO
Vc nomoca u apamareJJhHoro BOKpyr MrHoBeHHoil ocH CP, npoxo.n;HJUeii: ttepe3 3TOT nomoc (eM. § 63). TipH 3TOvt, KaK noKa3aHo B § 63, cKopoCTh vk JIIOOOH TOtJKH TeJJa Bk CJJaraeTCH !13 CKopocTH Vc noJIJOCa H CKOpOCTH,
KOTOPYIO TOttKa noJiyttaeT npu apameHHII TeJia BoKpyr noJIIOCa (BoKpyr ocu CP) H KoTopyiO Mbi o6o3HaiiHM vk, T. e. v;. =vc+~. TipH 3TOM no Mo,a;yJIIO vk_=ffihk, r,n;e hk- paccroHHHe TOtJKH B" oT ocn CP, a ffi -
yrJ10BaH CKOpOCTh TeJia, KOTOpaH (CM. § 63) He 3aBHCHT OT BhJOOpa llO· JIIOCa. Tor,n;a *
v: = V~ = (vc +~)~ = Vt+Vk2 + 2vc."vi,.
Tio,n;cTaB.'lHH3TO 3HatteHue v~ a paaeHcrao (41) u YIIHTbiBaH, ttTo vk= =ffih~t, Haii:,a;eM
T = (1:mk) vV2 +(1:mkh%) ffi 2 /2 +vc1:mkv(,,
f)I.e OOIUHe MHOlliHTeJJH cpa3y BbiHeCeHbl 3a CKOOKH.
B nOJJyiieHHOM paaeHcrae nepaaH CKo6Ka .n;aeT Macey M TeJJa, a BTOpaH paBHa MOMeHTY IIHepUliH J CP TeJJa OTHOCHTeJihHO MfHOBeHHOll
* 113 onpe,n:eJieHHll cKa.1l!pHoro npOH3Be.:~eHHll .n:Byx BeKTopoB cJie.n:yeT, 'ITO fl=iJ. V~UVCOS 0°=V2 , T. e. CKa.1llpHblH KBa)lpaT BeKTOpa paBeH KBa.npaTy ero MO_ny,'lll.
JroT pesyJibTaT 3,n:ech HCllO.'lb30BaH;Mb16y)l.eM llOJib30BaThCll HM 6e3 OfOBOpOK H B
,~ta.'IbHeiuueM.
§ 110).
ocu CP. BeJIWIHHa *e 'Smuvk=O, TaK KaK ona rrpe.n.CTaBJIHeT co6oii KOJIH'IecTBoJI.BH}KeHIUI, rroJiyqaeMoe TeJioM npu ero apamemm BOKpyr ocH CP, npoxo.n.mJLeii qepe3 ueHTp Mace TeJia (eM.
B pe3yJibTaTe oKoH'laTeJibHO rroJiy'IHM
T = Mv~/2+ lcpffi2 /2. |
(45) |
TaKHM o6pa30Vl, KUHemUt-teCKaJl :mepcUfl meAa 8 06U{e.M cAyttae aeu-
~eflUfl (B '-!aCTHOCTH, H I1pH IIJIOCKOI1apaJIJI€JibHOM }l.BIDKeHIIH) paeHa KU!lemtttteC/WU :mepi!UU nocmynameAbfW20 OBU~eflUfl CO CKOpocmbfO l{eflmpa .Mace, CAO~e/-UlOU C KUHemutteCKOU :mepzueii 13paU{ameAbH020 013U~e HUfl eoKpyz ocu, npoxoaflU{eii ttepes WHmp Mace.
Ecmr 3a nomoc Il3HTb He neHTp |
Mace C, a KaKyr-o-HHOYJI.b ,n,pyryJO |
TO'IKYA TeJia H MriiOBermaH ocb AP |
rrpH 3TOM He 6y.n.eT Bee npe:..m npo- |
XOJI.IITb 'Iepe3UeHTp Mace, TO }l.JIH 3TOH OCH 'Smh.Vk=/=0 H cpopMyJihl BH)l.a (45) Mbl He IIOJIY'IHM.
PaccMoTpHM npnMepbi.
3a,~~;aqa |
136. |
Bhi'!HCJIIlTh Klll!CTJI'!CCKYJO 9Heprmo |
KaTliW:erOC5! OC3 CKOJ!h)KCHHll |
CIIJ!OlllHOfO |
UHJI!!H,ll,pH<!CCKOrO KOJieca Maceo£'! M, CCJIH |
CKOpOCTb ero UCHTpa |
paBHa |
t'c (rM. pHc. 308, a). |
|
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|
p c Ill e H II |
e |
KoJieco COBCplllaCT IIJIOCKOIIapaJIJieJihi!Oe ,ll,Bil)KCHH€. no |
¢op- |
MyJie (44) |
HJIH |
(45) |
|
|
|
0tl!T3CM KOJieCO CIIJIOillHbiM O.QHOpO.QHblM UHJIHH,ll,poM; TOf,ll,a (CM. § JQ2) |
Jc= |
=MR212, r,Qe R - |
pa,n,Hyc KOJieca. C ,Qpyroil: CTOpOHbl, TaK KaK |
TO•IKa 8 SIDJI5!CTt'll |
1J.JI5! K0,1eCa |
MfJIOBCHHblM UCHTpOM CKOpOCTeH, TO Vc=W·BC=wR, |
OTKy.n:a CfJ=VcfR. |
ilO,I\CTaBJISISI BCC |
9TH Slla'!CHH5!, I!aH.QCM |
|
|
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T = Mv~f2+ MR 2t•U4R 2 = (3/4) Mv~.