Practica #1 Movimiento Circular
July 8, 2022 | Author: Anonymous | Category: N/A
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Jlvejefbtl Nernu`kr Dfcrukry 33, 3?;5
VBETFS^EIKI JE@EYKS BVFTK ASKBKIK DKNV@YKI IF NEFBNEK^ CË^ENK^ U K_@ENKIK^ IF_KSYKJFBYL IF DÊ^ENK @KCLSKYLSEL IF NK@LS U LBIK^
Yljës Lrtfaþb, u6=??6?;Oubeje`etkr.fiu.nl Nreskb Kauif`l, u6=??419Oubeje`etkr.fiu.nl Hfdfrslb Tkraks, u6=??454Oubeje`etkr.fiu.nl ^fcksëb Nkjpls, u6=??416Oubeje`etkr.fiu.nl
_SKNYENK B.¸ ; JLTEJEFBYL NESNV@KS
SF^VJFB ^f u`ezk ub tucl if k`ujebel if`akil, ilbif sf mknf pkskr ubk nufrik plr f` jfiel if å`, ilbif fstf vk k slstfbfr ubk jksk ; y ubk jksk 3. ^eb fjckral, `k jksk ; nujp`f `k ubneþb if tfbselbkr `k nufrik y jksk 3 fs `k fbnkrakik if mknfr aerkr f` nufrpl. @k jftk fs mknfr ub jlvejefbtl nernu`kr nlb `k jksk 3, ilbif fstk ``fauf k qufikr mlrezlbtk` pkrk plifr jfier `ls fjpls quf sf ifjlrkck fb ikr `k vuf`tk. ^f mknfb trfs në`nu`ls pkrk fvetkr quf `ls plrnfbtkhfs if frrlr sfkb juy k`tls y ksfaurkrsf if quf `k jfieik tljkik plr f` nrlbþjftrl sfk `k nlrrfntk. ^f tljkb 4 rkiels `ls nuk`fs slb if kprlxejkikjfbtf ;6 nj, 3; nj, >? nj, >6 nj, 9? nj y 91 nj.
_k`kcrks n`kvf8 (Skiel, plrnfbtkhf if frrlr, jksk, fjpl)
KC^YSKNY
;
Jlvejefbtl Nernu`kr Dfcrukry 33, 3?;5
K tmeb k`ujebuj tucf es usfi, wmfrf k rlpf es pkssfi tmrluam tmf jeii`f l et, wmfrf et we`` ml`i k jkss ; kbi k jkss 3. Mlwfvfr, jkss ; u```s tmf ubnlb l tfbselbeba tmf rlpf kbi jkss 3 es tmf lbf eb nmkraf l jkgeba tmf cliy turb. Ymf alk` es tl jkgf k nernu`kr jlvfjfbt wetm jkss 3, wmfrf et es mlrezlbtk` tl cf kc`f tl jfksurf tmf jf et tllg tl turb krlubi. Ymrff nk`nu`klbs krf jkif tl kvlei tmkt tmf pfrnfbtkafs l frrlr krf vfry meam kbi tl jkgf surf tmkt tmf jfksurfjfbt tkgfb cy tmf nmrlbljftfr es nlrrfnt. ^ex splgfs krf tkgfb wmenm krf kpprlxejktf`y ;6 nj, 3; nj, >? nj, >6 nj, 9? nj kbi 91 nj.
Gfy wlris8
;. EBYS EBYSLI LIVN VNNE NEÞB ÞB @k prënn prënnk k rfk`ez rfk`ezkik kik slcrf slcrf jlveje jlvejefbt fbtl l ner nernu` nu`kr kr bls kyuikr kyuikrë ë k nl nljpr jprfbi fbifr fr y mk mk``k ``krr fxpfrejfbtk`jfbtf `k rf`kneþb fbtrf f` rkiel, f` pfrelil y `k rltkneþb if ub jlvejefbtl nernu`kr ubelrjf, sf kbk`ezkrë `ks iefrfbtfs nkrkntfrêsnks if `ks vkrekc`fs senks tk`fs nljl nlj l f` pfreli pfrelil, l, rfnuf rfnufbn bnek, ek, rkpeif rkpeifzz ebe ebenek nek`, `, rkpeif rkpeifzz kbau`k kbau`krr knf`frk knf`frkneþ neþb b y ufrzk ufrzk nfbtrêpftk `l nuk` kyuikrë k nljprfbifr if jkbfrk prënnk `ks iefrfbtfs ftkpks if` jlvejefbtl nernu`kr
3. JKSN JKSNL L YFÞ YFÞSE SENL NL
Jlvejefbtl nernu`kr ubedlrjf8 Nukbil ubk pkrtênu`k sf jufvf fb ub nêrnu`l nlb rkpeifz nlbstkbtf, tefbf ub jlvejefbtl nernu`kr ubedlrjf. Vb kutljþve` quf ik vuf`tk k ubk nurvk if rkiel nlbstkbtf nlb rkpeifz nlbstkbtf, ub sktå`etf fb þrcetk nernu`kr y ub pktebkilr quf ifsnrecf ub nêrnu`l nlb rkpeifz nlbstkbtf slb fhfjp`ls if fstf jlvejefbtl. _frelil8 F` pfrelil jeif f` tefjpl quf sf tkrif fb ikr ubk vuf`tk nljp`ftk y sf jeif fb sfaubils. Fs `k ebvfrsk if `k drfnufbnek. :; Y : _frelilWsZ d : Drfnufbnek WMzZ Drfnufbnek8 @k drfnufbnek jeif `k nkbteiki if vuf`tks quf sf ikb fb ub pfrelil if tefjpl (blrjk`jfbtf ub sfaubil). : @k ubeiki jës ute`ezkik fs f` Mfrtz quf fquevk`f k ubk vuf`tk fb ub sfaubil. ; ℂ: ; ; 3
Jlvejefbtl Nernu`kr Dfcrukry 33, 3?;5
Ksê quf if kjcks ifdebenelbfs sf pufif rf`knelbkr `k drfnufbnek nlb f` pfrelil if `k seauefbtf jkbfrk8
:; (;) d : Drfnufbnek WMzZ Y : _frelil WsZ Knf`frkneþb y knf`frkneþb tkbafbnek`8 Bl ℂky nljplbfbtf if knf`frkneþb pkrk`f`k (tkbafbtf) k `k trkyfntlrek7 se `k ℂucefrk, `k rkpeifz nkjcekrek. F` vfntlr if knf`frkneþb fs pfrpfbienu`kr (blrjk`) k `k trkyfntlrek y plr `l tkbtl, sf iereaf ℂknek kifbtrl (bubnk ℂknek kdufrk) k` nfbtrl if `k trkyfntlrek nernu`kr. Dufrzk nfbtrêpftk8 @k dufrzk nfbtrêpftk sf ifdebk nljl `k nljplbfbtf if dufrzk quf kntøk slcrf ub lchftl quf sf fbnufbtrf fb jlvejefbtl y fstk iereaeik ℂknek f` nfbtrl if nurvkturk if `k trkyfntlrek y nlb fstl f` lchftl pufif tfbfr ub jlvejefbtl nernu`kr. Skpeifz `ebfk`8 Fb ub tefjpl Y. ubk krtenu`k rfnlrrf ubk iestkbnek eauk` k `k nernubdfrfbnek 3 ksê quf su rkpeifz fs8
:3 (3) Knf`frkneþb nfbtrêpftk8 K` vkrekr `k vf`lneiki fb `k trkyfntlrek if` lchftl, fstk prliunf ubk knf`frkneþb nfbtrêpftk, `k nuk` ifpfbif if `k jkabetui if `k vf`lneiki y if` rkiel if` jlvejefbtl, `l quf seabedenk quf k jkylr `lbaetui if` rkiel sfrë jkylr :3 Tf`lneiki kbau`kr8 Fb ub jlvejefbtl kbau`kr fs rfprfsfbtkik nljl8 :3, k` ifspfhkr f` pfrelil if `k drfnufbnek sf tefbf8 :3, if kquf``l sf ifiunf quf k jkylr drfnufbnek if rltkneþb fb f` sestfjk, fs jkylr `k vf`lneiki kbau`kr, `k nuk` fs sefjprf nlbtrkstf fb tlil ebtfrvk`l if tefjpl.
:3 (>) Ejplrtkbnek jlvejefbtl nernu`kr8 @ks ejplrtkbneks prkntenks if` jlvejefbtl nernu`kr slb ckstkbtfs yk quf sf vfb tlil f` tefjpl7 nljl fb `ks ℂå`enfs if `ls ℂf`enþptfrls, fb `k rltkneþb if `k tefrrk k`rfifilr if` sl`, nukbil n ukbil `ls nkrrls tljkb `ks nurvks k vf`lneiki nlbstkbtf fb `ks vêks, fb `ks rufiks if `ks cenen`ftks l fb `ls nkrrls.
>
Jlvejefbtl Nernu`kr Dfcrukry 33, 3?;5
>. _SLNFIE _SLNFIEJEF JEFBYL BYL F]_FS F]_FSEJF EJFBYK BYK@ @ Ifspuås if tfbfr tliks `ks ` ks fstrunturks jlbtkiks sf pfskb `ks jksks tfbefbil fb nufbtk quf fstks slb if iefrfbtf pfsl, fstls pfsls sf ifcfb fsnrecer pkrk tfbfr`ls fb nufbtk pkrk f` ifskrrl``l if `k prënnk y if `ls rfsu`tkils k lctfbfr if fstk. Ifspuås if pfskiks `k jksk sf nl`lnk ubk fb f` fxtrfjl if` crkzl if `k jkquebk aerktlrek, k` nljfbzkr k aerkr sf nufbtk f` bøjfrl if aerls y f` fjpl fb quf sf ifskrrl``krlb `ls aerls, Ifspuås fb f` nljputkilr lctfbirfjls lctfbirfjls `ks arënks quf slplrtkrkb bufstrks mepþtfses slcrf f` jlvejefbtl. ^f rfpetf fstls prlnfiejefbtls nl`lnkbil if ubk fb ubk `ks jksks y kujfbtkil `k vf`lneiki nlblrjf sf tfrjebf f` nen`l if nkrak if jksks. Fb tltk` slb ;3 tljks if iktls `ks nuk`fs sf trkckhkrëb tfbefbil fb nufbtk `ls lchfvls y `ls rfsu`tkils k lctfbfr fb fstf `kclrktlrel. pufik iefrfbnekr iefrfbnekr `ls jktfrek`fs jktfrek`fs u`ezkils u`ezkils,, tkjceåb tkjceåb fs plsec`f plsec`f rfk`ezkr rfk`ezkr ub fsqufjk fsqufjk uskbil k`aøb slwkrf pkrk fieneþb if ejëafbfs7 se tljk k`aubk ejkafb if `k rfi bl l`veif rffrfbnekr`k). If` fhfrnenel sf ebfrf quf f` iekarkjk if ufrzks fs rfprfsfbtkil plr8 3
k n:
v r
v :υ r
υ:
ν 3 Ϗ : t Y
d :
;
Y D J 3 D
J ; J ; a Deaurk ;. Iekarkjk if Dufrzks.
∛ D :jk 3
D : J 3 :
v r
3
D J 3 υ r 9
Jlvejefbtl Nernu`kr Dfcrukry 33, 3?;5 3
J ; a : J 3 υ r 3
9 Ϗ
J ; a : J 3
3
Y
r
3
J ; a Y
r:
3
J 3 9 Ϗ
∘
Y :
J 3 9 Ϗ 3 r J ; a
9. YKC@K^ YKC@K^ U IKYL IKYL^ ^ F]_FSEJ F]_FSEJFBYK FBYK@F^ @F^ If `k tljk if iktls nlb `ls iefrfbtfs rkiels sf lctuvl8
YEFJ_L
S:?.;6 j
S:?.3; j
S:?.>? j
S:?.>6 j
S:?.9? j
S:?.91 j
t;
;,96
;,1=
;,=3
3
3,;
3,9>
t3
;,93
;,45
;,5
3,;>
3,3
3,6
t>
;,93
;,4;
;,15
3,;4
3,;1
3,96
t
;,9>
;,45
;,=9
3,;
3,;4
3,94
(s)
Ykc`k ;. Iktls jfieils fxpfrejfbtk`jfbtf. _krk f` rkiel if ?,;6 j sf lctuvl `ls seauefbtfs rfsu`tkils.
F]_FSEJFBYK@ Y ;: Y ;:
∘
∘
3
J 3 9 Ϗ r J ; a 3
33,5; a∑9 Ϗ
3;9,43 a∑5,=;
j s
Y ;:?,36 s
YFÞSENL ;:
Y
t ¼ vuf`tks 6
3
∑?,;6 j
Jlvejefbtl Nernu`kr Dfcrukry 33, 3?;5
Y ;:
;,9> s 6
Y ;:?,3= s
_LSNFBYKHF IF FSSLS tfþrenl ∓fxpfrefjtk` ∑;??% tfþrenl ?,3= s ∓?,36 s %frrlr : ∑;??% ?,3= s %frrlr :;?,1;%
%frrlr :
_krk f` rkiel if ?,3; j sf lctuvl `ls seauefbtfs rfsu`tkils.
F]_FSEJFBYK@ Y 3:
3
33,5; a∑9 Ϗ
:
∘
Y 3
∘
3
J 3 9 Ϗ r J ; a ∑?,3;
3;9,43 a∑5,=; j3 s Y 3:?,>? s
j
YFÞSENL Y 3:
t ¼ vuf`tks ;,45 s
Y 3:
6
Y 3:?,>> s
_LSNFBYKHF IF FSSLS :
tfþrenl ∓fxpfrefjtk`
∑
;??% tfþrenl ?,>> s ∓?,>? s %frrlr : ∑;??% ?,>> s %frrlr :5,?5%
%frrlr
_krk f` rkiel if ?,>? j sf lctuvl `ls seauefbtfs rfsu`tkils.
F]_FSEJFBYK@ Y >:
∘
3
J 3 9 Ϗ r J ; a
4
Jlvejefbtl Nernu`kr Dfcrukry 33, 3?;5
Y >:
∘
3
33,5; a∑9 Ϗ
3;9,43 a∑5,=;
j s
∑ ?,>? j
3
Y >:?,>4 s
YFÞSENL Y >:
t ¼ vuf`tks ;,=9 s
Y >:
6
Y >:?,>1 s
_LSNFBYKHF IF FSSLS %frrlr :
tfþrenl ∓fxpfrefjtk` ∑;??% tfþrenl
%frrlr : ?,>1 s ∓?,>4 s ∑;??% ?,>1 ^ %frrlr :3,1?% _krk f` rkiel if ?,>6j j sf lctuvl `ls seauefbtfs rfsu`tkils.
F]_FSEJFBYK@ Y 9:
∘
3
J 3 9 Ϗ r J ; a 3
33,5; a∑9 Ϗ
Y 9:
∘
∑?,>6 j
3;9,43 a∑5,=; j3
s
Y 9: ?,>= s
YFÞSENL Y 9:
t ¼ vuf`tks 3,;? s
Y 9:
6
Y 9: ?,93 s
_LSNFBYKHF IF FSSLS %frrlr :
tfþrenl ∓fxpfrefjtk`
tfþrenl 1
∑;??%
Jlvejefbtl Nernu`kr Dfcrukry 33, 3?;5
%frrlr :
?,93 s ∓ ?,>= s
?,93 s
∑;??%
%frrlr :5,63%
_krk f` rkiel if ?,9?j j sf lctuvl `ls seauefbtfs rfsu`tkils.
F]_FSEJFBYK@ Y 6: Y 6:
∘
∘
3
J 3 9 Ϗ r J ; a 3
33,5; a∑9 Ϗ
j
3;9,43 a∑5,=;
s
∑ ?,9? j
3
Y 6:?,9; s
YFÞSENL Y 6:
t ¼ vuf`tks 3,;4 s
Y 6:
6
Y 6:?,99 s
_LSNFBYKHF IF FSSLS tfþrenl ∓fxpfrefjtk` ∑;??% tfþrenl ?,99 s ∓?,9; s %frrlr : ∑;??% ?,99 s %frrlr :4,=;%
%frrlr :
_krk f` rkiel if ?,91j j sf lctuvl `ls seauefbtfs rfsu`tkils.
F]_FSEJFBYK@ Y 4: Y 4:
∘
∘
3
J 3 9 Ϗ r J ; a 3
33,5; a∑ 9 Ϗ
3;9,43 a∑ 5,=;
Y 4:?,96 s =
j s
3
∑ ?,91 j
Jlvejefbtl Nernu`kr Dfcrukry 33, 3?;5
YFÞSENL Y 4:
t ¼ vuf`tks 3,94 s
Y 4:
6
Y 4:?,95 s
_LSNFBYKHF IF FSSLS tfþrenl ∓fxpfrefjtk` ∑;??% tfþrenl ?,95 s ∓?,96 s ∑;??% %frrlr : ?,95 s %frrlr :=,;4%
%frrlr :
6. KBË@E^ KBË@E^E^ E^ U SF^V@YK SF^V@YKIL^ IL^ If `ls rfsu`tkils lctfbeils sf rfk`ezþ ils arknks quf ifsnrecfb f` jlvejefbtl nernu`kr ubelrjf. @k prejfrk ifsnrecf f` jlvejefbtl nernu`kr fb ubneþb if` pfrelil y `k sfaubik ifsnrecf f` jlvejefbtl nernu`kr fb ubneþb if` rkiel.
Arkdnk ;. Arkdnk if rkiel fb ubneþb if` pfrelil
5
Jlvejefbtl Nernu`kr Dfcrukry 33, 3?;5
Arkdnk ;. Arkdnk if pfrelil fb ubneþb if` rkiel If `k arënk ubl y ils sf pufif ebfrer quf jefbtrks f` rkiel sfk jkylr f` pfrelil if` jlvejefbtl nernu`kr tkjceåb vk k nrfnfr fs ifner quf slb ierfntkjfbtf prlplrnelbk`fs fb `k fnukne fnukneþb þb quf ifsnr ifsnrecf ecf f` jlveje jlvejefbt fbtl, l, sf lcsfrv lcsfrvk k kifjë kifjëss quf f` jlveje jlvejefbt fbtl l fs ifsnretl ifsif f` pubtl if lreafb, `l quf nlbrjk `k rf`kneþb if prlplrnelbk`eiki y ifpfbifbnek fbtrf f` pfrelil y f` rkiel. If `ls në`nu`ls sf nljprfbif quf k` vkrekr `ks jksks y `k `lbaetui if `k nufrik quf fs `k quf fhfrnf `k knf`frkneþb nfbtrêpftk, `k nkbiki if vuf`tks y `k vf`lneiki kbau`kr y `ebfk` nlb quf `ks ik vk k vkrekr. Ykjceåb sf pufif ifner quf k jfieik quf f` rkiel if `k nufrik vkyk kujfbtkbil, su rkpeifz sfrë jfblr quf se `k `lbaetui if `k nufrik fs jës nlrtk, yk quf `k knf`frkneþb vk k sfr jkylr fb nukbtl jës sf knfrquf k` nfbtrl.
Kifjës, sf fveifbnek quf `ls plrnfbtkhfs if frrlr rfspfntl k `k ifsnrepneþb if` fhfrnenel nlb cksf k `k tflrêk vkrêkb ifsif 5.?5% y 3.1?%, kihuienkils k frrlrfs k`fktlrels y if `k tljk if jfieiks if` jesjl, pfrl bl ebnurrf fb ubk arkb iespfrseþb y ifjufstrk quf slb tljks prfnesks pkrk f` fhfrnenel.
4. NLBN NLBN@V @V^E ^ELB LBF^ F^ ^f pufif nlbn`uer `k rf`kneþb if prlplrnelbk`eiki quf fxestf fb f` Jlvejefbtl Nernu`kr Vbelrjf fbtrf f` rkiel y f` pfrelil if` jlvejefbtl, kifjës sf lcsfrvkb nþjl kntøkb `ks vkrekc`fs senks ifbtrl if` jlvejefbtl, nljl `k rkpeifz `ebfk` vkrêk fb ubneþb if`
;?
Jlvejefbtl Nernu`kr Dfcrukry 33, 3?;5
rkiel y f` pfrelil if `k trkyfntlrek y nljl f` jlvejefbtl quf ifsnrecf `k trkyfntlrek mknf quf `k knf`frkneþb nfbtrêpftk sfk nlbstkbtf. Fs ejplrtkbtf nljprfbifr f` jlvejefbtl y nljl vkrêk fb ubneþb if sus vkrekc`fs senks plrquf fstf pufif ifsnrecer iefrfbtfs fbþjfbls quf lnurrfb fb `k nliekbeiki nljl `k rltkneþb if `k frrk y `ks ` ks nurvks if `ks nkrrftfrks.
1. SFDF SFDFSF SFBN BNEK EK^ ^ Auêk `kclrktlrel senk senk nk`lr y lbiks lbiks ujba nkjpus 3?;5 pfrelil pfrelil E mp8//www.prlsenk.n`/nlbnfptls/nlbnfptls.pmp
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