Chuyen dpng ciia diem dau mpt chiec kim giay dong ho va diem dau mpt canh quat may co nhung diem gi gidng nhau va khae nhau ?
I - D I N H NGHIA 1. Chuyen dong tron
Chuyen dqng trdn Id chuyen dqng co quy dqo Id mqt dudng trdn.
Vi du : Khi chie'c du quay quay trdn, quy dao ciia diem treo cac ghe ngdi trdn chid'c du quay la nhung
dudng trdn cd tam nam trdn true quay (Hinh 5.1). Hmh 5.1
2. Toe do trung binh trong chuyein dong tron Tuomg tu nhu trong chuydn ddng thang, ta dinh nghia td'c do trung binh trong chuyen ddng trdn nhu sau :
Td'c dd ^ 9 dai cung trdn ma vat di dugc trung binh -ph^i gj^n chuyen ddng
3. Chuydn dpng tron deu
Chuyen dqng tron deu la chuyen ddng cd quy dao trdn vd cd toe dq trung hinh tren moi cung trdn la nhu nhau. (Hinh 5.2). Si
SS Hay neu mpt vai vf du ve chuyen dgng tron deu.
Hinh 5.2
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[ S Mpt chiec xe dap ehuyen dpng deu tren mdt dudng trdn ban kfnh 100 m. Xe ehay mdt vong het 2 phiit. Tfnh tdc dp dai ciia xe.
Hinh 5.3
Hinh 5.4
Khai niem tdc dp goc chi noi len sir quay nhanh hay cham ciia ban kinh OM.
II - T d c 0 0 DAI VA TbC DO GOC 1. Toe do dai
Ggi As la do dai ciia cung trdn ma vat di dugc tir die'm M dd'n didim M' trong khoang thdi gian rat ngan At.
Khoang thdi gian nay phai ehgn ngan dd'n mue ed the coi cung trdn nhu mdt doan thang. Ta ggi thuomg sd:
v - ^ (5.1) As
la tdc do dai ciia vat tai didm M. Tdc do dai chfnh la do ldn ciia van tdc tiic thdi trong chuyen ddng trdn ddu.
Trong chuydn ddng trdn ddu thi As ludn ludn ti Id
\'di At, ndn v la mdt dai lugng khdng ddi va bang tdc do trung binh ciia vat. Trong chuyen dcing iron deu, tdc dtp ddi ctia vcit khong ddi.
2. Vecto van toe trong chuy§n dong tron deu Trong didu kidn cung trdn cd do dai rai nhd. ed the coi nhu mgt doan thang. ngudi, ta dung mdt vecto
As vira de chi quang dudmg di dugc, vira de chi hudng chuydn ddng. As ggi la vecta dep dcri Khi dd. van td'c se dugc bidu didn bang vecta vein tdc, cung phuomg. ciing chidu vdi vecto do ddi :
^ _ A?
^' ~ ^
Vi As triing vdi mdt doan cung trdn tai M ndn nd nam dgc theo tiep tuyen vdi dudng trdn quy dao tai M. v ciing hucVng vdi As nen nd cung niim theo tidp tuyen tai M (Hinh 5.3).
Vecto vqn toe trong chuyen dong tron deu luon CO phuong tiep tuyen vdi ducmg tron quy dao.
3. Toe do goe. Chu ki. Tan so
a) Dinh nghia
Ggi O la tam va r la ban kfnh cua dudng trdn quy dao.
/W la vi trf tiic thjdi ciia vat chuyen ddng. Khi vat di dugc mdt cung A.v trong khoang thdi gian Al thi ban kinh OM quay dugc gdc Aa (Hinh 5.4).
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Thuoms sd :
CO = Aa
~At~
(5.2)
ggi la tdc dc) girc cita chuyen dcJng trdn. Trong chuydn ddng trdn ddu thi gdc Aa tang ti le thuan vdi thdi gian At. nen td'c do gdc co ludn khdng ddi.
Toe dq goc cuu cliuycn dqng tron la dqi luong do hdng gdc md han kinli OM quel duoc trong mqt dim vi thin gian. Toe do goc cua cliuycn dong trdn deu Id dqi luqng khong doi.
h) Dan vi do tdc do goc
Nd'u gdc Aa do bang dom vi radian, thdi gian Ar do bang dom vi giay thi tdc do gdc co do bang don vi radian tren gidy (vie't tat la radls). Sl
c) Chu ki
Chu kl T cua chuyen dong tron deu la thcri gian de vqt di duqc mot vong.
Cdng thuc lien he giua td'c do gdc co va chu ki T ;
7 = ^ (5.3)
(0
Dom vi chu ki la giay (s). [ S d) Tdn sd
Idn so f cua chuyen dong trdn deu Id so vong md vqt di duoc trong I giay.
Cdng thuc lidn he giiia chu ki va tiin sd :
J J (5.4)
Don vi ciia tan sd la vdng tren giav (vdng/s) hoac hec (Hz), ffi
c) Cdng tlufc lien he Ciifa tdc do ddi vd tdc do ecic Ta da bidt. trong hinh trdn thi :
do dai cung = ban kfnh x gdc d tam chan cung. Nhu vay. ta cd : A.s = / A«, vdi Aa do bang radian.
^ - . • . ' . - ^^ ^01
Tu he thuc tren. suy ra : — =; /•
Ar Ar hay
H3
V = roj (5.5)
Sl 0 6 loai dong ho treo tudng ma kim giay quay deu lien tue.
Hay tinh tde dp goe ciia kim giay trong dong ho nay.
L d H a y chdng mmh cong thue (5.3).
143 Hay ehu'ng minh cong thdc (5.4).
f.' Hay tfnh tdc do gdc cua chiec xe dap trong cau
--.-31
Ill - GIA TOc HLTONG T A M
M,
Hinh 5.5
1. Huong eua veeto gia toe trong ehuyen dong tron deu
Dt xet gia tdc ciia vat tai diem / (Hinh 5.5), ta khao sat su bid'n ddi vecto van tdc U ciia vat khi no chuyen ddng trong khoang thdi gian rat ngan Ar tir didm A/j dd'n didm M, trdn cung dudng trdn cd trung didm la /. Hai vecta van td'c ij^ va u., tai cae diem M^ va MT cd do dai bang nhau, nhung cd hudng khae nhau vl chiing lan lugt vudng gdc vdi cac ban kfnh OM, va OM^.
I nh 5.6
Can cii vao hai tam giac dong dang Iv.v^ \ii OM.M^ tren tfinh 5.5. ta co :
AT M|/W, OM, Ji.' = . suy ra : u^^ v-M
vM r
/Sv V
~ M ' r Vidii :
.\lpt ve tinh nhan tao chuyen dpng tron deu quanh Trai Dat tren mpt qus dao co Iam la tam Trai Dat va co ban kinh 7 000 km. Toe dp dai ciia
\e linh lii 7.57 km/s. Tinh gia tdc hucmg tam ciia ve tinh.
(7,57.10')-Giiii
7 000.10
= 8.2 m / s
-Neu tinh tidn hai vecto v va v.^ dd'n diem /, ta se tim dugc vecto AS bie'u didn su thay ddi hudng ciia van tdc (Hinh 5.5) :
v^ + Av = iJ-, hay Av - v^ - iJ^
Vi cung MiMo rat nhd va vat chuydn ddng trdn ddu. nen ta cd the: coi hai didm Mj va M-, gan nhu triing nhau tai / va vecto At; bidu didn su thay ddi ciia van tdc tren doan dudng M^M~, nay.
Cd the chung minh vecta Ar; ludn ludn nam dgc theo ban kfnh va hudng vao tam O ciia quy dao.
Vecta gia td'c a ciia chuydn ddng trdn deu cung dugc xac dinh bang cdng thiic (3.1b) :
(7 =
A ^ Af
Vecto d ciing hUdng vdi vecta Av ndn nd cung nam dgc theo ban kfnh va hudng vao tam (Hinh 5.6). Do dd ngudi ta ggi gia td'c trong chuyen ddng trdn deu la gia tdc hudng tdm va kf hidu la a^^.
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Trong ehuyen dong trdn deu, tuy van toe co do lan khong doi, nhung cd hucrng luon thay doi, nen chuyen dong ndy co gia toe. Gia toe trong chuyen dqng trdn didi luon hucrng vdo tam cua quy dao nen gqi Id gia toe hudng tam.
2. Do Ion eiia gia toe huong tam Cdng thurc tinh gia td'c hudng tam la :
.2
«ht = V
r (5.6) HflHay chimg minh cdng thdc :
m am = rco^ (5-7)
''r. Chuyfen ddng trdn deu la chuydn ddng cd cac dac di6m : Quy dao la mdt duong tron :
Tdc dd trung binh tren moi cung tron la nhu nhau.
S Vecto van tdc cua vat chuyen dpng trdn deu cd : phirong tiep tuydn vdi dirong tron quy dao ; do Idn (tdc dd d a i ) : i ' = ' '
Toe dd goc : CO = ; A a l a gdc ma ban kinh ndi t u t a m den vat quet duoc trong
Al'
thdi gian At. Don vi tdc dd gdc la rad's.
Cdng thuc lien he giua toe do dai va tdc do gdc : v = ro).
Chu ki cua chuyen ddng trdn deu la thoi gian de vat di diroc mdt vdng.
Cong t h u t lien he giua chu ki va tdc dd goc : 2n
" • - , . . . . i
Tan sd cua chuyen ddng tron deu la sd vdng ma vat di duoc trong 1 giay. Oon vi tan .>:, so la vdng/s hoac htc ( H i i .
, Cdng thirc lien he friira chu •<; •-! lan so ;
' '' Gia tdc trong chuven done u o r ..e;j •uon huon ; vno tam quv d.io va rn •_(• ipp ia :
3A - VAT Ll 10 3 3
-. .„ HOI VAB Al TAP
a>^ I B. Tdc dp goc cua chuyen dpng trdn deu phu
~" 1. Chuyen dong trdn deu la gi ? thupe vao ban kfnh quy dao.
2. Neu nhung dac diem cua vecto van tdc cua ^' ^^^ ^ '^ ^ ^h° ^'^^'' ^'' * ° ' ^^"^"^ *'"^
ehuyen ddng tron deu phu thudc vao ban kinh quy dao^
D. Ca ba dai luong tren khong phu thuoc vao 3. Td'c dp goc la gi ? Tdc dp goe dugc xac dinh j^gp, y^^^^ ^uy ^^^
nhu the nao ? ..A ,-u' - •
10. Chi ra cau sai.
4. Viet cong thirc lien he giua td'c do dai va tdc _, .-. ,. . . ,.. , , .- ,.;j„ ^„
^. . , ,_ ., ^. , , ,.: Chuyen dong tron deu co cac dac diem sau:
do goc trong chuyen dong tron deu. / . r
^ • , , • „ , A. Quy dao la dudng trdn;
5. Chu ki cua chuyen dpng tron deu la gi ? Viet g ^ ^ ^ j ^ ^. ^ ^.^ ^^^^g 3...
cdng thiic lien he giUa chu ki va toe dp gdc. ^ j^^ ^^ g^^ ^^^^ng ddi;
6. Tan so cua chuyen dpng trdn deu la gi ? Viet D. Vecto gia td'c ludn hudng vao tam.
cong thirc lien he giUa chu ki va tan sd. ^ -, _ |^5t q^at may quay vdi tan sd 400 vdng/phiit.
7. Neu nhung dac diem va vie't cdng thirc tinh Canh quat dai 0,8 m. Tinh td'c dp dai va tdc dp gia td'c trong chuyen dpng trdn deu. goc cua mpt diem 0 dau canh quat.
12. Banh xe dap co dudng kinh 0,66 m. Xe dap chuyen dpng thang deu vdi van tdc 12 km/h.
Tinh td'c dp dai va td'c dp goc cua mpt diem 8. Chuye'n ddng cua vat nao dudi day la chuye'n *^^" ^^"^ banh ddi vdi ngudi ngoi tren xe.
dpng trdn deu ? 13. Mpt dong ho treo tudng co kim phut dai 10 cm va A. Chuye'n dpng cua mpt con lac dong ho. kim gid dai 8 cm. Cho ring cac kim quay deu. Tinh B. Chuyen dpng ciia mdt mat xich xe dap. tdc dp dai va tdc dp goc cua diem dau hai kim.
^ _, .. ,. , ... J J... 14. Mot diem nam tren vanh ngoai cua mot lop xe may C. Chuyen dong cua cai dau van xe dap doi ,• ^ ,_. ,_ ^„ ,, , .,• ^ ,z
;., . u J- cach true banh xe 30 cm. Xe chuyen donq thanq voinguoi ngoi tren xe, xe chay deu. ... ,,:.... ^ ^.. .' ,.-.^,, .^
, , deu. Hoi banh xe quay bao nhieu vpng thi so chi tren D. Chuyen ddng cua cai dau van xe dap ddi ^g^g ho tdc do cua xe se nhay mdt sd iJng viS 1 km.
vdi mat dudng, xe chay deu. ._ ...^ u - .- ^ ,
15. Mpt chiec tau thuy neo tai mpt diem tren Cau nao dung ? 3^;grlg xfch dao. Hay tinh td'c dp goc va td'c dp A. Tdc dp dai ciia chuyen dpng trdn deu phu dai cua tau doi vdi true quay cua Trai Dat. Biet thuoc vao ban kinh quy dao. ban kfnh ciia Trai Da't la 6 400 km.