XAC DINH MOMEN QUAN HNH CUA VAT RAN SJl OUNG PHUONG PHAP OilY v l HAM MUT BIlN TRONG OAY HOC GIAI BAI TAP PHAN CUHIIE m m 6 CAC TROiiNG CAO BANG SO PHAM ThS N G O G I A VINH* Trong chucmg trinh dao la[.]
Trang 1XAC DINH MOMEN QUAN HNH CUA VAT RAN SJl OUNG PHUONG PHAP OilY vl HAM MUT BIlN TRONG OAY HOC GIAI BAI TAP PHAN
CUHIIE m m 6 CAC TROiiNG CAO BANG SO PHAM
ThS N G O G I A V I N H *
Trong chucmg trinh dao lao giao vien vat li d
cac Irudng cao dang su pham cdphan Cahgc
vit rin Ndi dung phan nay ed rat nhieu bai
lap (BT) lien quan den khai niem vat li: "Momen quan
tinh cua vit rin'va dua ra cdng thu'c tinh Momen
quan linh cua mdt sd vat r^n cd linh chat ddi xung
degiai cae BT Trong kTthuat tim Momen quan linh
eua vat r i n , phai xay dung bleu thij'e tieh phan, tinh
tich phan nhieu Idp cua ham nhieu bien; phan ldn
bieu thuc ducfi dau lich phan la rat phtic tap, sinh vien
(SV) ehua du kien thdc loan de tinh tare liep cac lich
phan nay Tuy nhien, neu biet each phan tich bai
loan thanh cac van de nhd va quy ve bai loan mdt
bien sd lhi viec linh loan se trd nen dan gian han,
SV cd the tu giai cae BT d nha va hieu sau sac hon
ban chat eua cae dai lugng vgt li, ddng thdi cung cd
dugc kien Vndc
I C a soli thuyet
Khi nghien cuu ddng luc hpc eua he nhieu hat,
vat rin trong ehuyen ddng quay xung quanh mot
laic xuat hien bieu thu'c; Z " ' < i ' , neu he lien kel chat,
phan bd lien lye trong khdng gian (vat r&n) lhi cd
bieu thuc luang duong la J/^'-"'''^ Tuy theo suphan
bd cua vat r§n trong khdng gian ma mien V cd the
la khdng gian 1,2 hoae 3 chieu, tuong ijmg vdi tich
phan 1,2 hoae 3 Idp cung sd bien sd Dai lugng vat
li duge xac djnh id hai bieu thii'c tren dugc ggi la
Momen quan tinh eua vat r4n ddi vcri tnjc quay da
cho (gpi tat la Momen quan tinh ciia vat rin), ki hieu:
/=Jp(r)rVl'jij
Ve y nghia vat li, Momen quan linh cua vat r^n I
dae tn/ng eho muc quan linh cua vat trong chuyen
ddng quay xung quanh mpi true (tuang tu nhu khdi
lugng ctJa vat trong chuyen dgng tjnh lien) Biaj thuc
(1) cho Ihay, neu vat r§n cd hinh thii bat kl, phan bd
khdng dong nhat lhi bieu thde (r) rat pht/c lap, viee
601 Tap chi Giao due so 304
xac dmh I se rat khd khan Thdng Ihudng, vat ran duoc xem nhu mdl vat ddng nhait va p(r) = const, viec linh I lu cdng thuc (1) chi phu Ihudc vao dp phuc lap ve hinh dang cua vat rin (mien V)
Neu Injc quay khdng di qua khd'i tam, ap dyng edng thuc Huyghen thdng qua Momen quan linh eua vat r i n ddi vdi tn^c quay di qua khdi tam 1^, ta
ed: / = /, + ci'M Trong qua trinh giang day, ehung
ldi nhan thay ddi vdi SV, cdng thirc (1) d l nhd nhung cac em gap khd khan khi van dyng vao ^iai BT, ngay ca doi vdi bai loan dan gian nha't (vat ran phan
bd theo khong gian mdl chieu) Nguyen nhan cd the
la do SV: + Chua biet each chpn gdc tpa dd phii hop, cac em gap khd khan trong viec xac dinh r trong he tpa dp (khoang each tir chat diem dang xel de'n taic quay) hay nham lan vdi gia tri r trong de BT; + Cdn lung lung trong viec xac djnh can eua tieh phan tuong ting vd^ cac bien so; + Khdng tinh dugc lieh phan trong tardng hgp nhieu bien sd
Oe giup SV khae phyc cae nguyen nhan tren, dudi day, ehung tdi hudng d i n SV each ehuyen ve bai loan mpt chieu (tuang iimg 1 bien)
2 Mot so BT c u t h e
BT 7.-Tinh Momen quan tinh cua thanh thing
ddng nhat cd chieu dai L, khd'i lugng M quay xung quanh taic vuong gde vdi thanh di qua khdi lam cua
nd
Chpn gdc tpa dp 0 nhu hinh 1 Chia thanh thanh
nhung doan nhd dx sao chp mpi chat diem tren dx coi nhu mpt chat diem cd khoang each la x den gdc
0
Ap dyng cdng thire (1), ta dugc:
' f - "r , 2 ,\LI2
1= ^p.x'd\ ~2p jx'dx = px\ =
' Pkoig BT - QIKH • QHQT, Tnrang Cao daag stf pham 8ac Niaii
Trang 2mdng hinh ehunhaldong nhat cd khdi lugng M, kich
ttiude a, b quay xung quanh toic vudng gde vdi mat
phang eiia nd va di qua khd'i lam
Oay la bai loan vat cd kich thude phan bd trong
khdng gian 2 chieu (x, y) quay xung quanh laic Oz
(xem hinh 2) Mdi chat diem tren vat cd toa do x, y
lhi khoang each den taic quay la r = yfPTT^ SV cd
the giai BT nay theo
cac each sau:
Caeh 1 (tinh
thdng Ihudng): Ap
dyng edng thiirc (1):
/ - | f |ptj^'+j'')<«.U
Cac/7 ^ (quy ve , ^'"^^
ham 1 bien): Chia mat p h i n g bdi cac dudng thing
song song vdi Cy cd^phuang trinh x va x + dx, la cd
thS'coi phan mat phang trong khoang giua x va x +
dx nhu mpt thanh t h i n g trong BT 1 ed khdi luang
dm = pbdx
Ap dyng ket qua s r M a ed:
Hinh 3
BT 3: Tinh Momen quan
tinh cua hinh taj dSc ddng nha't
khdi lugng M, ban kinh day R
quay xung quanh taic cua nd
{hinh Si
Bay la bai loan vat phan bd
tren khdng gian 3 chieu, mien
lay tieh phan la mien V (loan bd the tich hinh tai) Viec
xay dung va tinh loan bleu thuc dudi dau tieh phan rat
phuc t ^ c d t h e q u y v e ham 1 blen nhu sau:
Gpi H la ehieu cao hinh tnj Chia the lieh hinh tnj
bing nhQng m^t tm dong lam cd ban kinh day la r
var + dr Cac chat diem trong phan the lich hinh tai
nim giua 2 m5t tai cd ciing khoang each den Inj
quay la r (dr rail nhd) nen Momen quan tinh eua nd
ddi vdi Injc quay la: d / = r - i / A / = 2 ; r / / r V r suy ra
l=^2irHp.ydt =
^nHpR*=>jMli'-Ket qua 1 khong phy thude H nen ed the ap dyng
ket qua nay eho dia trdn dong nha't
BT 4: Tinh Momen quan tinh cua hinh ndn
dong nha't cd chieu cao H, ban kinh day R, khdi
cua nd {hinh 4)
Day la bai loan vat phan bd trong khdng gian 3 chieu, theo cdng thuc (1) lhi bieu thuc tinh Momen quan linh eua vat la tich phan 3 Idp, vdi 3 blen s d
la X, y, z Neu tinh true tiep theo cdng Ihue (1), SV se gap rail nhieu khd khan khi xay dung bleu thdc dudi dau tich phan, can lay tich phan va tinh tich phan 3 ldp Ta cd the dan gian hda bai loan quy ve mdt bien theo each sau: chia hinh ndn bdi cac mat phang song song vdi day, cac mat cd toa dp la z va z + dz Khoang each dz rat nhd sao eho cac chat diem tren khoang giira z va z +dz cd cung dp eao so vdi day K h i d d , cd the coi phan hinh ndn n i m gii/a
z va z + dz la mdt dTa trdn ddng nhat ed ban kinh
r, khdi lugng dM va thu duae:
r = R—~;dM = pnr^-dz^p}rR-^^ ^±; Momen
quan tinh cua nd dd'i vdi laic quay Oz (ap dung kel qua 57" 5) la'
dl = -r- tIM p^rR' '•"';'' dz
2 2 II'
Vay, Momen quan linh cua hinh ndn ddivdilnjc quay Oz la:
2 ,', H 2H' 3 |0 10
0 1 = —MR' ( v d i S1 = -irR-H)
3 BT ap dung TinhMomenquan tinh cua mdl sdvat r i n trong cac trudng hgp sau:
1) Hinh cau dae ddng nhat ban kinh R, khcS lugng
M quay quanh tnjc di qua tam
Hudng din: kp dung each giai nhu BT4
2) DTa Iron dcng nh^, khdi luong M, ban kinh R quay quanh true nim trong mat phang dTa va di qua tam
Hudng din: Chgn he tpa dp Oxy, tning vdi mat
phang dTa, gdc tpa dp la lam tJia Khdng mail tinh tdng quat, ta gia thiel dTa quay quanh loic Ox Chia mat dTa bang cac dudng thang vudng gde vdi laie
Ox cd phuang trinh x va x + dx, khi dd, phan dia
n i m giu'a x va x + dx ed the eoi la mdl thanh thang dong nhait cd ehieu dai / - V A ' - J - va ap dung ket qua 6 7 / d e g i a i tiep
Tap chi Gido dye so 304 61
Trang 3eao H, quay quanh tmc (D) vudng gdc vdi tme ciia
hinh tm va di qua khdi tam cua nd
Hudng din: Chpn taic tpa dp Oxyz gde tai trpng
tam cda hinh tai, Oz tmng vdi tryc cua hinh tm Chia
hinh tm bdi cac mat phing song song vdi Oz cd loa
d p j a z va z + dz Phan hinh tm n i m giira 2 mat
phang ed the coi la dia trdn ddng nhat, chpn tmc quay
(D')diquatam cuandva//(D) A p d y n g k e l q u a f l T
3vadinh li Huyghen de xay dung bleu thuc dudi dau
tich phan va giai bai loan,
Tren day la kTthuat xay dung tich phan va dan
gian hda nhung bai loan phdc lap trong viec tim
Momen quan tinh cua mdl sdvat r i n ed linh eha't
ddi xung trong phan Cahgc vat rin Van dung kT
thuat nay, SV cd the gial quyet cac bai loan tTnh dien
(su tich dien cua mpt sd vat ed kich Ihudc gay ra
dien tmdng d xung quanh no, ) cung nhu cac bai
loan ve tt; tn/dng (cam ung Id gay ra tai mdt diem
khacnhau) G
T^i lieu tbam k h a o
1 Nguyen HQu Minh Cffhoc NXB Cidoduc H 1999
2 David Halliday Co- s& vflt 1( NXB Gido d^c,
H 1999
SUMMARY
In training college physics teachers curriculum (Teachers of physics, of mathematics bachelor of Informatics ) The conten of this section has a lot
of exercises related of physical concepts "Moment of inertia of a solid" and stated the formulas for calcu-lating the moment of inertia of some solid symmertiical mature to apply the relevant exercies However, if you know how to analyze the problem into smaller problem for you on one-variable problem, the calcu-lation becomes fairly self explanatory that students can do at home In doing so all the formulas pre-sented in the program can be demonstrated, stu-cal quantity and strengthen math - an important tool
In the study of physics
Tinh trang "hoc tru chan"
(Tiep theo trang 64)
bao SU duy tri sinh hoat vathuc hanh de mdi nhdm
SV (10 SV/ nhdm)_dugc tham gia it nhat mdt lan
- Nha ta/dng kel hpp chat ehe vcS eac ban, nganh
huu quan trong tinh xay dung, thuc hanh, trai nghiem
he thd'ng KNS cho MS d eae cap hpc giiip cac em
hieu dugc y nghTa cua cupc sdng ddng thdi cd nhung
quyel djnh dung d i n trong viec lya ehpn nghe n g h i ^
cho ban than trong tuong lai
Hien tugng "hpc tru chan" cua SV d eac trudng
OH, CO da lam anh hudng khdng nhd de'n chat
lugng day va hoc cua nha irudng; gian liep phan
anh su non kem, thieu hut cac KNS cua S V V i vay,
viec giao due, tao lap cho SV he thd'ng KNS de b i t
nhjp dugc v(^ cudc sdng hien dai, vdi xu the hgi
dugc 4 J m c d t trong^hpc tap do UNESCO de ra:
'Hoc debief 'Hoc delam vied', "Hgc decung ehung
son^ va 'Hgc detukhing dinh minti'.U
(1) Qudc Viet " 8 3 % SV Ihi^u kl nSng sdng" http://
phapluatlp.vn
Tai li$u t h a m k h a o
I Nguyen Thanh Binh Giiio t r i n h chuy£n de giao
62 Tap chi Gido due so 304
due ki nSng stfng NXB Dgi hpc su phgm Hd N^i,
2010
2 Nguyin Vfin L& Hoc sinh, sinh vien vdi \&n h6a dao due ti-ong iing xu- xa h^i NXB Gido due H 2006
SUMMARY
Incontemporary liefe livingskills of students In University level are concerned issue of the whole and solf skills) considerately effect on their future Thewayofunsetted studyin the way they show the absence of living skills of big part students It di-rectly effect on their result and traning Besides In indirectly effects on the education process of col-leges and universities
Chat lirpg nguon nhan lire
(Tffip theo trang 64)
dai bieu toan qutfc l^n thii X I , NXB Chfnh tri
qudc gia • Su thdi, H 201 I
2 Tinh uy Ki&n Giang Vfln ki^n Dai h$i dai bi^u Dang bd tinh Idn I h i i l X , nhiSm ki 2010 - 20IS 2010
.1 Oy ban nhan dan tinh Kien Giang "Quyit dinh phi
duyit quy hogch phdl triin nhdn t^c linh Kiin Giang giai dogn 2011 - 2020" (ng^y 23/02/2012)
4 Cue Thdng kfi Kien Giang "Sdliiu thdng kikinh li
• xd hpi Kiin Giang 30 ndm (1975- 2005) " Kifin Giang
2007
-(kl2-2/2013)