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[.]
XAC 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 CAC TROiiNG CAO BANG SO PHAM ThS N G O G I A V I N H * T rong chucmg trinh dao lao giao vien vat li d cac Irudng cao dang su pham cdphan Cahgc vit rin Ndi dung phan ed rat nhieu bai lap (BT) lien quan den khai niem vat li: "Momen quan tinh cua vit rin'va dua 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 Tuy nhien, neu biet each phan tich bai loan 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 ehuyen ddng quay xung quanh mot laic xuat hien bieu thu'c; Z " ' < i ' , neu he lien kel chat, phan bd lien lye khdng gian (vat r&n) lhi cd bieu thuc luang duong la J/^'-"'''^ Tuy theo suphan bd cua vat r§n khdng gian ma mien V cd the la khdng gian 1,2 hoae chieu, tuong ijmg vdi tich phan 1,2 hoae 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 chuyen ddng quay xung quanh mpi true (tuang tu nhu khdi lugng ctJa vat 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 van dyng vao ^iai BT, ca doi vdi bai loan dan gian nha't (vat ran phan bd theo khong gian mdl chieu) Nguyen nhan cd the la SV: + Chua biet each chpn gdc tpa dd phii hop, cac em gap khd khan viec xac dinh r he tpa dp (khoang each tir chat diem dang xel de'n taic quay) hay nham lan vdi gia tri r de BT; + Cdn lung lung viec xac djnh can eua tieh phan tuong ting vd^ cac bien so; + Khdng tinh dugc lieh phan 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 bien) Mot so BT c u t h e BT 7.-Tinh Momen quan tinh cua thing ddng nhat cd chieu dai L, khd'i lugng M quay xung quanh taic vuong gde vdi di qua khdi lam cua nd Chpn gdc tpa dp nhu hinh Chia thanh nhung doan nhd dx chp mpi chat diem tren dx coi nhu mpt chat diem cd khoang each la x den gdc Ap dyng cdng thire (1), ta dugc: 'f "r , ,\LI2 1= ^p.x'd\ ~2p jx'dx = px\ = ' Pkoig BT - QIKH • QHQT, Tnrang Cao daag stf pham 8ac Niaii -(ki 2-2/2013) BT 2: Tinh Momen quan linh cua vat phang mdng 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 khdng gian chieu (x, y) quay xung quanh laic Oz (xem hinh 2) Mdi chat diem tren vat cd toa x, y lhi khoang each den taic quay la r = yfPTT^ SV cd the giai BT theo cac each sau: Caeh (tinh thdng Ihudng): Ap dyng edng thiirc (1): / - | f |ptj^'+j'')