530 076 K300T PGS.TS N G U Y E N Q U A N G L A C S N G U Y E N T H I N H I - T S C H U V A N L A N H KI THUAT GIAI NHANH BAI TAP TRAC NGHIEM irl*if TAP! • D O N G LTJC H O C V A T R A N D A OD O N G C O • SONG C O • D A O D O N G V A S O N G D I E N TU" D O N G DIEN XOAY CHIEU • Danh cho hoc sinh Idp 12 chiidng trinh chuan va nang cao • On tap va nang cao ki nang lam bai Bien scan theo npi dung va cau true de thi cua bp GDSfDT BAN D A IH O C QUOC GIA H AN O I fi — ¥ & r N G U Y E N T H I N H l - Tfc> (Jhtu VAJN £ A m r Kl THUAT GIAI NHANH • BAI TAP TRAC NGHIEM • D O N G L U C H O C VAT RAN • DAO DONG CO • S6NG CO • DAO D O N G VA SONG D I £ N T f D N G DI$N XOAY C H I E U • Danh cho hpc sinh Idp 12 chUcfng trinh chuan va nang cao • On tap va nang cao k i nang lam b^i • Bien soan theo noi dung va cau triic de thi cua bp GD&DT THIJ ViFNTiNHBINMTHUAN DCK] NHA XUAT BAN DAI H O C Q U O C GIAH A NOI CHCJ LOfI N O I D A U DONG L U C HOC VAT RAN Quyen sach giiip cac em hoc sinh lop 12 va cac em dang on luyen de thi CD - D H h^ thong hoa kien thuc ly thuyet va luy^n tap each tra loi cau hoi trac nghiem Kien thuc ly thuyet duoc he thong hoa theo chuan chuang trinh Bai tap trac nghiem dugc phan cac dang phu h^p vai npi dung ly thuyet va mot so'each giai dac bi?t dugc cap nhat mot each kip thai t u cac de thi thu dai hoc ciia cac truong nhu THPT chuyen Phan Boi Chau, THPT chuyen Dai hpc Vinh, THPT chuyen DHSP Ha Noi, va de thi CD - D H cac nam gan day, ke ca de thi CD- D H nam 2013 vua qua Mot so'bai tap kho dugc danh dau * de cac em luu y doc Quyen sach dugc tach hai tap de c6 d i i dung lugng cho vi^c chuyen tai ngi dung ly thuyet va khoi lugng bai tap day dii, phong phii * Tap bao gom: - Chu de 1: Dong luc hgc vat ran; - Chu de 2: Dao dgng ca - Chu de 3: Song co; - Chu de 4: Dao dgng va song dien tu - Chu de 5: Dong di^n xoay chieu; * Tap bao gom: - Chu de 6: Tinh chat song anh sang; I H E T H O N G H O A K I E N THLfC Mot vat ran quay quanh mot true co'djnh thi mgi diem tren vat ran vach nen nhOng vong tron cac mat phang vuong goc vai true quay, c6 tam nam tren true quay va ban kinh bang khoang each tir diem den true quay Moi diem ciia vat quay cung mot goc cung mgt khoang thai gian N h u v^y, chuyen dgng quay quanh mgt true ciia vat ran la tong hgp nhiing chuyen dgng tron tren vat ran Chuyen dpng quay ciia vat ran quanh mpt true co dinh Su tuong t u gii>a cac dai lugng goc dac trung cho chuyen dgng quay ciia vat r ^ quanh mgt true co djnh va dai lugng dai dac trung cho chuyen dgng thang: Chuyen dgng thang Chuyen dgng quay (chieu khong doi) (true quay co djnh, chieu quay khong doi) Tga do: x Tga goc: (p Toe do: v = x' Toe goc : ( = cp' Gia toe: a = v' = x" Gia toe goc: y = co' = cp" Chuyen dgng thSng deu: Chuyen dgng quay deu: V = hang so; a = 0; x = xo + vt 0) = hang so; y = 0; (p = cp,, + cot Chu de 7: Lugng t u anh sang Chuyen dgng thSng bien doi Chuyen dgng quay bien doi deu: - Chu de 8: Thuyet tuong doi hep; deu: - Chu de 9: Vat ly hat nhan nguyen t u a = hang so' - Chu de 10: T u vi mo den vT mo V = vo + at X nen chi dgc quyen sach bang mat nhu doc tieu thuyet ma nen c6 gia'y but = xo + vot + -at^ de ghi lai nhOng dieu tam dac va tinh toan cac dai lugng vat ly ma bai tap yeu v ^ - V o =2a(x-Xo) cau theo ggi y huong dan giai da cho Lam dugc nhu vay, cac em cam chac kha Cong thuc lien he giOa cac dai lugng goc va dai lugng dai: \ • • De C O kien thuc virng chac va luyen dugc each giai bai tap, cac em khong nang lam trgn ven de thi CD - D H sap toi Dau da C O be day kinh nghiem lau nam va da co'gang bien soan quyen sach tot de phuc vu dgc gia nhung chung toi luon vui long don nhan nhirng y kien quy bau t u cac thay c6 giao va cac em hgc sinh Nhom tac gia y = hang so' CO = COQ + yt (p = (P(,+C0(,t + ^yt^ s = r(p, co^-cog =2y((p-(Po) V = rco; at = ry; a„ = rco^ Chii y: Dan vj ciia cac dai lugng hf don vj SL x(m); v(m/s); a(m/s^); (p (rad); CO (rad/s); y (rad/s2) Phuang trinh dgng luc hgc ciia vat tin quay quanh mpt tr\ic co dinh a Moi lien h^ giira gia toe goc va momen lyc > Momen life dot vai mot true quay Momen M ciia luc F doi vai true quay A co Ian bang: M = Fd (1) Cty TNHH T r o n g d o d la canh tay d o n cua luc F (khoang each tie t r y c A den gia cua Ivc F ) • T h a n h d o n g chat, c6 k h o i l u g n g m va c6 tie't d i ^ n n h o so v o i chieu dai 1 = -lml2 C h p n ehieu quay cua vat l a m chieu d u o n g , ta c6 q u y uoe: - M > k h i F eo tac d u n g l a m vat quay theo ehieu d u o n g - M < k h i F eo tac d u n g l a m vat quay theo ehieu ngupe ehieu d u o n g > Mot lien he giita gia toe goc va momen luc T r u o n g h p p v^t ran la m p t qua cau n h o eo kho'i l u g n g m gSn vao m p t dau t h a n h rat nh? va dai r Vat quay tren mat phMng n h a n n a m ngang x u n g q u a n h m g t true A th^ng d u n g d i qua m p t dau eiia t h a n h d u o i tae d y n g a i a lye F , t h i m o m e n lye tac d u n g len vat ran la: M = (mr2)y 12 • V a n h tron d o n g chat eo k h o i l u g n g m , ban k i n h R, t r y c quay A di qua tarn v a n h va v u o n g goc v o i mat p h a n g v a n h tron: I = m R • D i a t r o n m o n g d o n g chat c6 k h o i l u g n g m , eo ban k i n h R, t r y e quay A di qua t a m dia t r o n va v u o n g goc v o i mat dia: I = - m R • Qua cau dac d o n g chat eo k h o i l u g n g m , eo ban k i n h R, t r y c quay A di (2) t r o n g d o y la gia toe goc ciia vat ran m qua tam qua cau: I = - mR o c Phuong trinh dpng l y c hpc a i a vat tin quay quanh mpt tryc co d i n h la: T r u o n g h g p vat ran g o m nhieu chat d i e m c6 k h o i l u o n g Ian l u g t la mi, mj, each true quay A n h u n g khoang n, r\, khac n h a u t h i m o m e n lye tae d y n g len vat ran la: M = ly (5) T r o n g do: I la m o m e n quan t i n h ciia vat ran d o i v o i t r y c quay A; M la m o m e n lye tac d y n g vao vat ran d o i v o i trye quay A; y la gia toe goc ciia vat (3) ran t r o n g ehuyen d o n g quay q u a n h true A Momen dpng lugmg d i n h luat bao toan momen dpng l u g n g a Momen dpng l u g n g L eiia vat rin t r o n g ehuyen d p n g quay q u a n h t r y e la: b M o m e n q u a n t i n h T r o n g p h u o n g t r i n h (3), dai l u g n g Y^mj^ dac t n m g cho m i i e q u a n t i n h i cua vat quay va d u g e g o i la m o m e n quan rinh, k y hi$u la I M o m e n q u a n t i n h I d o i v o i m o t true la dai l u g n g dac tnmg cho m u c quan t i n h ciia vat ran t r o n g ehuyen d g n g quay quanh true ay (4) M o m e n q u a n t i n h c6 d o n vj la kg.m^ > M o m e n quan tir\ ciia m g t vat ran khong chi phy thuoe vao khoi l u g n g a i a vat ran ma eon p h u thuge vao ea sy phan bo khoi l u g n g xa hay gan true quay > D i n h l y ve trye song song: I Q = Vift ciia no, t r y c quay A d i qua t r u n g d i e m ciia va v u o n g goc v o i t h a n h : D o n v j cua m o m e n l y e la N m * MTVDWirKK^g + md^ T r o n g do: d la khoang each tir true quay O den true song song qua t r o n g tam G ciia vat; lo; IG t u o n g l i n g la m o m e n quan h'nh ciia vat d o i v o i t r y c O va trye G > M o m e n q u a n t i n h ciia m g t so vat ran eo trye quay do'i x i i n g : L = lo) (6) T r o n g do: I la m o m e n quan t i n h ciia vat ran d o i v o i t r y e quay; co la toe dp goc eiia vat ran t r o n g ehuyen d p n g quay q u a n h tryc D o n vj eiia m o m e n d p n g l u g n g la kgmVs b Phuong trinh dpng l y c hpc ciia vat tin quay quanh mpt tryc dupe viet duoi dang khac: M = -AL At (7) T r o n g do: M la m o m e n lye tae d y n g vao vat ran; L = Ico la m o m e n d p n g •trgng ciia vat ran d o i v o i trye quay; AL la dp bien thien m o m e n d p n g l u g n g ciia vat ran t r o n g t h o i gian At c D i n h luat bao toan momen dpng l u g n g K h i M = t h i L = L(o = hang so N e u t o n g eac m o m e n lye tae d u n g len m g t vat ran (hay he vat) d o i v o i m p t true hang t h i tong m o m e n d p n g l u g n g ciia vat ran (hay h ^ vat) d o i v o i t r y c dupe bao toan • T r u o n g h g p I k h o n g d o i t h i w k h o n g d o i : vgt ran (hay h | v^t) d u n g yen ho§e quay deu Cty TNHH MTV DWH Ki thuatgiai nhanh BTTN Vat Li 12, tap - Nguyen Quang Lac • T r u o n g h g p I thay d o i t h i co thay d o i : vat ran (hay he vat) c6 I g i a m t h i co tang, C O I tang t h i co g i a m (Ico = hang so' hay I^co^ = I2CO2) a D p n g n a n g W d cua v a t r a n quay q u a n h m p t true eo d i n h l a : (8) Vi : M p t b a n h xe quay deu q u a n h true co d j n h v o i tan so goc k h o n g d o i 6000 v o n g / p h i i t T r o n g 2,5s banh xe quay d u p e m p t goc la ^ 1257T rad B 250n rad T r o n g d o : I la m o m e n quan t i n h cua vat ran d o i v o i true quay, co la toe d o goc ciia vat ran t r o n g chuyen d o n g quay q u a n h true C 500 n rad D 750TI r a d Huong dan giai: Ta CO f = 6000 v o n g / p h i i t = 100 v6ng/s T u (6) va (8), d p n g nang Wd ciia vat ran quay q u a n h m o t t r y c co' d i n h co the vie't d u o i d a n g : Suy ra: CO = 27tf = 2007t (rad/s) D o do: cp = cot = 20071.2,5 = VVd=^ (9) T r o n g do: L , I Ian l u g t la m o m e n d o n g l u g n g va m o m e n q u a n t i n h cua vat ran d o i v o i true quay D o n g nang cua vat ran co d o n v i la j u n , k i h i e u J quay q u a n h m p t true co d i n h bang t o n g cong thuc hien b o i m o m e n ngoai luc tac d u n g vao vat Ta co: • AW,=llco2-llco?=i(co^-co2) = A (10) T r o n g do: I la m o m e n quan t i n h ciia vat ran d o i v o i true quay, coi la.to'c dp goc liic d a u ciia vat ran, C02 la to'c dp goc liic sau ciia vat ran, A la t o n g cong ciia cac m o m e n ngoai luc tac d u n g vao vat ran, AWd la d p b i e n t h i e n d p n g nang ciia vat ran Dang B A I T A P L I E N Q U A N D E N C H U Y E N D O N G Q U A Y D E U (rad) => C h p n C 50m, quay deu v o i toe dp 120 v o n g / p h i i t Toe d p d a i tai m p t d i e m n a m a v a n h canh quat bang: A 112,6m/s B 314 m/s C 412 m/s D 538 m/s Huang dan giai: in rad/s; ^r = ^— = 25m Ta co: co = 120 v o n g / p h i i t = in D o do: v = co.r = 4.3,14.25 = 314(m / s) Chpn B V i d u 3: M p t vat ran quay q u a n h m p t true co d m h x u y e n qua vat v o i p h u a n g t r i n h tpa d p goc cp = 5,6 + 4,5t, t r o n g cj) t i n h bang r a d i a n (rad) va t t i n h bang giay (s) M p t d i e m tren vat each true quay k h o a n g r = 6em t h i co toe d p dai bang: A 12cm/s VI D V MINH HQA SOOTI V i d u 2: M p t canh quat ciia m a y phat dien chay bang sue gio c6 d u o n g k i n h b D i n h l y b i e n t h i e n d p n g n a n g : D o bien thien d o n g n a n g cua m o t vat ran I I C A C D A N G B A I T A P vA = (vi m i v o n g vat ran quay d u p e m p t goc la 2rc rad) D p n g n a n g ciia v a t r a n q u a y q u a n h m p t true W,=llco2 So' v o n g vat ran quay dupe: " = ^ Khattg Viet B 18 cm/s C 27 cm/s D 35 cm/s Huang dan giai: T u phucmg t r i n h cp = 5,6 + 4,5t ta suy ta: co = cp' = 4,5rad / s Vay V = co.r = 4,5.6 = ( c m / s) => C h p n C CUA VATRAN P h u o n g p h a p g i a i : V a n d u n g cac kien t h i i c ve chuyen d p n g quay deu ciia vat ran: • Dang B A I T A P L I E N Q U A N D E N C H U Y E N D Q N G Q U A Y B I E N To'c d p goc: CO bang hang so' DOI DEUCUAVAT RAN • Gia toe goc: Y = • Tpa d p goc ( p h u o n g t r i n h chuyen d p n g ciia vat ran quay deu q u a n h m p t t r v c c o ' d j n h ) : (P = (PQ + cot ' ' ' L i e n he giCra to'c d p goc va to'c dp d a i : v = cor Gia toe h u o n g tarn: a,., = — = a)^r P h u o n g p h a p g i a i : Sii d u n g cac p h u o n g t r i n h chuyen d p n g quay bien d o i deu ciia vat ran q u a n h m p t true eo d j n h n h u sau: co = coo + y t ; ; g'v; i , ; cp = (p(,+coot + - Y t ; co^-co^ =2y((p-cpy) ^ ^ „"J— ^ ^ Trong c}>o la toa goc tai thai diem ban dau t = 0; coo la toe dp goc tai thai diem ban dau t = 0; cf) la toa dp goc tai thai diem t; co la toe dp goc tai thai diem t; y la gia toe goc (y la hang so) > Khi giai toan, ta neu xet vgt quay theo mpt chieu nhat dinh va chpn chieu quay ciia vat la chieu duong Khi do: • Neu vat ran chi quay theo mpt chieu nhat dinh va toe dp goc tang dan theo thai gian thi chuyen dpng quay la nhanh dan (y > 0) • Neu vat ran chi quay theo mpt chieu nhat dinh va toe dp goc giam dan theo thai gian thi chuyen dpng quay la cham dan (y < 0) > Khi khong de y den chieu quay ciia vat ma vat chuyen dpng quay nhanh dan deu thi co va y cung dau (coy > 0), chuyen dpng quay cham dan deu thi co va y khac dau (coy < 0) v^ , > Thanh phan gia toe phap tuyen a„ co dp Ian: a„ = — = co r > Thanh phan gia toe tiep tuyen co dp Ian: a, = — = ry > Vec to gia toe a dupe xae dinh: a = a„ + a(; ve dp ion: a = -Ja^+a^ V i dy 1: Mpt banh xe quay nhanh dan deu tir trang thai dung yen, sau 4s banh xe dat van toe goc 24 rad/s Goc ma banh xe quay dupe thai gian la: A.23rad B.37rad C 48 rad D 55 rad Huong dan giai: _ , co-cog - ^ , Ta co: y = = = 6rad / s t-to Tu co^ - co^ = 2yAcp =>Acp = ^ 2y =^ i ^ 2.6 Huong dan giai: j w ,^ A p dung cong thuc: co = cO(, + y t , coy = r a d / s , vi banh xe quay ch|m dan deu nen y = -6rad / s^ Do phuang trinh van toe goc la: CO = 12 - 6t (rad/s) 12 Khi banh xe dung lai thi co = => = 12 - 6t t = — = 2s Vay sau 2s thi banh xe dung lai Chpn moc thoi gian t = tai thai diem banh xe bat dau chju lye ham tac dyng, tpa dp goc ban dau cpg = Chpn chieu duong la chieu quay cua vat ran, do, ap dung cong thuc: cp = (P(, +cOot + i Y t ^ =0 + 12.2-i.6.2^ =12rad ChpnD V i d u 3: Mpt banh xe co duong kinh 54 cm quay nhanh dan deu, giay van toe goc tang t u 180 vong/phiit len 480 vong/ phiit Gia toe huong tam ciia diem M a vanh banh xe sau tang toe dupe 3,5s la A 330,4 m / s l B 411,2 mls\ 456,3 m/s^ D 512,7 m / s l Huang dan giai: Ta co: COQ - 67irad / s va co = 16rcrad/s.^ y= CO-co,) = 167t-6K ^ , , = 27i:rad / s Sau 2s, van toe goc bang: co = COQ + yt = 671 +27i,5 = 137trad / s Gia toe huang tam: a^, = co^R = co^ ^ = (l37r)^ :% = 456,3m / Chon C = 48rad^ChonC V i d\ 2: Mpt vat ran dang quay deu quanh mpt true co dinh vai toe dp goc 12 rad/s thi chju mpt luc ham tac dung va chuyen dong quay cham dan deu voi gia toe goc rad/s^ Chpn moc thoi gian t = tai thai diem banh xe bat dau chju luc ham tac dung Chpn chieu duong la chieu quay eiia vat ran Thoi gian t u banh xe chju lire ham tac dung den liic dirng lai va goc quay khoang thai gian la A t = Is; cp = 6,7 rad B t = 1,5 s; cp = 7,5 rad C t = s; (p = 11 rad D t = s; cp = 12 rad / k Dang B A I TAP LIEN Q U A N DEN M O M E N Q U A N T I N H CUA V A T R A N , HE V A T R A N Phuong phap giai: Su dyng cac kien thuc sau: I = " ^ i ^ ^ > Momen quan tinh ciia mpt so vat ran co true quay doi xung: ^ • Thanh dong chat co khol lupng m va co tie't di?n nho so voi chieu dai ciia no, true quay A d i qua trung diem ciia va vuong goc vai thanh: U-lml^ ^2 ;,, K i thuatgidi nhatih BTTN Vat Li 12, tap - Nguyen Quanx Lac Cty TNHH • Vanh tron dong chat c6 khoi lu^ng m, ban kinh R, tryc quay A di qua tarn vanh va vuong goc voi mat phang vanh tron: I = mR^ • DTa tron mong dong chat c6 khoi lugng m, c6 ban kinh R, tryc quay A di • Qua cau dac dong chat c6 khoi luong m, c6 ban kinh R, true quay A di qua tam qua cau: I =—mR^ ; > Momen quan tinh cua he vat ran: I = Ii +12 + i do: Ii, I2, Ian l u ^ t la momen quan tinh cua eae vat ran m j , m^ V i du 1: Hai qua cau lie dac lam eung b3ng mot loai thep, dong chat eo ban kinh gap Ian R, = 4R2 He thiie lien he giua momen quan tinh cua hai qua cau doi voi true quay di qua tam ciia moi qua cau la =51211 C.I, =512 12 D.l2 = 314I, Huong dan gidi: Goi D la khoi lu-gng rieng cua; V i va V2 la the tich ciia cac qua cau Ta c6: m^ = D.V^ = B 0,27 kg.m^ C 0,54 kg.m^ Viet D 1,2 kg.m^ Huang dan gidi: Theo djnh ly true song song, ta c6: {'^ ) ^ ,: => Chgn C Trong do: d la khoang each vuong goc t u true quay O den true song song qua tam G ciia vat; lo; Ic; tuong ung la momen quan tinh eiia vat doi voi true O va true G B.I2 Khattg I = I c + md^ = | m R + mR^ = | m R = |.4.0,3^ = 0,54(kgm2) > Dinh ly ve true song song: IQ = I,- + md^ A I i = 314l2 DWH V i dy 3: Mot dia tron dong chat c6 ban kinh 30 cm, kho'i lugng m = 4kg Momen quan tinh ciia dla doi voi mot true quay vuong goc voi mat dla tai mot diem tren vanh c6 gia tri nao sau day? A 0,12 kg.m^ qua tam dia tron va vuong goc voi mat dla: I = — mR MTV D.y R^; = D.V2 = ^-^^l Dang 4: ,^ v BAI TAP LIEN Q U A N D E N PHl/ONG TRINH D Q N G H O C C U A V A T R A N Q U A Y Q U A N H M O T TRVC C O Ll/C D I N H Phuong phap giai: • Van dung phuang trinh dong lye hoc ciia vat ran quay quanh mot true CO djnh M = l y va phuong phap dong lue hoe de giai bai toan chuyen dong quay ciia vat rSn • Khi tinh momen lue, ta ap dung eong thuc M = Fd va luu y rang M c6 the nhan gia tri duong hoac am, thuoc vao tac dung lam quay vat theo chieu duong hay am ciia tung lue, sau tinh tong momen M • Neu he gom hai vat chuyen dong quay thi each khao sat moi vat thuc hien nhu tren Neu he vat gom mot vat chuyen dong quay thi ap dung djnh luat Newton va eae eong thue nhu da biet lop 10 cho vat chuyen dong tinh tien (xem vat nhu chat diem) V i du 1: Mot vanh tron dong chat, khoi lugng m = 2kg, ban kinh R = 0,5m, true quay qua tam va vuong goc voi mat phang vanh Ban dau vanh dung U2J = 45=512=>Ii=512l2 ^ C h p n C yen thi chiu tac dung boi mot lue F tiep xiic voi mep ngoai vanh Bo qua moi V i du 2: Mot manh eo khoi luong m = kg, chieu dai 1,2 m Doi voi true quay di qua khoi tam va vuong goc voi thanh, momen quan tinh ciia bang: A 0,3 kgm^ B 0,6 kgm^ C 0,9 kgm^ Huang dan gidi: Ta c6: I = ^ m l ^ = ^ , ^ = 0,6kgm2 =^ Chon B D 0,12 k g m l ma sat Sau 3s vanh tron quay dugc mot goe 36 rad Do Ion eiia lue F la A, I N B N C 4N, D 8N Huang dan gidi: Taco: {p = | t ^ =36(rad)=>y = r a d / s ^ I = mR^ - , ( k g m ^ j Momen lue: M = F.R = I7 = 8.0,5 = ( N m ) Do Ion ciia lye F la: F = ^ = ( N ) => Chon D V i dy 2: Mpt dia dac dong chat, khol lupng 0,4kg, ban kinh 20cm, c6 tryc quay A di qua tam dia va vuong goc voi dla, dang dung yen Tac dung vao dTa mpt momen luc khong doi 0,16 N.m Tinh quang duong ma mpt diem tren vanh dia di dupe sau 5s ke tu liic tac dung momen luc A 50m B 32m C 64m D 128m Huang dan gid i: Momen quan tinh cua dia: I = ^mR^ = ^.0,4.0,2^ = 8.10"^ (kg.m^ Gia toe goc cvia dia: y = y = 20rad/s^ Dang 5: BAI TAP LifiN Q U A N D E N D I N H L U A T BAO T O A N MOMEN D O N G LU'ONG Phuang phap giai: Su dung cac kien thuc sau: «*• • Momen dpng lupng L cua vat ran chuyen dpng quay quanh true la: L = I{o Trong do: I la momen quan tinh cua vat ran doi vai true quay; co la toe dp goc ciia vat ran chuyen dpng quay quanh true • Tinh Momen dpng lupng cua h^ vat ran doi vai tryc quay theo cong thuc: n # L = Li + L + +Ln= Goc ma dia quay dupe: cp - -^yt^ = -^.20.5^ = 250(rad) Quang duong ma mpt diem tren vanh dia di dupe sau 4s la: s = R(p = 250.0,2 = 50 (m) => Chpn A Vi du 3: Mpt banh xe chju tac dung cua mpt momen luc M i khong doi Tong cua momen M i va momen luc ma sat c6 gia tri bang 24 N.m Trong 5s dau, toe dp goc ciia banh xe bien doi tu rad/s den 10 rad/s Sau momen M i ngung tac dyng, banh xe quay cham dan va dung hSn l^i sau 50s Gia su momen luc ma sat la khong doi suo't thai gian banh xe quay Momen luc M i CO gia trj A M l = 11,3 N.m C M l = 33,4 N.m B M l =26,4 N.m D M i = 48,6 N.m i=i Trong do: Lj=IjCOj , • Neu momen luc bang khong thi ap dyng dinh luat bao toan momen dpng lupng: Ltnrac = Ls.iu • Neu momen luc khac khong thi ap dung djnh ly ve dp bien thien mo men dpng lupng: ^ -M dt Vi dy 1: Mpt cung, nh^, manh dai Im, quay xung quanh mpt true vuong goc vai va di qua tam GSn vao hai dau hai chat diem c6 kho'i lupng la m, = 2kg va = 1,5kg Thanh quay deu quanh tryc, moi qua cau CO toe dp la m/s Tinh momen dpng lupng cua he A 3,55 kgm^s B 4, 65 kgm^s Huang dan gidi: C 6,75kgm^s D 8,75 kgm^s Huang dan gidi: Ban dau: M = M j + M^^ = 24(N.m) Toe dp goc cua moi qua cau: Toe dp goc ciia banh xe liic CO M i : =^ = - lO(rad) Momen dpng lupng ciia h^: CO = COQ + yt -> = 2rad / s^ L = Lj + L = IiCOj + I2CO2 = (ij +12 )to Momen quan tinh ciia banh xe: , M 24 2\ I = - = - = 12(kg.m2) = ^miR^+m2R^)(o = (mi+m2)R^.a) = 3,5.0,5h^l0 = 8,75(kg.m2/sj Khi M l thoi tac dung: co' = to + y't = ' f t' y' = -0,2rad / s^ Suy ra: M^^ = y'l =-0,2.12 =-2,4(Nm) Vay M l = M - M ^ , =26,4(N.m).=>ChpnB => Chpn D Vi dy 2: Mpt nguoi c6 khoi lupng 50kg dung mep mpt san quay hlnh tron CO khoi lupng 200 kg, duong kinh 4m Bo qua ma sat true quay va sue can khong Ban dau san va nguoi deu dung yen Nguoi bSt dau chay voi toe dp khong doi 4,2 m/s (doi voi dat) quanh mep san a) San se quay n h u the'nao? Toe d p goc cua san la bao nhieu? A c u n g chieu v a i chieu chay ciia n g u o i v a i toe dg l , ( r a d / s) B nguoc eiiieu v o i chieu chay eiia n g u a i v o i toe d o - l , ( r a d / s) C eiing chieu v o i chieu chay eiia n g u o i v o i toe d o 3,05(rad / s) V i d u 3: M o t san quay h i n h t r u c6 k h o i l u g n g M = 180kg va ban k i n h R = 1,2m dang d u n g yen M o t n g u o i k h o i l u g n g m = 40kg chay tren m a t dat v a i toe d o 3m/s theo p h u a n g tiep tuyen v d i mep san va nhay len san Bo qua ma sat true quay T i n h toe d o ciia n g u o i k h i o tren san A 0,52 m/s B 0,72m/s lai chay theo p h u a n g tiep tuye'n eiia san tai M v a i toe d o n h u tren H o i toe ' '» ' ' C - , 5 ( r a d / s) B 1,425 (rad/s) L , = 1,(0, = m R ^ ^ = m R v j M o m e n d g n g l u g n g eiia he k h i n g u o i nhay len san: D -1,425 (rad/s) Huang dan gidi: L2=(li+l2)«2 K h i n g u o i chay q u a n h mep san t h : m o m e n d o n g l u g n g ciia he k h i d o la: Hay L | = IjCOj +I2CO2 Do m o m e n d o n g l u g n g duge bao toan, nen: L i = Lo Tir d o : V2 = - ^ ^ ^ i ^ _2m(o^ _ CO, D o 0)1, C02 khae dau nen san se quay theo chieu nguge v o i chieu chay ciia n g u a i v a i toe d o goc: ©2 = = = = - l , ( r a d / s) => C h g n B b) K h i n g u a i chay den d i e m M t h i : L2 = I,o), +12(02 D o m o m e n d g n g l u g n g d u g e bao toan nen: L2 = Lo Suy ra: ^=-M._ ^2 " ' 50 , Thay so: CO2 = - - — , = 2.200 ' Chgn C 14 mv ' 2 i M 40+ ^ Dang B A I T A P y2y T R O N G (0, = ^"^2 4,2 4.R 4.2 m + — M R.v ^ ' D E N D O N G N A N G C U A VAT D O N G RAN QUAY P h u o n g p h a p g i a i : Su d u n g eac kien thuc sau: • D g n g nang eiia vat ran quay q u a n h m o t true co d j n h : Wd = ^Ico^ • D g n g nang ciia vat ran vua quay vira chuyen d g n g tjnh tien: ^ + — mvr- ^ v o i V(^ la van toe k h o i tam mjCOj v 13 CHUYEN m2R^ v2 R = 2^.0,92(m/s) 180 LIEN QUAN W J == -ICO (0, ^ Chgn D r,coj +I2CO2 = Tudo: = m+ = mR2+-MR2 m R , = m + — M R.v Suy ra: + l2«;= ^ = Theo d j n h luat bao toan m o m e n d g n g l u g n g , ta eo: L2 = L i a) Ban dau he d u n g yen nen m o m e n d o n g l u g n g : Lo = 1,0, , M o m e n d g n g l u g n g ciia n g u o i truoc k h i nhay len san: goc cua san k h i d o la bao nhieu? A 0,525(rad / s) D 0,92m/s Hu&ng dan gidi: D nguge chieu v a i chieu chay eiia n g u o i v o i toe d o - , ( r a d / s ) b) N g u o i chay dan vao giua san k h i den d i e m M each true quay I m t h i C 0,82m/s V i d u : M o t k h o i cau dac d o n g chat eo khoi l u g n g m = 80 kg, ban k i n h 0,6m / \ = - , 5 ( r a d / s) K h o i cau quay q u a n h true d i qua tam ciia no T i m d g n g nang ciia k h o i cau k h i toe d o goc ciia khoi cau la 20 rad/s A 1234J B.2304J C 3156J D 4758J Huang dan gidi: Huong dan gidi: Do banh xe quay deu, nen tong momen lyc: Momen quan tinh ciia khoi cau la: I = - m R ^ = -.80.0,6^ = l l , ( k g m ^ ) Dgng nang cua khoi cau la: W j = ijco^ = 11,52.20^ = 2304(j) => Chon B M =M +M ^ =0 M „ , = - M = -60(N.m) fO-CO(, 0-50 r / ' j / \ Gia toe goc ciia banh xe: = — ^ — = = -5^rad / s j V i dy 2: Mot banh da hinh try khoi lugng m = 100kg, ban kinh R = 30cm chju tac dung ciia mot momen lyc khong doi M = 36 N.m , , , , M -60 Momen quan tmh: I = — = —r- = 12kg.m y b a) Can bao nhieu thoi gian de tang toe banh da t u trang thai nghi den toe dp goc bang 12 rad/s Cong cua lyc ma sat: A ^ , = AW, - W , o = - i l o ) ^ - =-15000(j) = -15kJ A 0,5s B 1,5s C.2,5s D 3,5s b) Dpng nang ciia banh da a toe dp goc bang bao nhieu? A- 123J B 231J C 324J D 543J Huang dan gidi: a) Momen quan tinh cua banh da: I = ^mR^ i.100.0,3^ = 4,5|kg.m^j Gia toe goc cua banh da: y = — = — = sf rad / s^) I 4,5 V / Thoi gian can thiet: t - ^^Z^ = => Chpn C V i du Mot banh da dupe lam quay quanh mot tryc thang dung voi toe dp goc khong doi 200 rad/s Mpt dTa kim loai dung yen eo 16 thiing tarn rod nh? xuong banh da dang quay eho tryc xuyen qua 16 thung Ma sat giiia dla va banh da lam cho dia quay nhanh dan deu den toe dp goc 200 rad/s thoi gian 0,5s Momen quan tinh ciia dia doi voi true quay la 6.10"^ kg.m^ Xae djnh: a) Momen lye ma sat tac dung len dia = ] ( ) ^ Chpn B A 0,6Nm b) Dpng nang ciia banh da toe dp goc la: A.40J D 3,6Nm B.60J C.80J D 120J c) Nang lupng toan phan da truyen cho dia A 80J B A I T A P L I E N Q U A N D E N D I N H L Y B I E N T H I E N C 2,4Nm b) Dpng nang dia nhan dupe = i l t o ^ = 1.4,5.122 = 324(J) =^ Chpn C ^ang B l,2Nm B 120J Phuong phap giai: Djnh ly ve dpng nang:: AWd = Wd2 - Wdi = ll(co2 - 0)2) = A = MA(p Trong do: As = rAcp Chu y: Doi voi cong phat dpng c6 gia trj duong (A > 0), doi voi cong can c6 gia tri am (A < ) V i dy 1: Tac dyng vao banh xe mot momen lyc khong doi M = 60N.m thi banh xe quay deu voi toe dp goc co = 50rad/s Thoi tac dung momen lyc M thi sau 10s banh xe se dung lai Tim cong ciia lyc ma sat tac dung vao banh xe ke t u thoi tac dung momen lyc M den banh xe dung lai A -3kJ B.-9kJ C.-15kJ D -23kJ D 240J Huang dan gidi: D Q N G N A N G C U AV A T R A N Q U A Y C 200J a) Gia toe goc cua dia: y = =^ = 400(rad / s^) Momen lyc ma sat tac dyng len dia: M = ly = 6.10"^.400 = 2,4(N.m) =>ChpnC b) Dpng nang dia nhan dupe: W j = ^Ico^ = i.6.10"^2002 = 120(j) • => Chpn D c) Nang lupng de thang c6ng cua lye ma sat can tro ehuyen dpng eua banh da, giir cho banh da quay voi t6c dp goc khong doi (thanh phan chuyen nhi?t): AW = A = AWd - Wd - Wdo = 120 G) Nang lupng toan phan truyen cho dia la: W = W , + A W ^ + _ ^ ( j ) => Chpn D THUV!ENTiNHBINH25^U^ 17 -•— E4ttJiiM0t cM\m dao d9ng dieu h6a tr^n tryc Ox c6 phuong trinh x = 4eos Ant-T Huang dan gidi: m ^_ /0,25 _ 71 ^j^u ki dao dpng ciia v|t: = ^ — = 271^ 100 ~10^ c m Trong 1,125s dSu ti^n v$t d5 di dugt mpt quang du'6ng la: A I6em B, 24em C> 48cm D 32cm po khoang thai gian * = dau tien diing bSng chu ki dao dpng ^ khoang thoi gian do, vat chi thuc hi^n dupe dao dpng An Chpn D £&a88.Mpt vat dao dpng dieu hoa voi tan so Hz Thoi gian n g ^ nha't de vat B 28cm C 32cm D 36cm ''It tir vj tri bien phai sang v| tri bien trai la: A I s B.ais .•; C.0,5s D.2s Huong dan gidi: f ^ i thai diem ban dau t = vat c6 van toe: Bieu dien dao dgng dieu hoa bang vecta quay Ta thay, vgt di tCr vj (j bien phai sang vj t r i bien trai thi vecta quay dugc mpt goc a = 7t Suy th^ gian t ma vat chuyen dpng t u vj tri bien phai sang vi tri bien trai: t = —= —= (0 = — = 0,1s=>Ch9nB CO 27if V d^i cua v^t la 0,6m/s Khi v^t qua vj tri N each vj tri can bang 3\/2cm thi dgng nang va the nang lac bSng Van toe cua vat tai N : A lOsJlcm ! s B 3Q4icm / s C 20>/3cm / s 5uy 13 vat chuyen dpng ngupc chieu duong ciia tryc tpa dp j ^ i vat chuyen dpng tir vi tri eo l i dp XQ = - ^ ( c m ) den vj tri bien thi vecto quay di*