Phân loại và phương pháp giải chi tiết bài tập trắc nghiệm vật lí 12 trọng tâm-trần thanh bình

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ThS. TRAN THANH BINH PHAN LOAI VA PHUOING PHAP GIAI CHI T I E T BAI TAP TRAC NGHI|M V A T L I 12 B I ^ N S O A N T H E O C H U O N G T R I N H M(5| D A N H C H O H Q C S I N H B A N N A N G C A O VA B A N C O B A N • T6m t i t If thuyet. • Phan logi theo tCfng van de. • C6c phudng phap gi^i bai t§p + b^i t§p. mlu cho tCrng v§'n de. • B^i t$p va If thuyet trie nghiem. • Bai tap luyen tap cuoi m6i chUdng. N H A Y I I A T R A M FiAi w n r o i i o c G I A T P HO CHf MINH 1 Ldf N O I D A U C^' h k m giijp cdc em hoc s i n h c6 t a i lieu t o t k h i hoc m o n V a t l i 12, chiing t o i bien soan quyen " P h a n loai va philcfng phap g i a i c h i t i e t b ^ i t a p trac n g h i e m V a t h' 12 t r o n g t a m " . T r o n g quyen sach n a y c6 10 chUofng. M o i chucfng deu c6 cau triic nhif sau: PHAN I: TOM TAT LI THUYET TRQNG TAM CUA CHUdNG. ( N h ^ m giup cac em hoc s i n h nMm vufng l i thuyet de c6 t h e l a m cdc cau h o i trSc n g h i e m l i thuyet cua chucfng). P H A N II: P H A N LOAI TL/NG V A N DE VA PHLTONG P H A P GIAI BAI T A P TLTNG VAN D E . ( M o i v a n de, m o i l o a i deu c6 cac b ^ i t a p mau, cac cau t r i e n g h i $ m b a i t a p ciia tiTng v a n de, t i f n g l o a i , b a i t a p luyen t a p cua chucfng). PHAN III: DAP AN CUA CAC CAU TRAC NGHIEM LI THUYET + BAI TAP TRAC NGHIEM VA BAI TAP LUYEN TAP. (Tat ca cac cau t r i e n g h i e m va b a i t a p deu c6 hudng d a n g i a i va dap dn). C h i c c h i n r i n g , neu cae em hoc s i n h chiu k h o l a m cac eau t r i e n g h i e m va hki t a p t r o n g quyen sach nay v i n i m t h a t vi^ng tCrng v a n de t r o n g quyen sach n a y m p t each day dii t h i c i c em se eo k e t qua t o t m o n V a t l i t r o n g c i e ki thi. Day eung la t a i lieu t h a m khao cho g i i o v i e n eung n h u phu h u y n h hoc sinh t r o n g viee giup c i e em hoc to't m o n V a t l i 12. Tuy t i c gia c6 r a t nhieu eo g i n g t r o n g qua t r i n h bien soan, n h u n g c h i c r i n g quyen s i c h k h o n g t h e t r a n h k h o i nhiJng t h i e u sot. M o n g q u i v i gido v i e n , cac bac phu h u y n h va cac em hpc s i n h c6 nhiirng y k i e n d6ng g6p de l i n t d i b a n quyen s i c h se h o a n ehinh han. Chan t h a n h c a m an. Tdc I / I gia ChiTtfng I . DQNG LlTC HOC 1 VAT RAN P H A N I: T O M T A T L I T H U Y E T Van de 1: CHUYEN DQNG CUA VA T RAN QUA Y MQTTRUC CODINH QUANH 1. Tpa d6 g6c * K h i v a t r a n quay quanh m o t true eo' d i n h t h i : - M o i diem tren vat vach mot dUcfng t r o n n k m trong mat phang vuong goe v d i true quay, c6 ban k i n h bkng khoang caeh tiT diem do den true quay, eo tarn d t r e n true quay. - M o i d i e m t r e n v a t deu e6 eung m o t goe quay. * Tpa do goe (p = ( O x , O M ) De don g i a n t a c h i xet v a t quay theo m o t ehieu va thiJdng ehon chieu quay eiia v a t la chieu diTcfng -> k h i do (p > 0. 2. Tdc do g6c a) Toe do goc trung binh (conJ _ (p - cPo _ A(p t-t„ Trong At do: • (po: Toa do goe lue dan t a i thc(i d i e m to (rad). • (p: Toa dp goc liie sau cf t h d i d i e m t (rad). • to: T h d i d i e m lue dau k h i v a t eo cpo (s). • t i : T h d i d i e m liic sau k h i v a t c6 (p (s). • cotb: Toe dp goe t r u n g b i n h t r o n g t h d i gian At (rad/s). • Acp: G6c ma m o t v a t quay dupe t r o n g t h d i gian At (rad). • A t : T h d i gian quay goe Aep (s) b) Toe do goc tiic thai (co) Toe dp goc ttre thdi t a i thdi diem t la dai lupng dac tntog cho miJc dp quay cham hay quay nhanh cua v ^ t r ^ quanh mpt true eo' dinh t a i thdi diem do. m = lim ^'-0 Acp dcp At dt = T , f k h o n g doi. • Y > 0 k h i v a t quay n h a n h d a n deu (co t a n g dan deu theo At) • Y < 0 k h i v a t quay cham d a n deu (co g i a m dan deu theo At) • T o n g quat: • co.Y > 0 -> vat quay nhanh dan deu. • oj.Y < 0 ^ vat quay cham dan deu. i X Van de 2: PHL/ONG TRINH DQNG Ll/C HQC CUA VA T RAN QUA Y QUANH MQT TRUC CO DINH 1. Momen lUc ddi v6i true quay Momen lue M cua life F d o i v d i v a t r a n co true quay co d i n h l a d a i lucfng dac t r u n g cho tdc dung c o d i n h l a d a i lifcfng dae trUng cho tae dung l a m quay v a t r ^ n quanh true co d i n h do va dUOe do bang t i c h so ciia lUc va each tay don. M = F.d = F.r.sina c) V a t l a h h i h t r u r o n g hoac v ^ n h t r o n quay quanh true d i qua tarn. Trong do: • M : M o m e n cua life ( N . m ) . , • F: Luc tAc dung (N). (A) I • d: C a n h tay don (m). (Khoang each tCr true quay den gid cua life) I = m.R= 2. Momen quSn tinh (I) - Momen quan t i n h I d o i v6i m o t true la d a i lu'Ong dac t r u t i g eho miJe quan t i n h cua v a t rMn t r o n g chuyen dong quay quanh true ay. 1= 1 m, .r d) V a t Ik h i n h t r u dSc hay dia t r o n mong quay quanh true d i qua tarn. (A) - Momen qudn t i n h c6 dp I d n phu thupe vao k h o i iMng v a t r ^ n , phu thupc vao sir p h a n bo' k h o i li^png eiia v a t r ^ n d o i vcJi true quay (gan h a y xa true quay). 3. PhUdng trinh dong luc hoc cua vSt r3n quay quanh m6t true cd dinh (A) c I = -mR'^ 2 M = I.y Trong do: e) V a t l a h i n h cau d i e quay quanh m p t true d i qua t a m . • M : M o m e n lire (N.m) • I : M o m e n qudn t i n h (kgm^) • y: Gia toe goe (rad/s^) I = -mR^ 5 Nhqn xet: Ydi cung m o t M o m e n t h i • Neu I i d n y nho - > k h o t h a y doi toe dp goe. • Neu I nho -> y i d n -> de t h a y doi to'e dp goe. 4. Momen quSn tinh cilia m$t s6 v$t dfing ch^t a) V a t l a t h a n h m a n h dong chat, k h o i lupng m , chieu d a i I eo true quay l a dudng t r u n g true cua t h a n h . (A) I = —ml' 12 1. Momen dOng ladng. Momen dong liTpng eiia v a t r ^ n d o i v d i m p t true quay b^ng t i c h so eua momen quan t i n h cua v a t doi v d i true quay do va toe dp goe cua v a t quay J b) V a t l a t h a n h m a n h dong chat, k h o i liTpng m , chieu dai / c6 true quay d i qua m p t dau t h a n h v a vuong gde v d i t h a n h . Van de 3: MOMEN DQNG LI/0NG DINH LUAT BAO TO AN MOMEN DQNG LU0NG quanh true do. L = I.a) (u)>0-»L>0;a)<0-^L<0) Trong do: • L : Momen dong lirpng (kgm^/s) • I : M o m e n quan t i n h cua v a t r ^ n (kgm^) (A) I = -m.l' 3 • (o: Toe dp goe eiia vat (rad/s) 2. Djnh lu$t b^o to^n momen d6ng lUdng L = h k n g so hay L, + + ... = L \ L'j + ... Dieu kien dp dung dinh ludt: TRAC NGHrEM LI THUYET K h i t o n g d a i so cua cac momen ngoai lye dat l e n mot v a t r ^ n (hay h$ v a t ) doi v d i mpt true quay b^ng k h o n g (hay cac momen ngoai lire t r i $ t tieu) Luu y: K h i I doi v d i true quay k h o n g doi -> to = 0 hoac w - h k n g so. (Vat k h o n g quay hoae v a t quay deu) Van de 4: DQNG NANG CUA VAT RAN QUA Y QUANH MQTTRUC CODfNH 1. D6ng nSng cCia m6t vat rjn quay quanh m6t true c6 dinh C a u 1. M p t d i e m t r e n v a n h dia t r o n each true quay d i qua t a m m p t k h o a n g R k h i dia quay t r 6 n deu quanh true t h i toe dp d ^ i va toe dp goc eiia d i e m do c6 quan he v d i nhau theo bieu thiJe nao t r o n g cac bieu thiifc sau? A v - - . B. v = - . R CO C. 0 3 = - . D . R = vlco. R C a u 2. H a i hpc s i n h A va B diing t r e n mpt ehiec du quay t r o n deu quanh true C O d i n h d i qua t a m . Hoe s i n h A d ngoai r i a , hoc s i n h B d each t a m m p t doan b^ng mpt p h a n t u b a n k i n h chiee du quay. Gpi T A , TR la ehu k y quay cua hoc sinh A va hoe s i n h B . Lue nay t a cd: • W,i: D o n g n ^ n g eua v a t r a n quay quanh m p t true (J) • I : M o m e n quan t i n h cua vat (kgm^) • co: Toe dp gdc cua v a t (rad/s) 2. Dinh li dong nSng Trong do: A = W, Trong do: Luu y: + Vp; fe = 2iv. B. VE = D- VE = 2VF; h = fp- Vp; = dia. Gpi (DA, COB, YA, YB I a n lupt l a toe dp gdc va gia toe gdc cua ede d i e m A va B . Chpn cau k e t l u a n diing. A. COA = 2(0B; YA = YB- B. C. D - " A = COR; YA = YB- tOA = COB; YA = YB- (OA = cou; YA = 2YB. C a u 5. M p t dia CD quay t r d n deu quanh true d i qua t a m dia. M p t d i e m bat k y 3. Djnh li v l true song song 1(0) = ngoai r i a , B l a d i e m each true quay m p t doan b a n g mpt p h a n ba ban k i n h • Neu v a t thuc h i e n dong thcfi h a i ehuyen dpng la quay quanh true va t: tinh tien thi: W j = VE C a u 4. M p t dia quay t r o n deu quanh true doi xii'ng d i qua t a m . Gpi A la d i e m d : Dong nftng lue sau (J) = eiia dia. Gpi E va F I a n lupt la d i e m d ngoai r i a va d i e m d each t a m dia m p t C. vp = 2VE; ffi = fp- Neu v a t chi c6 chuyen dpng quay quanh true t h i : W j = 1(A) D . T A = 4T„. C. T A > T R . doan b^ng nuTa ban k i n h cua dia. Gpi VR, V F , fs, fp I a n lupt la toe dp d a i va A. ,^ : Dong nftng lue dau (J) • Wj B . TA < TB- t ^ n so ciia cac d i e m E va F. K e t l u a n nao sau day la diing? - Wd,,,-,„ • A: Cong eiia ngoai lue (J) • A. T A = T B - ' ^ C a u 3. Klpt dia CD coi n h u chuyen dpng t r d n deu xung quanh true d i qua t a m n k m d mep dia se: + inx^ A. k h o n g cd gia toe t i e p t u y e n I a n gia toe phap tuyen. Trong do: B . cd gia tdc phap t u y e n n h u l i g k h o n g cd gia toe t i e p tuyen. • 1(A): M o m e n quan t i n h eiia m p t vat doi v d i true quay ( A ) (kgm^) C. C O gia tdc t i e p tuyen va ed ea gia toe phap tuyen. • IQ: Momen quan t i n h eiia true di qua trong tarn G song song vdi (A) (kgm^) • m: K h o i lupng v a t rSn (kg) D. ed ea gia tdc t i e p t u y e n va gia to'e phap tuyen n h u i i g gia toe phap t u y e n • x: K h o a n g each vuong gdc giSa true ( A ) va true song song qua (G) (m) Hinh minh hga dinh li: (A) (G) ' Idn hon gia toe t i e p t u y e n . C a u 6. M p t v a t rSn quay t r o n deu quanh true eo' d i n h d i qua v a t t h i m p t d i e m t r e n v a t d each true quay m p t doan r A. toe dp gdc thay doi. 0 se cd B . ehu k y quay t h a y doi. C. tdc dp dai t h a y doi. 0) G D. vecto van tdc dai t h a y doi n h u n g to'e dp Aki eiia d i e m dd, k h o n g ddi. C a u 7. M p t vat r ^ n quay t r o n deu quanh mpt true cd d i n h . Gpi N la so dao dpng ma vat thue h i e n t r o n g t h d i gian At, cpo va cp la tpa dp gdc lue dau va lue sau, co la tdc dp gdc cua vat r a n . Chpn bieu thiire sai t r o n g cac bieu thde sau: A. T : . — . CO B T = — . N C. N = ^ ^ ^ . 27; D. (p = (po - «At. C a u 8. Bieu thiJc nao sau day l a dung k h i n 6 i ve dp I d n cua gia toc ph^P t u y e n (gia toc hudng tarn)? V v^ A. an = - . B. an = w.R. C. an = — . D. a^ = (w.R)^. C a u 9. Bieu thiJc nao sau day l a dung k h i n o i ve do I d n ciia gia toc t i e p t u y e n cua v a t rSn quay b i e n d o i deu quanh mot true co dinh? A. at = r.y. B. a t = - . C.at=-. D. at = — . r r C a u 10. M o t v a t r ^ n quay b i e n d o i deu quanh m o t true d i qua v a t r ^ n . Chon Y goc t h d i gian to = 0 la luc v a t bat dau quay. Goi t i , t 2 l a cac t h d i d i e m liic sau (t2 = 2 t , ) . N e u xet m o t d i e m t r e n v a t r ^ n each true quay T ^0 t h i : A. a,, = 2a,^. B. a,^ = 2 a , . C. a,_ = ^ D. a, = a,^. . C a u 11. Bieu thiJc nao t r o n g eac bieu thiic sau k h o n g the ap dung cho v a t r ^ n quay bien d o i deu quanh m p t true co d i n h d i qua vat? A. 9 C. cp = (po + - cpo = o)o-t + • cD.t. B. (0^ - D. © = (OQ = 0)0 + 2Y((P - cpo)- y.t. C a u 12. Bieu thiJe nao t r o n g eae bieu thiJe dudi day l a sai k h i t i n h gia toe t o a n p h a n ciia v a t r ^ n quay b i e n d6'i deu quanh m o t true eo d i n h d i qua vat? A.a= J ^ ^ . B. al=a'-al C a u 16. M p t v a t rMn quay bien d o i deu quanh m p t true co d i n h d i qua v a t rin. Chon phat bieu sai t r o n g cac p h d t bieu sau: A. Gia toc goc l a h k n g so. B. Toe dp goc l a m p t h a m bac n h a t d o i v d i t h d i gian. C. Toe dp gdc 1^ m p t h k n g so. D. T r o n g chuyen dpng quay b i e n d o i deu ciia v a t r k n quanh m p t true co' d i n h di qua no t h i toe dp goc tSng hay g i a m nhiJng luang eo dp I d n b k n g nhau t r o n g nhiJng k h o a n g t h d i gian b k n g nhau. C a u 17. M p t v a t r k n quay v d i toc dp goc k h o n g d o i quanh m p t true ed d i n h d i qua vat. So' vong quay m a v a t quay dUde t r o n g t h d i gian t ke til luc v a t b a t dau quay se: A. t i le v d i t l B. t i le v d i t . A. t i le v d i t^. B. t i le v d i t . C. t i le v d i D. t i le v d i - . t C a u 18. M p t v a t r k n quay v d i gia toe goc k h o n g d o i quanh m p t true ed' d i n h d i qua vat. Goc ma v a t quay dupe sau t h d i gian t , ke tCr luc b k t dSu quay se . C. t i le v d i \ D. t i le v d i - . t t C a u 19. M p t v a t r ^ n quay n h a n h d a n deu quanh m p t true eo' d i n h xuyen qua vat. M p t d i e m t r e n v a t r S n k h o n g n k m t r e n true quay va each true quay m p t doan r ^ 0. Chpn p h a t bieu dung t r o n g eac p h a t bieu sau: A. Td'c dp gdc k h o n g phu thupc r. B. Gia to'c gdc phu thupc r. C. Gia toe t i e p tuyen k h o n g phu thupc r. D. Gia toe phap t u y e n k h o n g phu thupc r. C.rV = a^-f—1. I r j D. a'= ^co^r + ry . C a u 13. P h d t bieu nao sau day 1^ d u n g d o i v d i v a t r ^ n eo chuyen dpng quay deu quanh m o t true? A. Toc do goc l a m o t hSng so. B. Toe dp goc l a m o t h a m bae n h a t doi v d i t h d i gian. C. PhUdng t r i n h chuyen dpng l a m o t h a m bac h a i doi v d i t h d i gian. D. Gia toe goc 1^ m o t hkng so. C a u 20. M p t v a t r k n quay quanh m p t true co' d i n h xuyen qua v a t . Cac d i e m t r e n v a t r k n k h o n g thupc true quay se A. vaeh n e n cac dudng t r o n n k m t r o n g m a t p h k n g vuong gdc v d i true quay. B. ed eung v a n toe d a i d eung m p t t h d i diem. C. quay dUde nhi^ng gdc k h o n g b k n g nhau t r o n g eung m p t k h o a n g t h d i gian. D. ed gia to'c gdc va to'c dp gde la h k n g so. C a u 21. H a i dia t r o n dang quay A. Gia toc goc ciia chiec du quay l a m o t h^ng s6'. dong true va eiing chieu v d i toe dp gde coi, 0)2. M o m e n quan t i n h cua h a i dIa 1^ I i , I 2 . M a sdt d true quay k h o n g dang ke. Sau do cho h a i d i a d i n h vao nhau va quay v d i to'c dp gdc 0). Bieu thde t h e h i e n m d i quan he giOfa ede d a i li/dng coi, ^ 2 , I i , I 2 , 0) l a : B. K h d i lUdng cua chiec du quay l a m o t h k n g so. A. I i ( O i = l2(02 + d i + 12)0). B. IiCO] + l2(02 = d l + l2)W- C. Toe dp cua chiec du quay 1^ m o t h^ng so. C. Iicoa + D. Iicoi - I2CO2 = d l + h)o^- C a u 14. Chpn phat bieu sai k h i n o i ve momen quan t i n h eiia v a t r ^ n A. Momen quan t i n h phu thupc vao h i n h dang va k i c h thude ciia v a t . B. Momen quan t i n h phu thupe vao k h o i liTpng ciia v a t r ^ n . C. Momen quan t i n h k h o n g phu thupc vao v i t r i true quay ciia v a t r ^ n . D. Momen quan t i n h k h o n g phu thupc v^o toc dp goc ciia v a t . C a u 15. M o t chiee du quay ehiu tac dung eiia m o t momen lue k h o n g doi. Chon phat bieu sai t r o n g eac p h a t bieu sau: D. M o m e n qudn t i n h l a m o t h k n g so. l2(0i - d i + l2)(i). v./a)2 C a u 22. H a i dia t r 6 n m 6 n g n ^ m n g a n g c6 c u n g t r u e q u a y t h S n g diJng d i q u a t a r n cua h a i d i a . M o m e n q u a n t i n h ciia 2 d i a l a I j , I2. L u c d a u d i a 1 d i J n g y e n , d i a 2 q u a y v d i to'c do CO2. B o q u a m a s a t do'i v d i t r u e q u a y . T h a n h e d i a 1 xuo'ng d i a 2 sau m o t t h d i g i a n n g S n t h i ca h a i d i a q u a y v d i Cling mot toe dp goe A . 0) = C a u 28. H a i d i a t r 6 n c6 c u n g m o m e n q u d n t i n h d o i c u n g m o t t r u e q u a y d i q u a cac t a m d i a . L u c d l u d i a m o t d i J n g y e n , d i a 2 q u a y v d i toe dp goe u)2. B 6 qua m a s a t d t r u e quay. Sau do h a i d i a d i n h v a o n h a u v a q u a y c u n g toe d p goe (o. C h p n k e t l u a n d u n g k h i n d i ve d p n g n a n g cua h e h a i d i a lue sau so v d i lue d a u . V_/co A. G i a m d i 2 I a n B. T a n g len 2 Ian. C. T a n g l e n 4 I a n D. G i a m di 4 Ian. C a u 29. H a i r o n g rpe 1 v a 2 cd k h d i l i i p n g l a m , v a m 2 = 2 m i , b a n k i n h la: B . (0 = D . 0) = C. w = C a u 23. M o t n g i r & i d i J n g t r e n m o t c h i e e b a n x o a y d a n g q u a y . L u c d a u n g u d i a y d a n g t a y r a t h i g h e v a n g u d i q u a y v d i t o e d p goe l a coi. B o q u a m a s a t d t r u e q u a y . S a u do ngurdi a y t h u t a y l a i s a t n g i r d i t h i g h e v a n g i r d i q u a y v d i t o e d p goe C02. B i e u thiirc n a o d i i n g t r o n g eac b i e u thuTc sau? A . Iicui - B . I1CO2 = l2Wi- I2CO2. C. IiCOi + 12(1)2 = 0 . D . coi > (02- C a u 24. M o t v a n d o n g v i e n t r U p t b a n g q u a y q u a n h m o t t r u e t h ^ n g d i J n g v d i h a i t a y d a n g r a v a c6 toe dp goe coi, m o m e n q u a n t i n h I i . S a u do v a n d o n g v i e n t h u t a y l a i d o t n g p t t r o n g k h o a n g t h d i g i a n n h o de ed t h e bo q u a a n h h u d n g eiia m a s a t do'i v d i m a t b a n g . L u c n a y v a n d p n g v i e n q u a y v d i t o e dp goe l a C02, m o m e n q u a n t i n h l a I2. C h p n k e t l u a n d u n g . A . M l = (02; I i = I2. B . coi = (02; I i < hC. COi > M2; I I > D . (Oi < (02; I i > 12- r d n g r p e 1 ga'p 4 I a n b a n k i n h c i i a r d n g r p e 2. T i so giCa j - Ik: h A . 2. B . 4. C. 6. D . 8. C a u 30. H a i d i a t r b n m o n g c6 cung d p n g n a n g quay, t i so giOfa m o m e n q u a n t i n h eiia dia 1 v a d i a 2 d i qua t a r n cua d i a 1 v a d i a 2 l a i - = 4. H m t i so' toe dp goe A . 1. B . 2. C. 3. —. D . 4. C a u 31. M o t t h a n h m a n h d o n g c h a t d i e n d i e n d e u , c h i e u d a i t h a n h l a I, k h o i l i i p n g t h a n h l a m . T h a n h ed t h e q u a y x u n g q u a n h m o t t r u e n ^ m n g a n g d i q u a m o t d a u eiia t h a n h v a v u o n g goe v d i t h a n h . B d q u a m p i m a s a t v a sdc c a n . B i e t m o m e n q u a n t i n h cua t h a n h l a I = v a g i a toe r o i ta. do l a g. H o i o n e u t h a n h diTpe t h a k h o n g v a n to'c d a u t i f v i t r i nhm n g a n g t h i to'c dp gdc cua C a u 25. M o t v a n d p n g v i e n triTpt b a n g q u a y q u a n h m o t t r u e t h ^ n g d i J n g v d i t o e dp goe (iJi, m o m e n q u a n t i n h I i k h i h a i t a y t h u l a i s a t n g u d i . S a u do v a n d p n g v i e n d a n g t a y r a t h i t h a y t o e d p goe lue n a y l a 0)2 = — . cua B o q u a m a s a t giiJa t h a n h k h i q u a v i t r i t h i n g d d n g l a bao n h i e u ? 3g 2g 3g C. (0 = B . (0 = A . (0 = 21 ^31 ' ^ I D . CO = 121 • C a u 32. M o t t h a n h A B d o n g chat ed chieu d a i I cd t h e quay t r o n g m a t p h a n g t h a n g n g u d i v d i m a t b a n g . G p i I i , I 2 , vf^^ , W j _ I a n l u p t l a m o m e n q u a n t i n h v a d p n g d i i n g qua m o t true n k m n g a n g d i qua m o t dau cua t h a n h v a v u o n g gdc vdi t h a n h . n a n g cua v a n d p n g v i e n k h i h a i t a y t h u l a i sat n g u d i va k h i h a i t a y d a n g r a . Chpn ket luan diing. T h a n h ed t i e t d i e n deu, k h d i liTpiig m , gia toe rcri t i l do l a g, I = ^ o A . I2 = 2I1; w, 1 C. I2 = 2 1 , ; w d, . -= - 2" wd ., • B . I , = 2I2; w. = 2w, D . I2 = 2I1; vv,^ = w<,_ . C a u 26. C h p n c a u d u n g k h i n d i ve b i e u thufc t i n h d p n g n a n g c i i a v a t r ^ n q u a y q u a n h t r u e eo d i n h A . W d = 1(0 B . Wd = . 21 C. W d = — . B o qua m p i m a sat va sure can. T h a n h d a n g d d n g y e n d v i t r i can b k n g . H o i can p h a i t r u y e n cho t h a n h m o t toe dp gdc l a bao n h i e u de t h a n h quay d e n v i t r i n k m n g a n g . 2g 6g 3g 3g D . (0 = C. (0 = B . 0) = A . (0 = / ^ / ^ / A/ 3/ C a u 33. M o t t h a n h A B d o n g cha't cd c h i e u dai / cd t h e q u a y t r o n g m a t phSng t h i n g d d n g q u a m o t t r u e nkm n g a n g d i q u a m o t d a u c i i a t h a n h v a v u o n g goe . D . Wd = 2 " 21' ' C a u 27. M o t d i a t r d n c6 m o m e n q u a n t i n h I d a n g q u a y q u a n h m o t t r u e eo' d i n h CO toe dp goe (o. M a s d t d t r u e q u a y k h o n g d d n g k e . M o m e n d p n g l u p n g v a d p n g n a n g q u a y se b i e n d o i n h u t h e n a o n e u toe dp goe cua d i a t a n g l e n 3 I a n ? A . M o m e n d p n g liTpng v a d p n g n a n g q u a y d e u t a n g 3 I a n . B . M o m e n d p n g liTpng t a n g 3 I a n , d p n g n a n g q u a y t a n g 9 I a n . C. M o m e n d p n g l u p n g t a n g 3 I a n , d p n g n a n g q u a y g i a m 9 I a n . D. M o m e n d p n g lifpng g i a m 3 I a n , d p n g n a n g quay t a n g 9 I a n . eua t h a n h . T h a n h ed t i e t d i | n deu, khd'i l i f p n g m , g i a to'c r p i t u do la g, I = ^ B d q u a m p i m a s a t va sdc c a n . T h a n h d d n g y e n d v i t r i c a n hkng. . H o i can p h a i t r u y e n c h o t h a n h m p t t d c dp gdc l a bao n h i e u de t h a n h q u a y d e n v i t r i t h i n g d d n g d p h i a t r e n t r u e quay? A . (0 = 3g . B . CO = 3g I C. CO = 6g D . CO = 12g P H A N II: B A I T A P T R A C NGHIEM C2.Tac6thld6itCr4^ phut Cu t h e n h u sau: + BAI TAP LUYEN TAP sang ^ . s 1 2 0 0 vong/phut = 1 2 0 0 . ^ ^ ^ ^ = 4 0 rad/s 60s Van de 1: VAT RAN QUA Y TRON DEU (0 = 4071 (rad/s) Trong PHlJolNG P H A P • t : T h 6 i gian quay N v o n g (s). (0 • N : So' vong. • V: Toe do d a i ( v a n toe d a i ) (m/s). • V = (o.r = oj .r = • co: Toe do goe (van toe goc) (rad/s). — diTcfc t r o n g t h d i gian 4 s 1^: (PQ = co.t cpo = 4071.4 <=> cp - cp,| = 1 6 0 7 c ( r a d ) B a i 2. Roto eiia mot dong ecf quay t r o n deu quanh m o t true co d i n h . B i e t r k n g eiJ m 6 i p h u t t h i Roto quay d M c 1 2 0 0 vong. T i m : a) Chu k y quay ciia Roto. b) Gc3c ma ROto quay d M c t r o n g 2 s. c) So vong ma Roto quay diiac t r o n g 2 s. ; • r : B a n k i n h quy dao cua v a t (m). r • Sin. Gia toe phap t u y e n (gia toe • a t = 0 (chuyen dong deu) • (p = (po — cp - • f: T a n so (Hz) (v6ng/s). T • an tp • T: Chu k i quay ciia v a t (s). I. C h u y e n dpng tron deu. N b) G6c ma v a t quay do hirdng tarn) (m/s^). + co.t • a t : Gia toe t i e p t u y e n (m/s^). • a = a„ • a: Gia toe t o a n p h a n (m/s^). • 0) = 271.f Tom • 9: Toa do goe luc sau (rad). => 1 2 0 0 vong/phut <=> M = = 4071 r a d / s T = ? b) cp - • oj > 0: Neu vat quay theo chieu e) N = ? b) Goe m ^ Roto quay ducfc t r o n g 2 s. cpo = ? => cp - cpo = co.t cp - cpo = 4 O 7 1 . 2 cp - cpg = 807i(rad) <=> diJOng. c) So vong ma Roto quay diJgrc trong 2 s. • 0) < 0: Neu v a t quay ngi/crc chieu ^ 9-9o ducfng. B a i 1. Mot banh xe quay deu quanh mot true eo d i n h vdi t a n so 1 2 0 0 v5ng/phut. a) T i m toe dp goe cua b a n h xe. b) Goc ma b d n h xe quay duoc t r o n g t h d i gian 4 s. Hudng ddn gidi xet: Do b a n h xe quay deu quanh m o t true co d i n h n e n t a can silr d u n g eac k i e n thiJe cua chuyen dpng t r o n deu. a) De cho t a n so 1 2 0 0 v6ng/phut Tom tat B&nh xe quay deu 1 2 0 0 vbng/phut a) CO = b) cp - Cl:=> f = 1200 ^ = 60s ? (po = ? 2 0 (0 = 2nf ^ CO = 271.20 CO = 407t ^ SOn 22 N = 4 0 (vong) BAI T A P M A U Nhdn 271 4071 T = 0,05(s) 60s a) K h i v a t r ^ n quay t r o n deu t h i : gidi 271 T = 1200.27Trad • co: K h o n g doi (la h ^ n g so). ddn a) Chu k y quay cua Roto Moi phut t h i Roto quay duoe 1 2 0 0 vong • cpo: Toa do goe liic dau (rad). I I . luvtu y HUdng tat (rad/s) ^ s B a i 3. M o t b a n h xe quay t r o n deu quanh m o t true co d i n h . B i e t toa do gc5c iue dau la - r a d va toa do g6c sau t h d i gian la i 3 b a n h xe la 50 em. T i m a) Toe do goe cua b a n h xe. b) Toe do d a i eua m o t d i e m t r e n v a n h b d n h xe. s la ^ 0 0 e) Gia toe huc?ng t a m cua m o t d i e m t r e n v a n h b a n h xe. = 2 0 Hz Tom • cpo = — 3 Hiidng tat rad ai) dan Toe do g6c ciia b a n h xe Ap dung cong thiic: (p - cpo = co.t gidi rad, ban k i n h • (p = — _ rad ? b) V ? = C a u 2. K i m p h i i t c i i a 1 chie'e d o n g h 6 g a p 4/3 I a n c h i e u d a i k i m g i d . C o i m k i m n h u q u a y d e u . T i so g i a t o e h i f d n g t a m giura d a u k i m p h u t v a d a u k i m V = M . R = 71.0,5 = c) G i a t o e h u d n g t a m c i i a m o t d i e m t r e n vanh b a n h xe gicf. Cac k i m coi n h u ' q u a y d e u q u a n h m o t t r u e co d i n h . T i m t i so giuTa to'c do d a i cua d a u k i m p h u t v a d a u k i m g i d . • Rphui pillit dan gidi N e u x e m k i m gid va k i m p h u t quay t r d n mot t r u e co dinh v d i t a n so 2400 d e u , cii: m o i p h i i t q u a y d u o c 3 6 0 0 vdng. B. 160;: (rad/s). C. 8071 ( r a d / s ) . D . 2407i ( r a d / s ) . Cau 4. R o t o cua mot dong co q u a y 120071 rad. B. 24007t rad. D . 4 8 007r r a d . 27T goc luc sau l a r a d t r o n g t h d i g i a n 2 s. B i e t b a n k i n h q u y d a o t r d n c i i a o A . 7t/120 m / s . B . 7t/60 m / s . C. 7i/240 m / s . D . 7i/360 m/s C a u 6. M o t v a t c h u y e n d o n g t r d n d e u q u a n h m o t t r u e v a t q u a y 10 v d n g h e t 20 s. B a n k i n h q u y d a o c u a v a t l a 20 c m . G i a t o e h u d n g t a m cua v a t l a * T h d i g i a n de k i m g i d q u a y m o t v o n g l a 12 g i d A . 1,25 m / s ^ T„i, ^ 12 g i d phut = 1 gid ^ B . 0,65 m / s l C. 0,85 xnJ&\. 1,97 m / s l C a u 7. M o t v a t q u a y t r d n d e u d e u co p h u o n g t r i n h : cp = 7[/2 + 27tt ( r a d ; s). • T h d i g i a n de k i m p h u t q u a y m o t v d n g l a 6 0 ^gid quanh d e u q u a n h m o t t r u e co' d i n h t h i : ^ _ deu v a t l a 10 c m . T o e do d a i c i i a v a t l a Hiidng tdt 2 Rgij,. = quay C a u 5. M o t v a t - c h u y e n d o n g t r d n d e u v d i t o a do goc l u e d a u l a — r a d v a t o a do 2 B a i 4 . K i n i p h u t c u a m o t e h i e c d 6 n g h o c6 c h i e u d a i b a n g 2 I a n c h i e u d a i k i m . T g i , = 12 gior. xe C . 360071 r a d . a„ « 4 , 9 3 ( m / s ^ ) xet: banh D . 200. A . 12071 (rad/s). A. _0A_ R Nhan Mot C. 1 9 2 . T r o n g 20 s t h i r o t o q u a y diroc m o t goc l a 1,57'^ 60 p h u t = 1 g i d . 3. B . 108. v d n g / p h i i t . T o e do goc c i i a b a n h x e n a y l a c) an = ? •Tphat= A. 92. Cau 0,571 V = l,57(m/s) Tom cac gid la b ) T o e do d a i c u a m o t d i e m t r e n v a n h b a n h xe. • R = 50 c m = 0,5 (0 = 3 ~ (0 = 7 t ( r a d / s ) . t = - s a) 1 3 IL _ 3 Tphut 1 gid. = * K h i x e t d i e m d d a u m i i t c i i a k i m g i d v a k i m p h u t t h i k h o a n g e a c h tCf t r u e q u a y d e n cac d i e m n a y b K n g d u n g c h i e u d a i cua k i m g i d v a k i m p h u t n e n Toa dp goc l i i c d a u v a c h u k i q u a y c i i a v a t l a A . 7i/2 r a d ; 2 s. B . 71/6 r a d ; 1 s. C. 71/6 r a d ; 1/2$. D . 7t/2rad; I s . C a u 8. M o t v a t q u a y t r d n d e u c6 p h u o n g t r i n h t o a d o : cp - n/4 + 6nt ( r a d ; s). Goc q u a y c i i a v a t s a u 2 s k e t i f l i i c t = 0 l a A. 871 r a d . B. IOTI rad. C. 127c rad. D. 147T rad. • T i m t i so t o e do d a i cua d a u k i m p h u t v a d a u k i m g i d Van de 2: VAT RAN QUA Y BIEN DO I DEU fv = C3.R T a co: ^ 271 =5" v = — .R (*) A p d u n g (*) cho d i e m d d a u k i m p h u t v a d a u k i m g i d 271 2n .R gid <=> 271 ' pllllt 1. Quay = nhanh dan t 2. Quay k i m gid la C. 3/4. deu 24 1 . K i m p h i i t c i i a m o t c h i e c d o n g h o co c h i e u d a i b f t n g 4/3 c h i e u d a i eiia B . 16. do * CO,): V a n to'c goc liic b a n d a u (rad/s) 0 10 20 60 80 0 2 4 6 8 chdm dan D . 4/3. ... ... * (o: to'c do goc l i i c sau ( r a d / s ) . * y: to'c do goc (rad/s^). * cpo: T o a do goc l i i c d a u ( r a d ) . deu w ... 8 0 60 40 20 0 t ... 0 1 2 3 4 k i m g i d . Cac k i m c o i n h u q u a y d e u . T i so toe do d a i c i i a d a u k i m p h u t v a d a u A . 1/16. Trong I. P h a n loai R phiit BAI TAPTRAC NGHIEM Cau PHl/CfNG P H A P * (p: T o a do goc l i i c sau ( r a d ) . * a„: G i a tdc h u d n g t a m (gia p h a p t u y e n ) (m/s^). to'c CO - xet (p = cpo + coo-t + cp - 12071 r a d / s t h i b i h a m l a i v a q u a y c h a m din d e u s a u t h d i g i a n 10 s t h i toe dp g(5c c o n 407t r a d / s . * r : B u n k i n h q u y c!ao e i i a d i e m = 2y(cp - cpo) ml la * a: G i n toe t o a n p h a n (m/s^). = coo + Y-t CO B a i 2. R o t o eua m p t d p n g ccf d a n g q u a y q u a n h m O t t r u e c6' d i n h v6i t6c d p g6c * a t : G i a t o e t i e p t u y e n (m/s^). I I . C a c c o n g thtfc. a) T i m g i a toe goc c u a R o t o . ( h a y v a t dutfc x e t ) ( m ) . b ) T i m gdc q u a y v a so v d n g mk R o t o q u a y dMc 2 t r o n g t h d i g i a n 10 s k e tiT liic h a m . c) So v 6 n g m a R o t o q u a y dugrc k e tiir l u c b i h a m c h o d e n k h i dCfng h i n 1^ ipo = (Oo-t + bao n h i e u ? + a. Tom HUdng tat ddn gidi a„ = CO . r • coo = 1207T ( r a d / s ) C h o n e h i e u q u a y cua R o t o at = r . y • CO = 407r ( r a d / s ) t h d i g i a n (t = 0) l a luc Roto b ^ t d a u b i h a m l a i . t = 10 s a) G i a t o e goe eua R o t o * Li/u y: C a c h n h a n b i e t v a t q u a y n h a n h d a n d e u h a ^ c h a m d a n d e u : a) y = ? • N h a n h d a n deu - Y = b ) cp - (po = ? N = ? t r o n g 10 s * (Oo = 0 • C h a m d a n deu ham * (o.y < 0 4071 -- 12071 - 10 quay eiia R o t o quay diTOc s a u 10 s k e tCr l u c b) Goc c) N = ? k e t d l i i c goc y = -87i(rad/s^) —»• ke tir luc h a m . * (o.y > 0 CO - cOo l a m c h i e u duc(ng, b ^ t d a u bi h a m l a i . cho d e n l u c ddng h^n. cp - cpo = COo.t + • Chuyen dong quay b i e n doi deu t h i y k h o n g doi yt^ (-87t).10' cp - cpo = 1207r.lO + BAI T A P M A U (p-cpo = 80071 ( r a d ) Bai 1. M o t b a n h xe q u a y n h a n h d a n d e u q u a n h m p t t r u e tiT t r a n g t h a i durng yen < So' v o n g rak Roto quay dircfe i l n g v d i g6c quay t r e n . v a sau 5 s t h i d a t d u g c t o e do goc l a 10 r a d / s . T i m : N= a) G i a toe goc c i i a b a n h x e . b ) Goc q u a y cua b a n h x e t r o n g t h d i g i a n 5 s k e t i r t r a n g t h d i d i l n g y e n . tat Hiidng dan C h p n c h i e u q u a y c u a b d n h x e l ^ m c h i e u ducfng, goe • t = 5 s t h d i g i a n (t = 0) l a liic v a t b ^ t d a u quay, • CO = 10 raci/s a) G i a toe goc e i i a b a n h xe. a) y = ? b) cp - Y = (po = ? (o-coo 10-0 N gidi • tOo = 0 = 0.5 + co^ - cof, = 2y (cp CO 2 cpo) 2 -COn 0 ' - (12071)=' 2y The ( 2 ) v a o ( l ) ^ 25 2.3,14 N = _ -1440071^ 2.(-87r) 90071 271 -16;: (2) o |N ^ 4 5 0 ( v d n g ) 2.5' B a i 3. M p t d I a m a i c6 b a n k i n h 4 0 c m hAi d a u q u a y k h o n g to'c dp goc l u c d a u v d i g i a t o e goc k h o n g d o i c6 d p I d n l a 27i (rad/s^). T i m : a) T o e d p goe m a d i a m a i d a t dugtc sau 4 s k e iii l u c t = 0. c) So v o n g m a b a n h x e q u a y dugc t r o n g t h d i g i a n 5 s d t r e n . 271 « | N = 400vong (1) 2K y = 2(rad/s') cp - (p„ = 2 5 ( r a d ) = 271 D o l u c sau R o t o dCtog l a i - > co = 0 b) G6c m a b d n h x e quay difcfc t r o n g t h d i g i a n 5 s k e tiT t r a n g t h d i diJng y e n . y.t^ ^ • T i m cp - cpo = ? c) N = N = cp - cpo = 90071 ( r a d ) cp - CPo = (Ofl.t + « N = e) So v d n g m a R o t o q u a y diToc k e tijf l u c h a m p h a n h cho d e n l u e di^ng h ^ n . c) So v o n g m a b a n h x e q u a y dugfe t r o n g t h d i g i a n 5 s d t r e n . Tom 271 N = 3,98 ( v o n g ) b ) G i a to'c t i e p t u y e n , g i a toe p h d p t u y e n c u a m p t d i e m t r e n v d n h d i a t a i _ t h d i d i e m t = 4 s k e t d l i i c t = 0. c) Gia toe toan ph^n ciia mot diem tren vanh dia tai thdi diem 5 s ke tCf luc t = 0. C a u 10. T a i th6i diem t = 0, mpt bdnh xe dap bdt dau quay quanli IUUL true vdi gia toe goc khong doi. Sau 4s no quay dupe mpt goc 20 rad. Toe dp goc va gia toe goc ciia banh xe tai thcfi diem t = 5 s la Tom Hu6ng ddn gidi Chon ehieu quay ciia dia mai lam chieu dUcfng va goe thdi gian (t = 0) la luc dia mai bdt dau quay, a) To'c do goe cua dia mai dat duoe sau 4 s. tat • R = 40 em • (Oo - 0 • y = 271 rad/s^ a) (0 = ? sau (I) = o t = 4s b) at = ? an = ? tai (0 0^0 + Y-t A. 12,5 rad/s; 2.5 rad/s'. B. 20 rad/s; 2,5 rad/s^ C.IO rad/s; 22 rad/s^ A. 10 rad/s; 12 rad/s"". C a u 11. Mpt banh xe eo ban kinh I m quay nhanh dan deu trong 4 s to'c dp goc tang tCf 20 rad/s len 30 rad/s. Gia to'c goe eiia banh xe v^ gia to'c hir(Jng tarn ciia 1 diem tren vanh banh xe sau 2s la = 0 + 271.4 A. 2 rad/ s'^; 400 mJs\. 2,5 rad/ s^; 625 m / s l C. 4 rad/s^ 300 m / s l w = 87t (rad/s) t = 4s D. 5 rad/ s^; 196 m/s^ C a u 12. Mpt banh xe C m = • m : kho'i lifdng t h a n h (kg) • /: chieu d a i t h a n h (m) 2. V a t la t h a n h m a n h dong chat kho'i lifcfng m , chieu d a i / cd true quay d i qua mpt dau t h a n h vk vuong goc v d i t h a n h . 1=-. 3 m.l^ Trong do • m : K h o i lucfng t h a n h (kg). • /: Chieu dki t h a n h (m). 3. V a t Ik h i n h t r u rSng hoSc v a n h t r 6 n quay quanh true d i qua t a m . l = m.R' Trong do • m : K h o i lucfng t r u r o n g hoac v ^ n h t r d n (kg). • R: Bkn k i n h t r u r o n g hoac yknh t r 6 n (m). MAU <=> 0,256 0,2' m = 6,4 k g B a i 2. Mot dia mai chiu tac dung ciia mot life F = 6 N t a i mot diem t r e n v a n h diem. Biet ban k i n h dia mai la 40 em va dia c6 k hoi liTOng la 2 kg. T i m momen lire va momen qudn t i n h cua dia mai trong ha i triTdng hgrp sau: a) ^ b) O. M Tom tat . F = 6 N • R = 40 cm = 0,4 m • m = 2 kg Tim M = ? I = ? Hu&ng dan gidi a) • M o m e n lufc tac dung l e n dia m a i M = F.d = F.R = 6.0,4 b) Gia toe goc cua h# M = Ihf.y M = 1,2 N . m M = 6.0,4.sin30" • M o m e n quan t i n h cua dia m a i <2 I = i n i R ^ = i . 2 , 0 , 4 ' 4^ 2 2 Tom Momen quan t i n h ciia dia m a i k h o n g thay ddi t r o n g h a i B a i 3. M o t t h a n h A B c6 k h o i lupng 0,6 k g , chieu dai t h a n h la 80 cm. B i e t t h a n h m a n h , dong chat c6 the quay xung quanh true quay la dudng t r u n g . y> 0 Luc dau: ^ ly = ly + I - 0,02y - M = ly -> I = ma A irithanh b) y = ? • • Vay ^ y + 0,02y + 0,02 = 0 y 0.12 + 0,02y + 0,02 = 0 + 0,02y - 0,12 = 0 ^y = 2 ( r a d / s ' ) y = -3(rad/s') y = 2 r a d / s ' (do y > 0) ;2 niA 1 — .0,6.0,8^ Iz 0,8 = 0,1 {2j I B = mB.Rn^ = me. BAI TAPTRAC NGHIEM B C a u 20. M o t dia t r o n mong, phang, dong chat co the quay xung quanh 1 true d i dung vao dia m o t liTc co phiicfng t i e p tuyen v d i v a n h dia co dp Idn la 40 N . B i e t ban k i n h v a n h dia la + 1B mthanh-/' = IA = HIA-RA^ = M qua t a m va vuong goc v d i m a t p h ^ n g dia. Tac a) Momen quan t i n h ciia he - 0,02. M gidi GE Tim Iihanh = (2) niA • M = 60 N . m . Ihe = Ithanh + M = I'.y' - > I . y = r.y' <->-! + 0,02y + 0,02 = 0 Vay • mu = 300 g = 0,3 k g . a) I h , = ? (1) Tim y = ? (A) 100 g = 0,1 kg. M - I.y -> r = I - 0,02 k g m l 0. K h i y t a n g 1 rad/s^ t h i momen quan t i n h ciia chat d i e m doi v d i true quay g i a m 0,02 kgm^. T i m gia toe goc ciia chat diem. b) » Momen life tac dung l e n dia m a i M = F.d = F.R.sina o 60 0,096 B a i 4. Tac dung mot lire co momen k h o n g doi bSng 0,12 N . m l e n chat d i e m ehuyen dong theo quy dao t r o n l a m chat d i e m ehuyen dong c6 gia to'c goc M o m e n quan ti'nh ciia dia m a i I = 0,16kg.m' xet: M Y = M = 2,4 N . m I = - m.R' = i . 2 . 0 , 4 ' 2 2 * Nhdn ^ 2 / = 0,3. 0,8 40 cm. D i a ehuyen dong quanh true v d i y = 2 rad/s^. Bo qua m o i siJe can. = 0,032 k g m l = 0,016 kgm^ = 0,048 kgm^ v .2, Ihe = 0,032 + 0,016 + 0,048 -> I,,^ = 0,096 (kgm^) K h o i lirong cua dia la A. 100 k g B. 200 k g C. 300 k g D. 400 k g C a u 21. M o t r o n g roc co ban k i n h 10 em va co momen quan t i n h d o i v d i true quay la 0,04 kgm^ ban dau r o n g roc diing y e n , tae dung vao r o n g roe mot lire k h o n g doi F = 6 N t i e p tuyen v d i v a n h ngoai cua no. Bo qua m o i sufe can. Gia toe goc ciia r o n g roc la A. 5 rad/s'. B. 10 r a d / s l C. 15 rad/s^ D. 20 r a d / s l C a u 2 2 . M o t t h a n h A B d o n g c h a t c6 t i e t d i # n n h 6 so v d i c h i e u d ^ i I . B i e ' t t r u e C S u 3 0 . M o t d i a t r 6 n khS'i l i r o n g m = 1 k g , hAn k i n h 20 c m q u a y x u n g quanh q u a y d i q u a t r u n g d i e m t h a n h v a v u o n g goc v d i t h a n h . M o m e n l y e l a m q u a y m o t t r u e ( A ' ) song song v a each true d o i xiJng ( A ) cua d i a k h o a n g 4 cm. t h a n h n h a n h d S n d e u l a 0,5 N . m . B o q u a m o i liifc c a n . T h a n h d a i 4 0 c m , M o m e n q u d n t i n h ciia d i a d o i v d i t r u e ( A ' ) l a nang 100 g. To'c do goc c u a t h a n h sau k h i t h a n h bMt d a u q u a y d u g c 4s tilf t r a n g t h a i diJng y e n l a A. 1500 rad/s. B . 1600 rad/s. C. 7 5 0 r a d / s . C a u 2 3 . T a c d u n g 1 l u c c6 m o m e n hkng D . 400 rad/s. 1,6 N . m l e n c h a t d i e m c h u y e n t h e o q u y d a o t r o n l a m c h u y e n d o n g c6 g i a to'c goc y dpng > 0. K h i y g i a m 4 rad/s^ t h i m o m e n q u a n t i n h c u a c h a t d i e m d o i v d i t r u e q u a y t a n g 0,2 k g . m ^ . G i a t o e goc c u a c h a t diem A. 8 r a d / s l . B. 6 rad/sl C. 4 r a d / s l A. 0,016 k g . m ' . B. 0,0326 k g . m ' . C. 0,0016 k g . m ' . D . 0,0216 k g . m ' . C a u 3 1 . M o t d i a t r o n ed k h o i l i / d n g m = 1 k g b a n k i n h 2 0 c m c h i u t a c d u n g eiia luc F t i e p t u y e n v d i v a n h d i a , d p I d n F = 1 N . M o m e n q u a n t i n h eiia d i a v a m o m e n lire d o i v d i t r u e q u a y q u a t a m 1^ A. 0,02 k g . m ' ; 0 , 1 N . m . C . 0 , 0 3 k g . m ' ; 0,2 N . m . B . 0 , 0 2 k g . m ' ; 0,2 N . m . D . 0 , 0 4 k g . m ' ; 0,2 N . m . C a u 3 2 . M o t d i a t r o n ed k h o i l U d n g m = 2 0 0 g b a n k i n h R = 2 0 e m d a n g q u a y D. 2 rad/sl C a u 2 4 . M o t q u a c a u c6 k h o i l i i p n g 5 0 0 g q u a y q u a n h m o t t r u e d o i x i J n g . Q u a v d i t o e d p gdc 2 0 r a d / s t h i b i m o t lire c a n F^ ed d p I d n k h o n g d o i t i e p x i i c v d i cau CO b a n k i n h l a 10 c m . M o m e n q u a n t i n h c i i a q u a c a u d a c q u a y q u a n h t r u e v ^ n h t h e o p h u d n g t i e p t u y e n v a dCfng l a i s a u t h d i g i a n t = 2 0 s. D p I d n l u c di qua tarn l a can tac dung l e n v a n h d i a l a A . 10"^ k g . m ^ B . 210"^ k g . m l C. 3.10"^ k g . m l D . 4.10"^ k g . m ' . A. 0,01 N . B . 0,03 N . C . 0,04 N . D . 0,02 N . C a u 25. M o t d i a t r o n b a n k i n h 20 c m k h o i lUdng 2 k g quay q u a n h 1 t r u e n ^ m n g a n g q u a k h o i t a m 0 ciia d i a . T a c d u n g 2 lye eung chieu Van de 4: BAI TAP VE PHL/ONG F , , F j tiep xuc v d i v a n h d i a t a i 2 dau d u d n g k i n h A B v a c6 d p I d n F i = I O N , RA N QUA Y QUANH = 12N nhu hinh PHL/OfNG ve. G i a to'c goc c u a d i a l a B. 9 rad/s^ C. 10 r a d / s ' . D. 11 r a d / s l hkng n h a u . Bie't m o m e n q u a n t i n h c u a h p d o i v d i d i i d n g t r u n g B . 2 0 0 g. C. 3 0 0 g. • M = I. • F,, = m . a V d i : F,„ = F, + F , + ... D . 4 0 0 g. C a u 2 7 . M o t b d n h x e ed m o m e n q u d n t i n h d o i v d i t r u e q u a y eo d i n h l a 4 k g . m ' , d a n g d i J i i g y e n t h i c h i u t a c d u n g ciia m o t m o m e n l u c 3 0 N . m doi v d i true q u a y . B o q u a m o i l u c c a n . S a u b a o l a u , k e tCr k h i hit d a u q u a y , b d n h x e d a t t d i t o e d p goc 7 5 r a d / s ? B . 1 1 s. C. 12 s. A . 8. = 8CO3. C . 1/64. D . 1/8. C a u 2 9 . M o t q u a c a u k h o i l u p n g m = 5 0 0 g, b a n k i n h R = 10 e m diTdc t r e o m o t s d i d a y m a n h mk k h o a n g hkng e a c h til d i e m t r e o d e n t a m q u a c a u l a I m . M o m e n q u a n t i n h c i i a q u i e a u d o i v d i d i e m t r e o Ik A. 0 , 5 0 2 k g . m ' . Ti d o i v d i t r u e q u a y d i q u a t a m c u a A v a B c6 g i d t r i Ik B. 64. B . 0,45 k g . m ' . C. 2.10"' k g . m ' . • V = • S = • Vt' - D . 0,326 k g . m ' . y ; M = F. d • Liiu y Q u a y theo c h i e u (+) => M = F . d Q u a y ngUde c h i e u (+) =^ M = - F . d , ( 0 = (OQ + y . t + at Vo . D . 2 0 s. C a u 2 8 . H a i b a n h x e A v a B ed c u n g d p n g n S n g q u a y , t o e d p gdc co^ so m o m e n q u a n t i n h ~ TRUC Quay bien doi d e u bien doi d e u true l a 11/60 k g . m ' . K h o i l u p n g m o i v i e n b i l a A . 10 s. CUA PHAP Chuyen dpng thgng C a u 2 6 . M o t t h a n h A B ed k h o i l i f d n g 1 k g , / = I m . H a i d a u g ^ n 2 v i e n b i n h o A . 100 g. T MQ DQNG C d c cong thiiCc A. 8 r a d / s l CO k h o i iMng TRJNH CHUYEN Vot at^ + Vo' ^ = 2a.s , 9 9o , 0)^ - = (Oo Wot = + ^ 2 Y ( I P - ( P O ) • a = Vaf, + a? an = .r, at = r. y VAT BAI TAP B a i 1. M o t t h i i n g nxidc 1 B^ a i MAU tha xudng gieng nhcJ dugc mot soi day d a i quan quanh h i n h t r u c6 ban k i n h R = 10 cm va momen quan t i n h I - 0,02 kgm^. K h o i lu'ong ciia day va momen quan t i n h cua tay quay k h o n g dang ke. H i n h t r u coi n h a tay quay O t y do k h o n g ma sat quanh mot true c6 d i n h . Kho'i iMng t h u n g nUdc la 8 k g . T i n h : a) Gia toe eiia t h i j n g niidc. b) Luc cang day treo. Cho g = 10 m/s^. Tom tat Hiidng Nhaii • R = 1 0 c m = 0,1 n i . dan gidi xet: T r o n g bai tap nay, chung t a can xac • ! = 0,02 k g m l d i n h duoc v a t nao chuyen dong quay quanh • m = 8 kg. true va v a t nao chuyen dong t i n h t i e n . • g = 10 m/s^. T r o n g b a i toan nay, chung ta t h a y r a n g r o n g Tinh: rpc a) a = ? CO chuyen dong quay va t h u n g n U d c t h i chuyen dong t i n h t i e n . b) T = ? a) A p dung d i n h luat I I N i u t o n cho t h i j n g n U d c va phuang t r i n h dong lire hoc cho chuyen dong quay ciia h i n h t r u . Ta c6: * Doi v d i t h i j n g nude. P-T-m.a (1) * Doi vdi h i n h t r u . M - ly T.R = I.y ma he thufc l i e n he giuTa gia t o e dai va gia toe goe la a = R.y -> T.R - I . R y= — R La T o mg = m +• a o • m2 = 2 kg. • R = 8 cm. • I = 0,04 k g m ^ • (Or, = 0. • t = 4 s - > N = 3 vong. • g = 10 m/s^. a) y = ? b) a i = ? a. = ? c) T i = ? T 2 = ? d) Cd ma sat giufa m2 va san khong? Neu cd t i n h he so ma sat R^ 0,1^ - » cp - 2TI (pi, = N.27t = 3.271 = 671 a = rad A p dung cong thdc (p - 6n = 0.4 + (PO = 0)0.t + y = 0,7571 ( r a d / s ' ) b) Gia tdc cua n i i va m2 ai = a2 = at ma a, = R.y = 0,08.0,75Tt = 0,1884 m/s^ • Lire cang day T| R^ mg 8.10 0,02 *Xetvatmi: Pi - T , = m i . a i a = 8(m/s') N2 c=> 2.10 - T, = 2.0,1884 » Ti Pz fi T, = 19,6232 (N) Ta c6: M , + M2 = ly o T = 1 6 (N) tLtl. m2 m,g - T i = miai nil * Xet r o n g roe: The a = 8 mJs^ vao (2) 0,02.8 N = e) Lire cSng day d h a i ben true r o n g roc o la Hitdng dan gidi a) Gia tdc gdc cua r o n g roc. Nhau xet: T r o n g t h d i gian 4 s r o n g roc quay 3 vong Nhau xet: Chieu (+) cua cac v a t nhir h i n h . b) Lyc cang day treo. (2) ^ T = Tom tat • n i l = 2 kg. a, = a„ = 0,1884 m/s" (2) R^ Cong (1) va (2) => P = ma + (+) 2. H a i vat m , = 2 k g , m2 = 2 k g dUcfc l i e n k e t v d i nhau b&ng mot day nhe, k h o n g dan, v ^ t qua mot r d n g roc CO ban k i n h 8 cm va momen quan t i n h la 0,04 kgm^. B i e t day k h o n g trUOt t r e n r o n g roc n h u l i g k h o n g biet giiJa v a t m2 va ban c6 ma sat hay khong. Luc dau eac vat duoc giii' duTng yen, sau do he vat ducfc t h a ra. NgUdi ta t h a y r a n g sau k h o a n g t h d i gian la 4 s t h i r o n g roc quay quanh true cua no ducfc 3 vong. B i e t gia toe cua cac vat m i va m2 khong doi. Bo qua ma sat d true cua rong roc. Lay g = 10 m/s^ a) T i n h gia toe goe cua r o n g roc. b) T i n h gia toe eiia m j va m^. c) T i n h lire cang day d h a i ben cua r o n g roc. d) Co ma sat giiTa v a t m2 va m a t san hay khong? Neu cd, hay t i n h he so ma sat giiifa m2 va m a t san. T i . R - T2R = ly 19,6232.0,08 - T2.0,08 = 0,04.0,75Tt T2 = 18,4457 (N) (+) d ) Nhdn C o n g (4), (5), ( 6 ) xet: • T2 = 1 8 , 4 4 5 7 ( N ) • m2a2 = 2 . 0 , 1 8 8 4 = 0 , 3 7 6 8 ( N ) P, - P2 = m i a + m2a + D o T2 > m2a2 n e n giOfa m2 v a m a t s a n c6 lire m a s a t - > L i i c n ^ y lire m a s^t giOra m2 v a s a n ngiroc h u d n g v 6 i T2 nhxi h i n h ve b e n d u d i . D o N2 c a n b k n g P2 n e n t a c6: (7) R M a t k h a c t a l a i co at = a i = 82 = a = Ry N2 T2 - F „ „ = m2a2 (*) ma = ^N2 = 1.1.P2 = i-imag (do N2 = P2) T h e (8) v a o ( 7 ) t a eo: (7) ( m i - m2)g = ( m i + ma + n e n t i f (*) ->• T2 - |im2g = m2a2 18.4457 - n.2.10 = 2.0.1884 a = H = 0,9034 (m, R= •)a -m,)g »2 R / B a i 3. C h o co h e n h i f h i n h v e : R o n g r o c c6 k h o i liTcfng 14 k g , b a n k i n h 10 c m . H a l v a t m i = 600 g v a m2 = 4 0 0 g diTcfc t r e o v a o r o n g r o c n h d Vdi I = i m , , . R ' = i . 1 4 . 0 , 1 - = 0,07 2 2 Nen a day k h o n g d a n , k h o i lucfng d a y k h o n g d a n g k e . R D a y k h o n g trucrt t r e n r o n g roc v a r o n g roc c6 t h e - chuyen dong. Cho g a = 0,25m/3^ = he T h e a = 0,25 m/s^ v a o ( 8 ) 10 m/s^ y = |K a) T i m g i a t o e gdc cua r o n g r o c v a g i a t o e eiia 2 k e tii lue t h a cho h e c h u y e n d o n g v a goe ma mi m2 r o n g roc quay duac sau 2 s t r e n . 14 0,1 HUafng dan Nhan kg Do • m , = 6 0 0 g = 0,6 k g T„ = 4 , 1 ( N ) c) • Q u a n g . d u 6 n g m , , m2 d i d u o e s a u 2 s k e tii l i i c t h a cho h $ c h u y e n xet: Pi = m , . g = 0,6.10 = 6 N Vat m i , m2, r o n g roc co ehieu a) T i m y = ? a i = ? a 2 = ? d o n g c u n g c h i n h l a c h i e u ducfng d a b) T , = ? T i = ? chuyen t r e n n h u h i n h ve. m2: - P 2 + T2 = m2a2 (3) (4) +%= (5) = 0,5 m S, = 8 2 = S = 0 , 5 ( m ) • Goe m a r o n g r o c q u a y dUcfc t r o n g 2 s T i . R - T2.R = l y P; - T, = m , a T2 T, (p Vdi T, Mo = (10) ^ m2ii (+) T - T = — , ' ' R S = 0.2 + (1) (2) D o a i = a2 = a n e n t a c6 h e eac phuomg t r i n h sau: m,a (9) 0 2 5 2^ (9) mi: Pi - T i = mjai -P2 at^ V d i vo = 0 a) Y = ? a i = ? 32 = ? R S = vo.t + chon e) S i = ? S2 = ?; (p - (Po = ? t = 2 s (6) PI dong. xet: D o d a y k h o n g d a n n e n q u a n g d u d n g m i , m2 d i l a b ^ n g n h a u . Nhan P , > P2 • m2 = 4 0 0 g = 0,4 k g T i - T2 = - m 2 g + T2 = m2a gidi P2 = m 2 g = 0 , 4 . 1 0 = 4 N R o n g r o c : M , + M2 = l y T, = 5,85 ( N ) (5) tat • R = 10 c m = 0 , 1 m • Xet y = 2,5(rad/s') = (4) - > m i g - T i = m i a c) T i m q u a n g d u d n g m a m i , m2 d i d u o c sau 2 s • TCirr = a. b) L u c c a n g d a y t r e o d h a i b e n r o n g roc v a t m i , m2^ b ) T i m lue c a n g cua d a y t r e o h a i b e n r o n g roc. Tom = 0 , 6 . 0 , 4 . ° ^ ^ quay q u a n h m o t true n k m n g a n g . B a n dau h a i v a t dUOc giU dutog y e n r o i sau do b u o n g n h e cho ( 0 , 6 - 0 , 4 ) . 10 kgm' o 2= 0 t2 = 20 s a) Gia toe gde eiia b a n h xe t r o n g giai doan I (quay n h a n h dan deu) 10-0 -'"o, y, = 2 ( r a d / s ' ) t, Gia toe goc ciia b a n h xe t r o n g giai doan I I (quay cham dan deu) Yi = CO, - 0-10 (0 0, Y2 = -0,5 r a d / s ' t^ 20 b) Momen quan t i n h cua b a n h xe d o i v d i true quay va momen M i • Tim I : 72 = Xet giai doan r o n g roe quay cham dan deu M „ , = Iy2 - > - 1 0 = I . ( - 0 , 5 ) ^ I = 2 0 k g m ' ' Tim M i : Xet giai doan r 6 n g roc quay n h a n h dan deu. M l + M„,, = l y i ^ M l - 10 = 20.2 <:> (p - Vay tii (•) 0),,^ . t i + (po = cpo = 0.5 + 2 2.5^ = 25 r a d N = f ^ = 3,98(v6ng) 2.71 BAI TAPTRAC NGHIEM C a u 3 3 . Cho m o t b a n h xe ehiu tdc dung ciia m o t momen lUc M i k h o n g d o i . Tong cua momen M i va momen lire m a sdt e6 g i d t r i b k n g BON.m. T r o n g 2s dau, toe dp goc cua b a n h b i e n d o i deu tii 0 rad/s d e n 10 rad/s. Sau do momen M l ngi/ng tac dung, b d n h xe quay cham d a n deu v^ difng h ^ n l a i 50s. G i a suf momen lire m a sat l a k h o n g d o i t r o n g suot t h d i gian b a n h xe quay. Dp I d n momen life m a sat la A. 12 N . m . B. 2 N . m . , C. 3 N . m . D. 4 N . m . C a u 3 4 . Cho m p t b a n h xe chiu tac dung ciia m o t momen lire M i k h o n g d 6 i . Tong eua momen M i va momen life m a sat cd gia t r i b k n g 18N.m. T r o n g 4 s dau, toe dp goc cua b a n h xe b i e n d o i deu ti^ 0 rad/s den 12 rad/s. Sau d6 momen M i ngii'ng tac dung, b a n h xe quay cham d a n deu v a dCfng h ^ n l a i 24s. Gia sijf momen luc m a sat l a k h o n g d o i t r o n g suot t h d i gian b d n h xe quay. Momen liic M J a A. 20 N . m . B. 21 N . m . C. 22 N . m . D . 23 N . m . C a u 35. M p t b a n h xe n h a n dupc m p t gia toe goc 2 rad/s^ quay n h a n h d a n deu ti^ t r a n g t h a i dUng y e n t r o n g 4s dudi tac dung eiia momen life M j v^ momen liie m a sat. Sau do momen lUc M i ngUng tac dung t h i b a n h xe quay c h a m dan deu va difng l a i sau 10 vong quay. Toe dp gde sau 4s va t h d i gian tii liic b a n h xe b^t dau quay cho den k h i diing l a i l a A. 8 rad/s; 19,7 s. B. 9 rad/s; 12,3 s. C. 8 rad/s; 12,3 s. D . 9 rad/s; 11,3 s. C a u 3 6 . M p t b a n h xe c6 k h o i lupng 2 k g va b a n k i n h 20 cm quay n h a n h d a n deu tii t r a n g t h a i ddng y e n va sau 4 s d a t toe dp gde l a 40 rad/s. B i e t r l i n g t r o n g 4 s n a y v a t chiu tac dung cua life F va liTc m a sat theo phupng t i e p tuyen b a n h xe. Sau 4 s t r e n luc F m a t d i , b a n h xe quay cham d a n deu diTcfc 10s t h i dCmg l a i . Dp I d n cua lUc F tdc dung l e n b d n h xe \k D. 3,6 N . A. 0,7 N . B. 1,4 N . C. 2,8 N . C a u 3 7 . M p t m a y A - t i i t dung de n g h i e n cUu chuyen dpng cua cac v a t . C6 k h o i lupng khac nhau n h i i = 50 N . m c) So r o n g roe m a b a n h xe quay dupe t r o n g giai doan quay n h a n h dan deu Ni = ^ cp - (*) 271 V d i goc quay ma rong roc quay dupc trong giai doan I (quay nhanh dan deu) h i n h . Cho m i = 1 k g , m2 = 3 k g r b n g rpe quay quanh m p t true n k m ngang. Gia t h u y e t spi day k h o n g dan va k h o n g trUpt t r e n r o n g roc. Cho kho'i lupng r o n g rpe la 2 k g , r = 10 em. Cho g = 10 m/s^. Gia toe m o i v a t m i va m2 l a A. 1 m / s l B. 2 m / s l ' C. 3 m / s l D. 4 vols C a u 38. M o t dia dac ban k i n h 0,25 m c6 the quay quanh mot true doi xiJng d i qua t a m eua no. M o t soi day m a n h nhe dUdc quan quanh v a n h dia. ngudi t a keo dau sgi day b k n g m p t life k h o n g d o i 12 N . H a i giay sau ke tix lue tdc dung lire l a m dia quay v d i to'c do g6c b ^ n g 20 rad/s. Gia toe goe eua dia va gia toe eiia dau day la A. 10 rad/s^; 2,5 m / s l C. 12 rad/s^ 4 m / s l B. 11 rad/s'^; 3 m/s^. D . 10 rad/s^ 3 m / s l BAI TAP B a i 1 . M p t dia m a i eo k h o i lupng 2 k g , ban k i n h la 14 cm quay t r o n deu quanh true doi xuTng d i qua t a m dia v d i to'c dp goe la 1200 vong/phiit. T i m momen quan t i n h va momen dpng liipng eiia dia m a i t r o n g sU quay quanh true cua no. , R = 14 cm = 0,14 m . I = i m . R 2 = - .2.0,14^ 2 2 CO = 1200 vong/phut. = D. 40 r a d ; 10 m . I = 0,0196 kgm= 1 2 0 0 . ^ . 60s • M o m e n dpng lupng cua dia m a i t r o n g sir qiiay = 40Tt rad/s. quanh true ciia no Tim I = ? L = I.co = 0,0196.4071 L = ? L = 2,46176 k g m ' / s B a i 2. M p t banh xe chiu tac dung eua m p t momen k h o n g d o i n e n quay n h a n h dan deu k h o n g to'c dp goc lue dau va sau 5 s t h i toe dp goc eua b a n h xe la 20 rad/s. B i e t m o m e n quan t i n h cua b d n h xe doi v d i true quay cua n6 1^ Van de 5: MOMEN DQNG LU0NG D!NH LUAT BAO TOAN MOMEN DQNG LU0NG 0,4 kgm/s^. T i m momen dpng lupng cua b a n h xe t a i t h d i d i e m 8 s. Hitcfng dan Tom tat PHl/dNG PHAP • lOo gia toe cua b d n h xe k h o n g d o i . • Gia toe cua b a n h xe. • M = 20 rad/s I.M • I = 0,4 kgm^ Trong do T i m L = ? Luc t = 8 s. • L : M o m e n dpng lupng (kg.mVs). • I : M o m e n quan t i n h (kg.m^). • M o m e n dpng iMng I I . D i n h l u $ t b a o t o a n m o m e n d p n g li^dng (1) - C O n t 20-0 5 = 4 rad/s' • To'c dp goc eua b d n h xe t a i t h & i d i e m 8 s eua b a n h xe t a i t h d i d i e m t = 8 s L = I.co = 0,4.32 <^ L = 1 2 , 8 k g m V s B a i 3. M p t t h a n h A B d a i 80 cm co k h o i liipng k h o n g dang ke. CJ m p t dau cua t h a n h , ngudi ta gMn v a t m = 1 k g l o n g vao t h a n h va co the triiPt t r e n • Hp gom 1 v a t quay. thanh. Lue dau vat d dau t h a n h va t h a n h dang quay vdi toe dp goc la 25 rad/s quanh true doi xiifng. Sau do vat triipt den v i t r i each true quay 0,2 m . T i m toe I l . C O i = I2. CO2 • He g6m h a i v a t quay, liic dau diing yen. I, .0); + Ij.COj Y= (0 = coo + y.t = 0 + 4.8 = 32 rad/s • co: V a n toe toe (rad/s). Cde t r i i d n g hpp dac biet: gidi Nhan xet: Do b a n h xe quay n h a n h dan deu n e n = 0 •t = 5 s I. M o m e n d p n g liitfng - gidi M o m e n quan t i n h ciia dia m a i m = 2 kg. C a u 40. M p t v a t n a n g 90 N diipc bupc vao dau 1 spi day nhe quan quanh 1 r o n g roc dac c6 b a n k i n h 0,2 m , k h o i liipng 2 k g . Rong roe c6 true quay co d i n h nkm ngang va d i qua t a m cua no. N g i i d i ta t h a cho v a t r p i t i i dp cao h xuong dat. Cho g = 10 m/s^. Luc c&ng eua day va gia toe cua v a t l a A. 9 N ; 4 m / s l B. 9 N ; 9 m / s l C. 4 N ; 6 mJs\. 4 N ; 9 m / s l L = HUc/ng dan Tom tat C a u 39. M o t dia dac b a n k i n h 0,25 m c6 the quay quanh mot true d o i xvJng d i qua t a m cua no. M o t soi day m a n h nhe du'cfc quan quanh v a n h dia, ngxXdi ta keo dau soi day b k n g m p t liic k h o n g doi I O N . B o n giay sau ke tii luc tde dung life t h i dia quay v d i to'c dp g6c hkng 40 rad/s. Cho g = 10 m/s^. Goc quay dupe ciia dia va c h i l u d ^ i doan day difpc keo la A. 40 r a d ; 5 m . B. 80 r a d ; 20 m . C. 80 r a d ; 4 m . MAU =0 _ dp goc ciia v a t luc n a y . Tom tat • ^ = 80 cm = 0,8 m • m = 1 kg HUdng ddn gidi Nhan xet: Do de cho t h a n h co k h o i lupng k h o n g dang ke va quay quanh true d o i xiJng n e n • (Oi = 2 5 r a d / s Ithanh = . r = 0,2 m Tim C02 = L u c nky ? — I".Z « 0. t a c h i x e t v a t c6 m = 1 kg long vao t h a n h v a c6 t h e trugt t r e n t h a n h . A. 6340 k g m ' / s . A p d u n g d i n h l u a t b^o t o ^ n m o m e n d p n g l u o n g . L i = L2 Vdi (2) = mR^ (3) l2 thanh R 2 = 0,2 vat m A— UC UB - R i = 0,4 0,4 m 0'4^25 0,2^ R A . 40,5 kg.m^/s. B. 30,608 kg.m^/s. C. 2 0 , 5 k g . m ^ / s . D. 22,608 kg.m^/s. t h ^ n g d d n g . N g U d i a y d a y cho b a n h xe q u a y v d i v a n td'c 6 0 v d n g / p h u t t h i ngu'di a y se c h u y e n d o n g n h u t h e n a o ? V d i v a n toe hkng m R j .0)1 = m R j .0)2 - D . 8 3 2 0 kgm^'/s. C a u 4 8 . M o t n g U d i d d n g t r e n g h e d a u G i u e o ' p s k i c a m 1 b a n h xe cd t r u e q u a y T h e (2). (3) v^o (1) (1) ^ C. 8 0 0 0 k g m ' / s . M o m e n d o n g l U t f n g c u a v a t cd do I d n hhng (1) I i = mR? B. 7320 k g m ' / s . C a u 4 7 . M o t v a t cd m o m e n q u a n t i n h 0,72 k g . m ^ q u a y d e u 10 v o n g t r o n g 2s. (A) I i C O i = I2CO2 C a u 4 6 . M o t s ^ n q u a y h i n h t r u dSc c6 k h o i l u g n g M = 2 0 0 k g , b d n k i n h R = 2 m d m e p s a n cd 1 v a t k h o i l u o n g 4 k g . S a n q u a y d e u v d i co = 20 r a d / s . M o m e n dong l u p n g ciia he l a bao n h i e u ? B i e t m o m e n q u a n t i n h c i i a n g u d i d o i v d i t r u e q u a y l a I = 2 k g m ^ v a c i i a b a n h xe m do'i v d i t r u e q u a y l a I = 1 k g . m ^ A . N g U d i a y c h u y e n d o n g c i i n g c h i e u q u a y c u a b a n h xe v d i v a n t o e gdc l a 2 0 = lOOrad/s vong/ phut. B . N g u d i a y c h u y e n d o n g ngi/cfc c h i e u q u a y c i i a b a n h xe v d i v a n toe gdc 1^ 2 0 BAI T A P T R A C vong/ phiit. N G H I E M C. N g u d i a y c h u y e n d o n g c i i n g c h i e u v d i v a n td'e gdc l a 3 0 v d n g / p h u t . C a u 4 1 . M o t d i a m a i c6 m o m e n q u a n t i n h d o i v d i t r u e q u a y c u a n o l a 0,5 k g . m ^ . D i a c h i u m o t m o m e n life k h o n g d o i l a 2 N . m n e n b ^ t d a u q u a y n h a n h d a n d e u v d i toe do goc luc d a u cOg = 0 . M o m e n d o n g liTpng ciia d i a t a i thcfi d i e m 10s l a A . 40 kg.m^/s. B. 80 kg.mVs. C. 20 k g . m ^ / s . C o i T r a i D a t q u a y t r o n d e u 2 4 g i d dUdc 1 v o n g . M o m e n d o n g l i f d n g c u a T r a i D a t t r o n g sif q u a y q u a n h t r u e c i i a n o l a C. 7 , 1 4 . 1 0 ' " k g . m V s . D . 5,83.10^' k g . m ' / s . C a u 4 3 . M o t d i a dac c6 b a n k i n h R, d i a c6 t h e q u a y x u n g q u a n h t r u e d o i xiJrng q u a y 0,25 m . T o e dp gdc c u a v a t l u c n a y l a A . 80 r a d / s . B . 100 r a d / s . PHU'GfNG life k h o n g d o i M = 5 N . m . Sau 2 s k e t i f l u c b d t d a u q u a y , t o e do goc c i i a d i a I. Dpng nang quay PHAP l a 30 r a d / s . M o m e n d o n g lUcfng c i i a d i a t a i t h d i d i e m 3 s l a B . 15 k g m ^ / s . C. 6 k g m ^ / s . W,, '' D. 7 kgm^/s. C a u 44. M o t t h a n h n h e d a i I m quay deu t r o n g m a t p h a n g n g a n g x u n g q u a n h t r u e t h a n g diirng d i q u a t r u n g d i e m c i i a t h a n h . H a i d a u t h a n h c6 2 c h a t d i e m k h o i l U d n g 2 k g v a 1 k g . V a n toe cua m o i c h a t d i e m l a 5 m / s . M o m e n dong l i / a n g cua t h a n h l a A . 10,5 k g . m ^ / s . C a u 4 5 . M o t t h a n h A B cd k h o i luang C. 12,5 k g . m ' / s . D . 7,5 k g m ^ / s . 1 k g , chieu dai 2 m , 2 dau t h a n h g^n 2 v i e n b i n h o m o i v i e n cd k h o i l u a n g l a 100 g. M o m e n d o n g lugrng c i i a t h a n h k h i t h a n h q u a y v d i co = 4 0 r a d / s l a A . ^0,2 k g m V s . Trong B . 2 1 , 2 kgm^/s. C. 2 2 , 2 k g m V s . D. 23,2 k g m/s. = - . W 2 do: • W , i : D o n g n S n g quay (J). • I : M o m e n q u a n t i n h (kg.m^). , B . 11,5 k g . m ^ / s . C. 2 0 0 r a d / s . D . 500 rad/s. Van de 6: DQNG NANG. DINH LI DQNG NANG CUA VATRAN TRI^C QUAY CO DINH d i q u a t a m v a v u o n g goc v d i m a t p h ^ n g d i a . D i a c h i u t a c d u n g c i i a 1 m o m e n A. 4 kgm^/s. m o t dau ciia t h a n h , n g U d i t a g a n v a t m = 0,2 k g l o n g v a o t h a n h v a cd t h e t r i f o t tren gdc 0) = 20 r a d / s q u a y q u a n h t r u e do'i x i i n g . S a u do v a t t r u p t d e n v i t r i e a c h t r u e C a u 4 2 . C o i T r a i D a t l a m o t q u a c a u d o n g c h a t c6 M = 6.10^'' k g , R = 6 4 0 0 k m . B . 5,56. l O ' ^ k g . m ' / s . C a i i 4 9 . M o t t h a n h A B d a i I m cd k h d ' i li/cJng k h o n g d a n g k e . 6 t h a n h . L u c d a u v a t d d a u t h a n h v a t h a n h d a n g q u a y d e u v d i td'c dp D . 2 4 0 k g . m V s. A. 6,28.10''kg.m'/s. D . N g U d i a y c h u y e n d o n g n g u p c c h i e u v d i v a n toe gdc l a 3 0 v d n g / p h u t . CO: V a n td'c gdc ( r a d / s). II. Djnh li dong ndnq Trong do: • Angi : C o n g n g o a i l u c ( J ) . » A : Dp b i e n t h i e n d o n g n S n g (J). CO
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