Kĩ thuật giải nhanh bài tập trắc nhiệm vật lí 12. - T.1

Huong dan giai: Vi 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 6 rad/s^

530 076 P G S T S 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

K300T

KI THUAT GIAI NHANH

BAI TAP TRAC NGHIEM

• 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

B A N D A I H O C Q U O C G I A H A N 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

• DONG L U C H O C VAT RAN

• DAO D O N G C O

• S6NG C O

• DAO DONG VA SONG DI£N T f

D 6 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 ki nang lam b^i

• Bien soan theo noi dung va cau triic de thi cua bp GD&DT

THIJ ViFNTiNHBINMTHUAN

DCK]

N H A X U A T B A N D A I H O C Q U O C G I A H A N O I

LOfI N O I D A U

Quyen sach nay 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 thanh 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 tu 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 khi doc Quyen sach dugc tach thanh hai tap de c6 dii dung

lugng cho vi^c chuyen tai ngi dung ly thuyet va khoi lugng bai tap day dii,

phong phii

* Tap 1 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 2 bao gom:

- Chu de 6: Tinh chat song anh sang; • •

\ Chu de 7: Lugng tu anh sang

- Chu de 8: Thuyet tuong doi hep;

- Chu de 9: Vat ly hat nhan nguyen tu

- Chu de 10: Tu vi mo den vT mo

De C O kien thuc virng chac va luyen dugc each giai bai tap, cac em khong

nen chi dgc quyen sach nay bang mat nhu doc tieu thuyet ma nen c6 gia'y but

de ghi lai nhOng dieu tam dac va tinh toan cac dai lugng vat ly ma bai tap yeu

cau theo ggi y huong dan giai da cho Lam dugc nhu vay, cac em cam chac kha

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 tu cac thay c6 giao va cac em hgc sinh

Nhom tac gia

nam tren true quay va ban kinh bang khoang each tir diem do den true quay

Moi diem ciia vat quay cung mot goc trong 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 do

1 Chuyen dpng quay ciia vat ran quanh mpt true co dinh

Su tuong tu 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:

Tga do goc: (p Toe do goc : ( 0 = cp' Gia toe goc: y = co' = cp"

Chuyen dgng thSng deu:

V = hang so; a = 0; x = xo + vt

Chuyen dgng quay deu:

0) = hang so; y = 0; (p = cp,, + cot Chuyen dgng thSng bien doi

Cong thuc lien he giOa cac dai lugng goc va dai lugng dai:

s = r(p, V = rco; at = ry; a„ = rco^

Chii y: Dan vj ciia cac dai lugng trong hf don vj SL x(m); v(m/s); a(m/s^);

(p (rad); CO (rad/s); y (rad/s2)

2 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 do Ian bang: M = Fd (1)

3

T r o n g do d la canh tay d o n cua luc F (khoang each tie tryc A den gia cua

Ivc F )

D o n vj cua m o m e n lye la N m

Chpn ehieu quay cua vat lam chieu d u o n g , ta c6 quy uoe:

- M > 0 k h i F eo tac d u n g lam vat quay theo ehieu d u o n g

- M < 0 k h i F eo tac d u n g lam 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 nho eo kho'i l u g n g m gSn vao mpt

dau thanh rat nh? va dai r Vat quay tren mat phMng nhan n a m ngang x u n g

quanh m g t true A th^ng d u n g d i qua m p t dau eiia thanh 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 nay la:

M = ( m r 2 ) y ( 2 )

t r o n g do y la gia toe goc ciia vat ran m

* T r u o n g hgp 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, 6 each true quay A n h u n g khoang n, r\, khac nhau t h i m o m e n lye tae

d y n g len vat ran nay la:

Cty TNHH MTVDWirKK^g Vift

(3)

b Momen 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 quan t i n h

i cua vat quay va duge goi la m o m e n quan rinh, ky hi$u la I

M o m e n quan tinh I doi v o i m o t true la dai l u g n g dac tnmg cho m u c quan

tinh ciia vat ran trong ehuyen dgng quay quanh true ay

(4)

M o m e n quan tinh c6 d o n vj la kg.m^

> M o m e n quan tir\ ciia mgt vat ran khong chi phy thuoe vao khoi lugng a i a

vat ran ma eon phu thuge vao ea sy phan bo khoi lugng xa hay gan true quay

> D i n h l y ve trye song song: I Q = + m d ^

T r o n g do: d la khoang each tir true quay O den true song song qua trong

tam G ciia vat; lo; IG t u o n g l i n g la momen quan h'nh ciia vat d o i v o i tryc O va

trye G

> M o m e n quan t i n h ciia m g t so vat ran eo trye quay do'i x i i n g :

• Thanh d o n g chat, c6 k h o i l u g n g m va c6 tie't di^n nho so v o i chieu dai 1 ciia no, tryc quay A d i qua t r u n g diem ciia thanh va v u o n g goc v o i thanh:

1 = - l m l 2

1 2

• Vanh tron d o n g chat eo k h o i l u g n g m , ban k i n h R, tryc quay A di qua

tarn vanh va v u o n g goc v o i mat phang vanh tron: I = m R

• Dia tron 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, trye quay A di

qua tam dia tron va v u o n g goc v o i mat dia: I = - m R

• Qua cau dac d o n g chat eo khoi l u g n g m , eo ban k i n h R, tryc quay A di

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

ran trong ehuyen d o n g quay quanh true A

3 Momen dpng lugmg dinh luat bao toan momen dpng lugng

a Momen dpng lugng L eiia vat rin trong ehuyen dpng quay quanh trye la:

L = lo) (6)

Trong do: I la m o m e n quan tinh ciia vat ran d o i v o i trye quay; co la toe dp

goc eiia vat ran trong ehuyen dpng quay quanh tryc

D o n vj eiia m o men 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:

AL

M =

Trong 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 dpng

•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 trong t h o i gian At

c D i n h luat bao toan momen dpng lugng

K h i M = 0 t h i L = L(o = hang so Neu tong 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 0 t h i tong m o m e n dpng l u g n g ciia vat ran (hay h ^ vat) d o i v o i tryc

do 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 khong d o i : vgt ran (hay h | v^t) d u n g yen ho§e quay deu

Ki thuatgiai nhanh BTTN Vat Li 12, tap 1 - Nguyen Quang Lac

• T r u o n g hgp I thay doi thi co thay doi: vat ran (hay he vat) c6 I giam thi co

tang, CO I tang t h i co giam (Ico = hang so' hay I^co^ = I2CO2)

4 D p n g nang ciia vat ran quay quanh mpt true

a D p n g nang Wd cua vat ran quay quanh mpt true eo d i n h la:

W , = l l c o 2 (8) Trong do: I la momen quan tinh cua vat ran doi v o i true quay, co la toe do

goc ciia vat ran trong chuyen dong quay quanh true

T u (6) va (8), dpng nang Wd ciia vat ran quay quanh m o t tryc co' d i n h co the

vie't d u o i dang:

V V d = ^ (9) Trong do: L, I Ian lugt la momen dong lugng va momen quan tinh cua vat

ran doi v o i true quay Dong nang cua vat ran co don v i la jun, k i hieu J

b D i n h l y b i e n thien d p n g nang: D o bien thien dong nang cua mot vat ran

quay quanh mpt true co dinh bang tong cong thuc hien boi momen ngoai luc

tac d u n g vao vat Ta co:

• A W , = l l c o 2 - l l c o ? = i ( c o ^ - c o 2 ) = A (10)

Trong do: I la momen quan tinh ciia vat ran doi v o i true quay, coi la.to'c dp

goc liic dau ciia vat ran, C02 la to'c dp goc liic sau ciia vat ran, A la tong cong ciia

cac momen ngoai luc tac d u n g vao vat ran, AWd la dp bien thien dpng nang ciia

• To'c dp goc: CO bang hang so'

• Gia toe goc: Y = 0 '

• Tpa dp goc (phuong trinh chuyen dpng ciia vat ran quay deu quanh mpt

trvcco'djnh): (P = (PQ + cot ' '

Lien he giCra to'c dp goc va to'c dp dai: v = cor

Gia toe h u o n g tarn: a,., = — = a)^r 0 g'v; i , ;

Cty TNHH MTV DWH Khattg Viet

So' vong vat ran quay dupe: " = ^ =

(vi m 6 i vong vat ran quay dupe mpt goc la 2rc rad)

V i 1: M p t banh xe quay deu quanh true co djnh v o i tan so goc khong doi

6000 vong/phiit Trong 2,5s banh xe quay dupe mpt goc la

^ 1257T rad B 250n rad C 500 n rad D 750TI rad

Huong dan giai:

Ta CO f = 6000 vong/phiit = 100 v6ng/s

Suy ra: CO = 27tf = 2007t (rad/s)

Do do: cp = cot = 20071.2,5 = S O O T I (rad) => Chpn C

V i d u 2: M p t canh quat ciia may phat dien chay bang sue gio c6 d u o n g kinh

50m, quay deu v o i toe dp 120 vong/phiit Toe dp dai tai mpt diem nam a

vanh canh quat bang:

Ta co: co = 120 vong/phiit = in rad/s; ^ = ^ = 25m

V i d u 3: M p t vat ran quay quanh mpt true co d m h xuyen qua vat v o i phuang trinh tpa dp goc cp = 5,6 + 4,5t, trong do cj) tinh bang radian (rad) va t tinh bang giay (s) M p t diem tren vat each true quay khoang r = 6em thi co toe dp dai bang:

A 12cm/s B 18 cm/s C 27 cm/s D 35 cm/s

Huang dan giai:

T u phucmg trinh cp = 5,6 + 4,5t ta suy ta: co = cp' = 4,5rad / s

Trong do c}>o la toa do 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^

Vi 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 trong thai gian

do la:

A.23rad B.37rad C 48 rad D 55 rad

Huong dan giai:

Vi 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 6 rad/s^ Chpn moc thoi gian t = 0 tai thai diem banh xe bat

dau chju luc ham tac dung Chpn chieu duong la chieu quay eiia vat ran

Thoi gian tu khi banh xe chju lire ham tac dung den liic dirng lai va goc

quay trong khoang thai gian do la

A t = Is; cp = 6,7 rad B t = 1,5 s; cp = 7,5 rad

C t = 3 s; (p = 11 rad D t = 2 s; cp = 12 rad

Huong dan giai: j w ,^

Ap dung cong thuc: co = cO(, + y t , trong do coy =12rad/s, vi banh xe quay

ch|m dan deu nen y = -6rad / s^

Do do phuang trinh van toe goc la: CO = 12 - 6t (rad/s)

12 Khi banh xe dung lai thi co = 0 => 0 = 12 - 6t t = — = 2s Vay sau 2s thi

6 banh xe dung lai

Chpn moc thoi gian t = 0 tai thai diem banh xe bat dau chju lye ham tac dyng, tpa dp goc ban dau cpg = 0 Chpn chieu duong la chieu quay cua vat ran,

khi do, ap dung cong thuc:

cp = (P(, +cOot + iYt^ =0 + 12.2-i.6.2^ =12rad ChpnD

Vi du 3: Mpt banh xe co duong kinh 54 cm quay nhanh dan deu, trong 5 giay van toe goc tang tu 180 vong/phiit len 480 vong/ phiit Gia toe huong tam ciia diem M a vanh banh xe sau khi tang toe dupe 3,5s la

A 330,4 m/sl B 411,2 mls\ 456,3 m/s^ D 512,7 m/sl

Huang dan giai:

Ta co: COQ - 67irad / s va co = 16rcrad/s.^

CO-co,) 167t-6K ^ , , 2

y = = = 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 /

k

Dang 3 BAI TAP LIEN QUAN DEN M O M E N QUAN T I N H CUA V A T

RAN, HE VAT RAN 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 1 ciia no, true quay A di qua trung diem ciia thanh va vuong goc vai thanh:

U - l m l ^

^2 ;,,

TI K i thuatgidi nhatih BTTN Vat Li 12, tap 1 - Nguyen Quanx Lac

• Vanh tron dong chat c6 khoi lu^ng m, ban kinh R, tryc quay A di qua

tarn vanh trong 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 tam dia tron va vuong goc voi mat dla: I = — mR

• Qua cau dac dong chat c6 khoi luong m, c6 ban kinh R, true quay A di

qua tam qua cau: I =—mR^

> Dinh ly ve true song song: IQ = I,- + md^

Trong do: d la khoang each vuong goc tu true quay O den true song song

qua trong tam G ciia vat; lo; Ic; tuong ung la momen quan tinh eiia vat doi voi

true O va true G

; > Momen quan tinh cua he vat ran: I = Ii +12 +

i trong do: Ii, I2, Ian lu^t la momen quan tinh cua eae vat ran m j , m^

V i du 1: Hai qua cau con lie dac lam eung b3ng mot loai thep, dong chat eo

ban kinh gap 4 Ian nhau 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

A I i = 314l2 B.I2 =51211 C I , =512 12 D l 2 = 314I,

Huong dan gidi:

Goi D la khoi lu-gng rieng cua; Vi va V2 la the tich ciia cac qua cau

Ta c6: m^ = D.V^ = D y R^; = D.V2 = ^-^^l

5 5

U2J = 45=512=>Ii=512l2 ^ C h p n C

Vi du 2: Mot thanh manh eo khoi luong m = 5 kg, chieu dai 1,2 m Doi voi

true quay di qua khoi tam va vuong goc voi thanh, momen quan tinh ciia

thanh bang:

A 0,3 kgm^ B 0,6 kgm^ C 0,9 kgm^ D 0,12 kgml

Huang dan gidi:

Ta c6: I = ^ m l ^ = ^5.1,2^ = 0,6kgm2 =^ Chon B

Cty TNHH MTV DWH Khattg Viet

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^ B 0,27 kg.m^ C 0,54 kg.m^ D 1,2 kg.m^

Huang dan gidi:

Theo djnh ly true song song, ta c6: {'^ ) ^ ,:

I = I c + md^ = |mR2 + mR^ = |mR2 = |.4.0,3^ = 0,54(kgm2)

=> Chgn C ,^ v

Dang 4: B A I T A P L I E N Q U A N D E N P H l / O N G T R I N H D Q N G L l / C

H O C C U A V A T R A N Q U A Y Q U A N H M O T T R V C C O D I N H

Phuong phap giai:

• Van dung phuang trinh dong lye hoc ciia vat ran quay quanh mot true

CO djnh M = ly 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, tuy thuoc vao tac dung lam quay vat theo chieu duong hay am ciia tung lue, sau do 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 6 lop 10 cho vat chuyen dong tinh tien (xem vat nay 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 yen thi chiu tac dung boi mot lue F tiep xiic voi mep ngoai vanh Bo qua moi

ma sat Sau 3s vanh tron quay dugc mot goe 36 rad Do Ion eiia lue F la

A , I N B 2 N C 4 N , D 8 N

Huang dan gidi:

Taco: {p = | 7 t ^ =36(rad)=>y = 8rad/s^ I = mR^ -0,5(kgm^j Momen lue: M = F.R = I7 = 8.0,5 = 4(Nm)

Do Ion ciia lye F la: F = ^ = 8 ( 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^ #

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 0 rad/s den 10 rad/s Sau do 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

Khi M l thoi tac dung: co' = to + y't = 0 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

Dang 5: BAI TAP LifiN QUAN DEN DINH LUAT BAO TOAN

M O M E N D O N G LU'ONG

Phuang phap giai: Su dung cac kien thuc sau: «*•

• Momen dpng lupng L cua vat ran trong 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 trong chuyen dpng quay quanh true

• Tinh Momen dpng lupng cua h^ vat ran doi vai tryc quay theo cong thuc:

A 3,55 kgm^s B 4, 65 kgm^s C 6,75kgm^s D 8,75 kgm^s

Huang dan gidi:

Toe dp goc cua moi qua cau: = ^ = - lO(rad) Momen dpng lupng ciia h^:

L = Lj + L 2 = IiCOj + I2CO2 = (ij +12 )to

= ^ m i R ^ + m 2 R ^ ) ( o = ( m i + m 2 ) R ^ a ) ' f

= 3,5.0,5h^l0 = 8,75(kg .m2/sj t '

=> Chpn D

Vi dy 2: Mpt nguoi c6 khoi lupng 50kg dung 6 mep mpt san quay hlnh tron

CO khoi lupng 200 kg, duong kinh 4m Bo qua ma sat 6 true quay va sue can

khong khi 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 dp goc cua san la bao nhieu?

A cung chieu vai chieu chay ciia nguoi vai toe dg l,05(rad / s)

B nguoc eiiieu v o i chieu chay eiia nguai voi toe do - l , 0 5 ( r a d / s)

C eiing chieu voi chieu chay eiia nguoi voi toe do 3,05(rad / s)

D nguge chieu vai chieu chay eiia nguoi voi toe do -3,05(rad /s)

b) N g u o i nay chay dan vao giua san khi den diem M each true quay I m thi

lai chay theo phuang tiep tuye'n eiia san tai M vai toe do n h u tren H o i toe

do goc cua san khi do la bao nhieu?

A 0,525(rad / s) ' ' » ' ' B 1,425 (rad/s)

C -0,525(rad / s) D -1,425 (rad/s)

Huang dan gidi:

a) Ban dau he d u n g yen nen momen dong lugng: Lo = 0

Khi nguoi chay quanh mep san th: momen dong lugng ciia he khi do la:

Do 0)1, C02 khae dau nen san se quay theo chieu nguge voi chieu chay ciia

nguai vai toe do goc: ©2 = = = = - l , 0 5 ( r a d / s)

=> Chgn B

b) Khi nguai chay den diem M thi: L2 = I,o), +12(02

Do momen dgng lugng duge bao toan nen: L2 = Lo Suy ra:

14

V i d u 3: M o t san quay hinh tru c6 khoi lugng M = 180kg va ban kinh

R = 1,2m dang d u n g yen M o t nguoi khoi lugng m = 40kg chay tren mat dat vai toe do 3m/s theo phuang tiep tuyen vdi mep san va nhay len san Bo qua

ma sat 6 true quay Tinh toe do ciia nguoi do khi o tren san

A 0,52 m/s B 0,72m/s C 0,82m/s D 0,92m/s

Hu&ng dan gidi: ,

Momen dgng lugng ciia nguoi truoc khi nhay len san:

Dang 6 B A I T A P L I E N Q U A N D E N D O N G N A N G C U A V A T R A N

T R O N G C H U Y E N D O N G Q U A Y

Phuong phap giai: Su dung eac kien thuc sau:

• Dgng nang eiia vat ran quay quanh mot true co djnh: Wd = ^Ico^

• Dgng nang ciia vat ran vua quay vira chuyen dgng tjnh tien:

Huong dan gidi:

Momen quan tinh ciia khoi cau la: I = -mR^ = -.80.0,6^ = ll,52(kgm^)

Dgng nang cua khoi cau la: Wj = ijco^ = 11,52.20^ = 2304(j) => Chon B

Vi 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

a) Can bao nhieu thoi gian de tang toe banh da tu trang thai nghi den toe dp

goc bang 12 rad/s

A 0,5s B 1,5s C.2,5s D 3,5s

b) Dpng nang ciia banh da a toe dp goc nay 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^)

Thoi gian can thiet: t - ^^Z^ = = ] 5(3) ^ Chpn B

b) Dpng nang ciia banh da 6 toe dp goc do la:

= ilto^ = 1.4,5.122 = 324(J) =^ Chpn C

^ang 7 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 D Q N G

N A N G C U A V A T R A N Q U A Y

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 < 0)

Vi 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 tu khi thoi tac dung momen lyc M den khi banh xe dung lai

A -3kJ B.-9kJ C.-15kJ D -23kJ

Huang dan gidi:

Do banh xe quay deu, nen tong momen lyc:

A ^ , = AW, - W , o =-ilo)^-1.12.502 =-15000(j) = -15kJ

=> Chpn C

Vi du 2 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 0 tarn rod

nh? xuong banh da dang quay sao 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 trong 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

A 0,6Nm B l,2Nm C 2,4Nm D 3,6Nm b) Dpng nang dia nhan dupe

A.40J B.60J C.80J D 120J c) Nang lupng toan phan da truyen cho dia

A 80J B 120J C 200J D 240J

Huang dan gidi:

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: Wj = ^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 nay chuyen thanh nhi?t):

AW = A = AWd - Wd - Wdo = 120 G) Nang lupng toan phan truyen cho dia la: W = W, + A W ^ 2 0 + _ 1 2 0 ^ 4 0 ( j )

17

V i dv 3*: Mgt banh xe khoi lu^ng m = 5kg, ban kinh R = 20cm chiu tac dung

ciia mpt l\tc F khong doi theo phuong tiep tuyen v6i vanh ciia banh xe

Tong lyc F va \\fc ma sat a vanh banh xe la 48N Trong 5s dau toe do goc

bien doi tii 0 rad/s den 10 rad/s Sau do lyc F thoi tac dung, banh xe quay

cham dan va dirng lai sau 5s Gia su luc ma sat la khong doi trong suo't qua

trinh banh xe quay Bo qua ma sat 6 tryc quay

a) Xac dinh lyc F va lyc ma sat

; A. I N v a l N B 2 N v a l N C l N v a 2 N D 2 N v a 2 N

b) Tim cong ciia momen lyc F va cong ciia momen lyc ma sat trong qua

trinh tren

A lOJ va -lOJ B 5J va -5J C lOJ va-5J D 5J va -lOJ

Huang dan gidi:

a) Gia toe goc ciia banh xe khi eo ngoai lyc F va khi khong c6 ngoai lye F Ian

Ap dyng djnh ly dong nang cho giai doan mpt, ta c6:

A, + A ^ , = AWj - - W,o = llco^ = lla)2 = 5(j)

Do Yj = 72 va ti = t2 nen: Amsi = Ams2 = -5 (J)

; Suy ra: A F = 5 - A m s i = 5 + 5= 10 Q) => Chgn C

III B A I T A P TV* L U Y E N C O H l / ^ N G D A N C A C H G I A I

CSu 1 Mot banh x e q u a y d e u q u a n h tryc c6' d i n h v o i t a n so' g o c k h o n g doi

^gOOvong/phiit Trong 2,5s banh x e q u a y dupe m p t g o c la

A. 2 0 0 7 T r a d B SOOn rad C 400 n r a d D. SOOTI raD

Huang dan gidi: > i

Ta CO £ = 4800 vong/phiit = 80 v6ng/s ,,

Suy ra: co = 27if = 160:: (rad/s)

Do do: (p = cot = 16071.2,5 = 40071 (rad) => Chpn C Cau 2 Mpt canh quat q u a y voi toe dp goc khong doi co = lOOrad/s Toe dp dai ciia mpt diem 6 tren canh quat va each true quay ciia canh quat mpt doan 25em la

A 12,5m/s B 25m/s C.27,5m/s D.35,8m/s

Huang dan gidi:

Toe dp dai ciia mpt diem tren canh quat va each true quay ciia canh quat 20

cm la: v = cor = 100.0,25 = 25 (m/s) => Chpn B Cau 3 Coi Trai Dat la m p t qua cau ran quay d e u quanh tryc co d i n h Bac -Nam Ban k i n h t r u n g binh ciia Trai Dat la 6370 km Van toe dai ciia m p t diem 6

x i e h dao co g i a tri nao sau d a y ?

A 435 m/s B 56 m/s C 756 m/s D 463 m/s

Huang dan gidi:

Ta co: ^ = ~ Trai Dat quay quanh dupe m p t vong het 24h nen:

CO - — — — * 7,3.10"^ rad / s

24.60.60 Suy ra van toe dai ciia mpt diem a xieh dao la: v = rco = 463m / s

Huang dan gidi:

Ta co: v = cor, voi co = 120 vong/phiit = 4n rad/s; = ^ = •^^m

Huang dan gidi:

T i r phuong trinh <p = 5 + 2,5t ta suy ta: co = (p' = 2,5rad/s

Vay V = co.r = 2,5.4 = 10 (cm/s) => Chpn B

Cau 6 Tren mot dia dong chat nam ngang quay deu quanh true doi xung c6

mgt vat nam each tam dla 20cm He so ma sat nghi giua vat va mat dTa ^ n = 0,5

De vat khong bi vang ra khoi dTa thi gia t r i eua toe do goe khong duoc Ion hon

A 3,5rad/s B 4,4 rad/s C 5 rad/s D 9,3 rad/s

Huang dan gidi:

De vat khong bi vang ra khoi dia thi lye quan tinh l i tam khong Ion han luc

ma sat nghi cue dai: F„ = mco^R < nmg => co < 5rad / s

N h u vay de vat khong bi vang ra khoi dia thi gia tri ciia toe do goe khong

duoc Ion hon 5 rad/s => Chon C

Cau 7 Mot canh quat dai 50cm, quay voi toe do goe khong doi co = 74rad / s

Gia toe eiia mpt diem 6 vanh canh quat bang

A n 2 3 m / s 2 B 1783m/s2 C 2738 m/s^ D 3412 m/s^

Huong dan gidi:

Vi vat ran quay voi toe do goe khong doi nen vat ran quay deu Gia toe goe

cua mot diem thuoe vat ran eiing ehinh la gia toe goc ciia vat ran

Taco: a = a,^, = co^r = 74^.0,5 = 2738(m / s^) ^ Chon C

Cau 8 Mot dTa CD quay deu voi toe do quay 400 vong/phiit trong mot 6 doc

cua may vi tinh Toe do goe cua dTa CD do tinh theo rad/s la

A 470 rad/s B 42 rad/s C 4,7 rad/s D 0,47 rad/s

Huang dan gidi:

„ , 400.271 , , ^ , „

Ta co: co = = 42rad / s => Chon B

Cau 9 MQt vat bat dau quay deu quanh mot true co djnh, sau 2 s dat duoc toe

do goe 5 rad/s Gia toe goe trung binh ciia vat trong thoi gian do la:

A 2 , 5 r a d / s ^ B l O r a d / s ^ C 1 5 r a d / s ^ D 2 5 r a d / s ^

Huang dan gidi:

Ap dyng cong thue: y = — = = 2,5rad / s^ => Chpn A

At 2 Cau 10 Toe do dai eua mpt diem tren vat ran quay deu quanh true co djnh va

each true co djnh mQt doan r = 20 cm la 20 m/s Toe do goc ciia diem do la

A 100 rad/s B 90 rad/s C 80 rad/s D 70 rad/s

Huang dan gidi:

Ap dung eong thue: v = cot=i>co = - = — = lOOrad / s => Chon A

20

Cty TNHH MTV DWH Khang Vift

Cau 11.Mot vat rSn quay deu voi toe dp goc 50 rad/s Tai thoi diem ban dau

'^J^tcStoa dp goc la 5 rad Sau 2s vat co toa dp goe la: | , ;

• A 100 rad B 105 rad C 110 rad D 115 rad

Huang dan gidi: ^ ,

Ta eo (p = (Po + = 5 + 50.2 = 105rad Chpn B Cau 12 Coi Trai Dat la mot vat ran quay deu quanh trye co djnh Bac - Nam

Toe dp goe ciia Trai Dat bang

C 73.10"^rad / s D 7,3rad / s

Huang dan gidi:

Ta co: co = ^ ma Trai Dat quay dupe mpt vong het 24h nen:

CO = — — — ~ 7,3.10"^ rad / s => Chpn A

24.60.60 Cau 13 Mpt banh xe dang quay voi van toe goc 32 rad/s thi b i ham lai v o i gia toe goc khong doi eo dp Ion 4 rad/s^ Goc quay dupe eua banh xe t u luc ham den liic banh xe dung han la

A 64 rad B 128 rad C 350 rad D 563 rad

Huang dan gidi:

A 7i(rad/s2) B 27i (rad/s^) C 47i (rad/s^) D 671 (rad/s^)

Huang dan gidi:

Taco: = ^ = 27t(rad/s^) Chpn B

Cau_15.Mpt banh xe chuyen dpng nhanh dan deu t u trang thai diing yen, sau 5s banh xe dat van toe goc 25 rad/s Gia toe goc cua banh xe la

A 1,07 rad/s2 B 2,38 rad/s^ C 5,0 rad/sl D 7,51 rad/s^

Huang dan gidi:

Taco: y = ^ 1 ^ = ^ = 5 r a d / = ^ Chpn C

t - t o 5 Cau_16,Mpt vat ran dang quay quanh mpt true co dinh xuyen qua vat voi toe

«lo goe 25rad/s thi bat dau quay cham dan deu va dung lai sau 5s Goc ma vat quay dupe trong Is cuoi cung truoc khi dirng lai la

A l , 2 5 r a d B 2,5rad C 5,0rad D 8,5 rad

Huang dan gidi:

Gia toe goc: y = — = - 5 r a d /

At ;, , •

P h u o n g t r i n h c h u y e n d p n g : (p = -yt^ + cogt '

Goc m a vat q u a y d u g c t r o n g 1 s c u o i c i m g t r u o c k h i d u n g l a i la:

^(t=5) ~ ^(1=4) = 2,5rad => Chpn B i , , ;•

Cau 17 M o t b a n h xe d a n g quay v o i v a n toe goc 40 rad/s t h i b j h a m l a i v o i gia

toe goc k h o n g d o i c6 d p I o n 4 rad/s^ T h a i g i a n tit liic ham t a i liic banh xe d i m g

han la

A 4,7 s B 6 , 9 s C 10 s D 17 s

Huang dan gidi:

Theo cong t h i i c : y = " => T h o i g i a n t i r liie h a m t a i l i i c b a n h xe d u n g

h i n l a : t = ^ = ° : i i ^ = 10s =^ C h p n C

y - 4

Cau 18 M p t vat ran quay b i e n d o i deu c6 p h u o n g t r i n h c h u y e n d p n g cp = 5 t l

Ket l u a n nao sau day la sai?

A Toe d p goc ban d a u ciia vat bang 0

B Gia toe goc eiia vat c6 gia t r i bang 10 rad/5^

\ Toe dp goc ban dau eiia vat c6 gia t r i bang 5 rad/s

D Tpa d p goc ban dau eiia vat d u p e ehpn bang 0

Huang dan gidi:

P h u o n g t r i n h eiia c h u y e n d p n g quay bien d o i d e u eiia v a t r a n q u a n g t r y c co

d j n h c o d a n g : (p = (pQ+a)Qt + i y t ^

\o dau bai (p = 5t^ =>(po = 0; y = l O r a d / s ^

Vay ket l u a n COQ = 5rad / s la sai => Chpn C

C a u 1 9 M o t banh xe d a n g q u a y v o i v a n toe goc ban dau 20n (rad/s), t h i bat dau

q u a y cham d a n d e u va d u n g l a i sau t h o i gian t = 20s So v o n g b a n h xe quay

d u p e cho den k h i d u n g hMn la

A 400 v o n g B 300 v o n g C 200 v o n g D 100 v o n g

Huang dan gidi:

C h p n m o c t h o i gian t = 0 tai t h a i d i e m banh xe bit dau quay cham dan deu,

tpa d p goc ban d a u cpg - ^ • C h p n ehieu d u o n g la chieu quay eiia b a n h xe

A p d y n g cong t h i i c : (p = (p(j + coQt + i y t ^

T h a y so ta d u p e cp = 0 + 20n.20 - ^ 7 t 2 0 ^ = 2007t(rad) ' ' ' ' ' ' ' ' ^ ^'

S o ' v o n g b a n h xe q u a y d u p e la: n = — = = JOO v o n g => C h p n D

Cau 20.Mpt banh da ciia d p n g ea quay nhanh dan deu, sau k h i k h o i d p n g

dupe 2s t h i goc q u a y ciia b a n h da la 14 r a d Toe d p goc t a i t h o i d i e m d o la:

A 13 rad/s B 14 rad/s C 15 rad/s D 16 rad/s

Huang dan gidi: , •

Ap d u n g cong thiie cp = (PQ + cogt + i y t ^ , chpn moc thai gian liic vat bat dau

k h o i d p n g v a eo tpa d p goc b a n d a u bang 0, suy ra:

1 2 2(p 2.14 ^ , 2

^ = - 7 ^ ^ = > y = - ^ = = 7 r a d / s

2 t 4

Mae khae y = ^ =^=> oi = yy = 7.2 = 14rad / s => Chpn B

Cau 2 1 M o t v a t r a n bat d a u q u a y q u a n h true ciia no v o i gia toe goc k h o n g d o i Sau 5s no q u a y d u p e m p t goc 50 r a d C h p n m o c t h o i g i a n t = 0 t a i t h o i d i e m v a t ran bat d a u quay, tpa d p goc ban d a u (pQ = 0 C h p n ehieu d u o n g la chieu q u a y ciia vat rSn Toe d p goe t a i t h o i d i e m t = 5s bang:

A 30 rad/s B 20 rad/s C 50 rad/s D 80 rad/s

Huong dan gidi:

C h p n m o c t h o i g i a n t = 0 tai t h a i d i e m v a t r a n bat d a u quay, tpa d p goc ban dau (py = 0 C h p n ehieu d u o n g la ehieu q u a y eiia v a t r ^

Ap d u n g cong thiie: (p = cpg + Wpt + i y t ^ , trong do: cpo = ^ ' ^ ' '^^^

quay nen toe d p goc b a n d a u

1 ^ 2(p 2.50 , , , 2 (OQ = 0 =>(p = —yt :=> y = = — — = 4 r a d / s

2 t^ 5^

V i vat q u a y v o i gia toe goe k h o n g d o i nen tai t h a i d i e m t = 5s gia toe goc ciia vat ran b a n g 4 r a d / s^

Ap dyng cong thiic: <B = COQ + yt = 0 + yt = 4.5 = 20rad / s

Chpn B

Cau 22 Mpt vat ran dang quay deu quanh mpt tryc c6' djnh vai toe dp goc

10 rad/s thi chiu mot luc ham tac dung va chuyen dpng quay cham dan deu

voi gia toe goc 4 rad/s^ Chpn moc thai gian t = 0 tai thai diem vat ran bat dau

chiu luc ham tac dung Chon chieu duong la chieu quay cua vat ran Thai gian

tir khi vat ran chiu luc ham tac dung den liic dirng lai va goc quay trong

khoang thai gian do la

A t = 4s; (p = 48 rad B t = 2,5 s; (p = 12,5 rad

C t = 3,5s;(p = 52,5rad D t = 7 s; (p = 54 rad

Huang dan gidi:

Ap dung cong thiic: a) = (Oo + yt, trong do COQ =10rad/s, vi vat ran quay

cham dan deu nen y = -4rad / s

Khi vat ran dtmg lai thi (o = 0 => 0 = 10 - 4t => t = — = 2,5s

4 Vay sau 2,5s thi vat ran dung lai

Chon moc thai gian t = 0 tai thai diem vat hit dau chiu luc ham tac dung

toe dp goc ban dau (pg ~ • Chpn chieu duong la chieu quay cua vat ran

Ap dung cong thue:

(p = (Po +(Oot + i y t ^ =0 + 10.0,25-i.4.2,5^ =12,5rad

=> Chpn B

Cau 23 Banh da cua mpt dpng ca, tir luc khoi dpng den khi dat toe dp goc

120 rad/s, da quay duac goc bang 240 rad Bie't banh da quay nhanh dan deu Thai

gian tu liic bat dau khoi dpng den khi banh da dat toe dp 4800 vong/phiit la:

t = ^ = 1 ^ 1 6 , 7 5 ( s ) = > C h o n C

Cau 24 Mot banh xe quay nhanh dan, trong 5s van toe goc tang tir 180 vong/

phut len 480 vong/ phut Gia toe goc cua banh xe la

A 1,571 rad/s^ B 27trad/s^ C 3 , 5 7 t r a d / D 5,5jtrad/s^

Huang dan gidi:

Taco:

COQ = 180 vong/phiit = 671 (rad/s); co = 480 vong/phiit = 16Tt (rad/s)

a)-cO( 1671-671 ^ / 7\ i

Gia toe goc: y = ^ = = 27r rad / => Chpn B

Caul5.Mpt chat diem nam tren vong tron c6 toe dp goc ban dau COQ = 120 rad/s

quay cham dan voi gia toe khong doi b5ng 4,0 rad/s^ quanh true doi xung vuong goe vol vong tron Thai gian va goc quay ke t u Iiic chat diem bat dau chuyen dpng cham dan deu den liie dung lai Ian lupt la

A t = 30s; (p = 1800 rad B t = 40s; (p = 3600 rad *

C.t = 20s; 9 = 1200 rad D t = 40s; 9 = 2400 rad

Huong dan gidi:

Ap dung cong thue: o) = C0(, + yt

Khi dung lai: co = 0 t = = 30(s)

Y

2 ,2

Goc quay dupe la: A 9 = — - — - = 1800(radj => Chpn A

Cau 26 Tai thoi diem t = 0, mpt vat ran bat dau quay quanh mpt trye eo' dinh xuyen qua vat voi gia toe goc khong doi Sau 8s no quay dupe mpt goc 80 rad

Goc ma vat r^n quay dupe tu thai diem Os den thai diem 10s la

A 45 rad B 38 rad C 75 rad D 125 rad '

Huang dan gidi: #

Sau ti = 8s taco: 9 , = i y t ? ^ y = ^ = ^ = 2,5f rad / sM

2 t^ 8^ ^ '

Tu do, suy ra goc ma vat ran quay dupe sau t2 = 10s la: |

92 = l y t ^ =1.2,5.10^ =125rad=> Chpn D

Cau_27.Mpt dia tron bit dau quay quanh true vai gia toe goe khong doi Sau 6s

dla quay dupe 36 vong So'vong quay dupe trong 6s tiep theo la

A 54 vong B 108 vong C 216 vong D 321 vong

Huang dan gidi:

Ta c6: 9 = — yt^ => y = — = 2 (v6ng/s^) Toe dp goc sau 12s la: co = COQ + yt = 24 (v6ng/s)

-So'vong quay dugc sau 12s la: Acp = " ^ =144 (vong)

So'vong quay dugc sau 6s tie'p theo: 144 - 36 = 108 (vong) =>ChQn B

Cau 28 M o t banh da dang quay quanh true v o i toe do goe 240 vong/phiit thi

quay eham lai v i c6 ma sat v o i o trye Sau 1 giay, toe d p ehi con 0,6 Ian toe do

ban dau, eoi ma sat la khong doi Toe do goc sau giay t h u hai la

A. CO = 0,27t rad/s B (o = 0,97trad/s

C w = l,27r rad/s D co = l,6rad/s

C Huang dan gidi:

Ta eo: COQ = = 87r(RAD /S), suy ra: = 0,6tOo = 4,87t(rad / s)

60

Gia toe goc eua banh da la: y = — = - 3 , 2 ( r a d / s^)

At \Toe d p goc sau giay t h u hai la: = O)Q + yt = 87i3,27t.2 = l,67t(rad / s)

=> C h p n D

Cau 29 M o t vat ran quay quanh m o t true co'djnh xuyen qua vat P h u a n g trinh

ehuyen d p n g eiia vat cp(t) = 2 + 2t + t^, trong do cf) tinh bang radian (rad) va t

tinh bang giay (s) M o t d i e m tren vat ran each trye quay R = 8em t h i c6 toe dp

bang bao nhieu vao t h o i d i e m t = I s ?

A 6cm/s B 14 cm/s C 26 em/s D 32 cm/s

Hwang dan gidi:

P h u o n g t r i n h van toe goc: co = cp'(t) = 2 + 2t

Tai thoi d i e m t = l s: (o = (p'(l) = 2 + 2.1 = 4 ( r a d / s)

Toe dp: v = coR = 32em/s => Chpn D

Cau 30 M o t vat ran quay quanh m o t trye theo p h u a n g t r i n h cp = 12 - 5t - 0,5t^

trong do cp t i n h theo rad, t tinh bSng s Phat bieu nao sau day k h o n g diing?

A Vat quay eham dan deu

B Toe dp goc eua v^t la h a m so'bae nhat theo thai gian

C Gia toe goc eua vat k h o n g thay doi theo thoi gian

D M o m e n lue tac d y n g len vat khong doi theo thoi gian

Huang dan gidi:

Ta eo: co = - 5 - t (rad/s)

^ y = - l ( r a d / s 2 )

Ket qua tren cho thay:

- Toe dp goc ciia vat 00 = - 5 - 1 (rad/s) la ham so'bae nha't theo thoi gian

=> B d u n g

- Gia toe goc eiia vat y = - 1 (rad/s^) khong thay d o i theo t h o i gian

=> C d i i n g

- V i gia toe goc ciia vat khong thay d o i theo thai gian nen m o m e n lye tac

d y n g len vat k h o n g d o i theo thai gian => D d u n g

- V^t ehi ehuyen dpng eham dan k h i coy < 0 => A sai => C h p n A

Cau 3 1 M p t cai dla dang quay v o i toe dp goc 5 rad/s thi bat dau quay eham dan deu, sau 5s t h i no d u n g lai So vong ma dia da quay dupe trong thai gian

do xap xi bang:

A 0,85 v o n g B 1,99 vong C 2,15 v o n g D 3,39 v o n g

Huang dan gidi: ^ ,^

( 0 - C0(, - 5 / T \

Gia toe goe eua dTa: y = — p ^ = — = - l | r a d / s j

Goc ma dia quay d u p e cho den k h i d u n g lai la:

<p = co„t + -^yt^ = 5.5 + ^ ( - l ) 5 ^ = - 1 2 , 5 ( r a d )

Suy ra so v o n g dTa quay dupe trong thoi gian do la: n

n = = * 1,99 vong = > C h o n B

£ju_32.Mpt banh da quay nhanh dan deu t u trang thai nghi, v o i gia toe goc

0,57t rad/s^ De banh da dat toi toe dp goe 247t rad/s t h i no phai quay bao nhieu vong (ke t u thai diem ban dau)? ,

A 144 vong B 288 vong C 342 vong D 563 v o n g

Huang dan gidi:

T a c o : co - co^ = 2y(p ^ (p = — - — = — = 5767i(rad)

So vong banh da quay dupe la: n = — = = 288 vong => C h p n B

Cau_33.Banh da ciia m p t d p n g co, t u liic khai d p n g den k h i dat toe dp goc 120 rad/s, da quay dupe goe b^ng 180 rad Biet banh da quay nhanh dan deu T h a i gian t u liie bat dau k h o i d p n g cteh k h i banh da dat toe d p 3600 v o n g /phut la

A 3,18s B 5,43 s C 7,89 s D 9,42 s

Huong dan gidi:

Ta c6: COQ = 0 (rad/s); coj = 120 (rad/s); coj = 3600 vong/ phiit = 120Tt (rad)

_ (Of - en

= cOg + yt => t = - ( 0

2cp

'0 _ 120^ - 0 2.180

Cau 34 M o t banh xe quay nhanh dan deu t u trang thai d u n g yen, sau 3s banh

xe dat van toe goe 12 rad/s Goe ma banh xe quay duge trong thoi gian do la

A 9,5 rad B 18 rad C 36,5 rad D 54 rad

Huang dan gidi: ^ i

Ta eo: y = (o-cop 1 2 - 0 2 = = 4rad / s''

t - t n 3

T u (0^ - COQ = 2yA(p

A{p = (0 - ( O n 1 2 ^ - 0 ^ = 18rad Chc)n B

2y 2.4 _

Cau 35 M o t banh xe c6 d u o n g ki'nh 2,4m bat dau quay v o i gia toe goc khong

doi bang 5 rad/s^ Gia toe huong tam ciia mot diem tren vanh banh xe a thai

diem 0,4s nhan gia t r i

A 4 , 8 m / s 2 B.9,6m/s2 C 15,8m/s2 D.24,7m/s2 |

Huang dan gidi:

Taco: a^, = (o^r = (yt)^ =(5.0,4)^2,4 = 9 , 6 ( m / s ^ ) Chc)n B

Cau 36 M o t vat ran quay quanh mot true c6' djnh theo p h u o n g trinh cp = 27 +

48t - 2t^ trong do (p tinh theo rad, t tinh bang s Goc vat quay duge ke tir thoi

diem ban dau cho den khi no d u n g lai la

A 288 rad B 435 rad C 567 rad D 982 rad

Huang dan gidi:

Taco: (o = 4 8 - 4 t = 0 t = 12 (s)

(p = 24 + 48.12-2.122 = 315 (rad); (po = 27 (rad) ,|

A(p = (p - (po = 315 - 27 = 288 (rad) => Chon A

Cau 37 M o t banh xe c6 d u o n g kinh 350cm hit dau quay t u nghi v o i gia toe goc

khong doi la 2,4 rad/s^ Toe do dai ciia mpt diem tren vanh banh xe 6 thai diem

2,5s la

A 14m/s B.2^^ C 3 5 m / s D 5 6 m / s

Huong dan gidi:

Ta c6: v = Q)r = (yt)r = (2,4.2,5).3,5 = 21 (m/s) => Chpn B

Cau38.Mot banh xe c6 d u o n g kinh 2,5m quay v o i gia toe goc khong doi

3,5 r a d M thai gian ban dau to = 0 la liic banh xe hk dau quay Van toe dai eiia

mpt diem N tren vanh banh xe 6 thoi diem t = 4 s bang

A. 21 m/s B 27 m/s C 35 m/s D 49 m/s

Huong dan gidi: ^ • i.i

V?in toe goe tai thai diem t = 4s la (o = coo + yt = 0 + 3,5.4 = 14 rad/s

=> Van toe dai v = (oR = 14.2,5 = 35m/s => Chon C

Cau 39^ M o t banh xe dang quay voi toe dg goe 28 rad/s thi bj ham lai v o i mpt

gia toe goe eo dp Ion khong doi 2,5 rad/s^ Thai gian t u luc ham den liic dirng lai la

Huong dan giai:

Khi d u n g lai thi (o = 0 , s u y r a : t = - ^ = l l , 2 ( s ) => Chpn B

Cau 40 M p t banh xe dang quay voi toe dp goc 32 rad/s thi bi ham lai v o i mpt

gia toe goc khong doi 4 rad/s^ Goe quay dupe t u luc ham den liic d u n g lai la

A. 72 rad B 132 rad C 144 rad D 128 rad

Huang dan gidi:

2 2 2 2

Ap d u n g cong thue: -^o ~ ^y.Acp => Aip = — ^ — ^ = ^ = 128(rad)

=> Chpn D

Cau 41 M o t banh xe eo d u o n g kinh 3m bat dau quay voi gia toe goc khong doi

la 4,5 rad/s^ Gia toe tie'p tuyen cua mpt diem tren vanh banh xe la

A 7,8m/s2 B 13,5 m/s^ C 15,6 m/s^ D 18,2 m/s^

Huang dan gidi: 1

Taco: a, - r.y - 3.4,5 = 1 3 , 5 ( m / s ' J ^ Chpn C

Cau 42 Do bj mat dien mpt chie'c may mai quay cham dan deu, biet van toe goc

ban dau la 360 vong/phut va gia toe goc la -3n^ rad/sl So vong ma may eon c6

the quay dupe truoe khi d u n g lai la

A 12 vong B 18 vong C 24 vong D 36 vong J

Huang dan gidi:

Ap d u n g cong thue:

(o2-(o2=2y.Acp=^A9 = — ^ = ^ - ^ ^ ^ = 247r(rad)

•'•v:'^ — 29

bo vong quay: n = —^ = = 12 vong =?> Chpn A

2n 2n

Cau 43 M o t banh xe c6 d u a n g ki'nh 60 cm quay nhanh dan deu trong 2s t h i toe

dp goe tang t u 180 vong/phiit den 240 vong/phiit Gia toe h u o n g tam ciia diem

M tren vanh banh xe sau 4s la

A 142m/s2 B 384m/s2 C 463 m/s^ D 600m/s2

Huang dan gidi:

Ta eo: coo = 180 vong/phiit = 6n (rad); coi = 240 vong/ phiit = 87t (rad/s)

Y = coj -At COQ _ 2 87t - 6n = 7 i ( r a d / s 2 j

Suy ra: a,^, = coj.r = ((Og + yt)^ r = (67t + 71.4)^ 0,6 = 60o|m / s^j =::> Chpn D

Cau 44 M o t banh xe quay nhanh dan deu quanh mpt true eo djnh t u trang thai

nghi Sau 4s ke t u liic bat dau quay, mpt diem each true quay 20 cm c6 gia toe

h u o n g tam la 80 m/s^ Gia toe goe ciia banh xe la

A.2,5rad/s2 B 5 rad/s^ C 7,5 rad/s^ D 12,5 rad/s^

Huang dan gidi:

Ta c6: a „ = =^ = ^ f " = = 20(rad / s)

y = ^ = ^ = 5 ( r a d / s ^ ) ^ C h o n B

Cau 45 M o t banh xe dang quay vai toe dp goe 20 rad/s thi hit dau quay cham

dan deu Sau 8s banh xe d u n g lai So vong da quay dupe eiia banh xe la

A 4,6 vong B 6,4 vong C 8,3 vong D 12,7 vong

Huang dan gidi:

Gia toe goe cua banh xe: y = — = -2,5(rad / s^)

Xe chuyen dpng nhanh dan deu, eu sau moi giay toe dp ciia xe lai tang them

Im/s Tai v i t r i tren quy dao ma dp Ion ciia hai gia toe huong tam va gia toe

tie'p tuyen bang nhau, toe dp ciia xe la

A 8,5m/s B 16m/s C 24,6 m/s D 32 m/s

Huang dan gidi:

Gia toe tie'p tuyen: a^ = ^ = 1 ( m /

Xheobaita, ta c6: a,,, = a , = l | m / s^) => ^ = 1 => v = 16m / s => Chpn B

47 M p t 6 to d i vao khiic d u o n g l u p n tron de chuyen huong Ban kinh ciia

^^^^J^lupn la 50m, toe dp 6 to giam deu t u 18 m/s xuong 10 m/s trong 3,2s

Gia toe goe ciia 6 to tren d u o n g lupn c6 dp Ion la

A Y = 0'05 rad/s2 B y = 0,1 rad/s^ C y = 0,125 rad/s^ D y = 2,5 rad/s^

Huang dan gidi:

Av 10-18 o r / , 2\

Gia toe hep tuyen: a, = — = ^ ^ = - 2 , 5 ^ m / s J , At 3,2

Suy ra gia toe goe: 2,5 ( r a d / s ^ j Chpn A

r 50

Cau 48 M p t dia tron quay nhanh dan deu tir trang thai nghi, sau 5s dat toi toe

dp goe 10 rad/s Trong 5s do dTa tron da quay dupe mpt goe bang

A 5 rad B 10 rad C 25 rad D 50 rad

Huang dan gidi:

Goe quay dupe la: A9 = — - — - = 25(rad) => Chpn C

Cau 49 M o t banh xe quay tir liic d u n g yen, sau 2s no dat dupe toe dp goe

10 rad/s Gia toe goe trung binh va goe quay dupe trong thoi gian do Ian lupt la

A y = 2 rad/s2; 4) = 4 rad B y = 4 rad/s^; (}) = 8 rad

C y = 3 rad/s^; (j) = 6 rad D y = 5 rad/s^; cj) = 10 rad

Huang dan gidi:

Gia toe goe trung binh ciia vat: Y = = S^rad / s^ (voi (oo = 0)

Goe quay dupe la: Aip = — - — - = 10(rad) => Chpn D

£a]i50.Mpt n g u o i d i xe dap khoi hanh dat dupe toe dp 18 k m / h trong 25s, biet

duong kinh ciia banh xe bang 80cm Gia toe goe trung binh ciia l i p xe la

A y = 0,125 rad/s2 B y = 0,25 rad/s^

C y = 0,34 rad/s2 D y = 0,65 rad/s^

Gia toe tie'p tuyen:

Huang dart gidi:

Gia toe goe t r u n g binh eiia l i p xe bang gia toe goc t r u n g b i n h ciia banh xe,

nen: y = ^ = a25(rad/s^j Chpn B

Cau 51. M o t banh xe nhan dugc mpt gia toe goc 5 rad/s^ trong 8 giay d u o i tac

d u n g ciia m p t m o m e n ngoai lue va momen lire ma sat Sau do, d o momen

ngoai lue n g i m g tac d y n g , banh xe quay cham dan deu va d u n g lai sau 10

vong quay Gia toe goc va thai gian banh xe d u n g lai ke tir liic ngoai lyc d i m g

Toe dp goc eua banh xe sau 8s la: co = yt = 40 (rad/s)

Goc quay eua banh xe ke t u khi momen ngoai lire thoi tac d u n g :

Cau 52. M o t banh da quay nhanh dan deu quanh true co d j n h v o i gia toe goc

bang 1 rad/s^ Tai thoi diem Os thi banh xe co toe d p goc 3 rad/s H o i den thoi

diem 5s thi banh xe co toe d p goc b^ng bao nhieu? ''^

A 2 rad/s B 4 rad/s C 6 rad/s D 8 rad/s

Huattg dan gidi:

Ap d u n g cong thuc: co = (oo + yt = 3 + 1.5 = 8 (rad/s) => Chpn D

Cau 53. M o t canh quat dang quay v o i toe dp 16 v6ng/s t h i bat dau quay cham

dan deu va d u n g lai sau thoi gian 8 giay Gia toe goe eua canh quat do co dp

Ion bang bao nhieu?

A 2 r a d / s 2 B 47i rad/s^ C 6 rad/s^ D 8 n rad/s^

Huang dan gidi:

Toe d p goe ban dau: coo = 16 v6ng/s = 32TI rad/s

D p Ion gia toe goe ciia banh xe la: y = = 47c rad / s => Chpn B • i>

^9 —

Q^u 54. M p t v|it ran dang quay quanh m p t tryc co'djnh xuyen qua v|t v o l toe

^5 goc 20 rad/s thi bat dau quay cham dan deu va d u n g lai sau 4s Goc ma vat ran quay dupe trong giay cuoi ciing truoc k h i d i m g lai (giay t h u t u tinh t u liic bat dau quay cham dan) la

A 1,25 rad B 2,5 rad C 5 rad D 7,5 rad

Huang dan gidi:

Gia toe goc eua banh xe: y = — = - s f r a d / s^)

At V / Goc ma vat quay dupe den k h i d u n g lai: A(p' = — ^ = 40(rad)

2y ^

Sau 3S ke tir k h i bat dau quay cham dan, toe d p goc cua v$t la:

Wj = ( 0 0+ y t = 2 0 - 5 3 = 5 ( r a d / s ) Goc vat quay dupe sau 3s la: Acp = 5^ - 20^ = 37,5 (rad)

2y - 2 ( - 5 ) Goc vat quay dupe trong giay t h i i 4 la: 40 - 37,5 = 2,5 (rad) => Chpn B

Cau 55. M p t vat ran quay quanh mpt tryc eo d i n h xuyen qua vat v o i p h u o n g trinh toe dp goe: co = 2 + 0,5t, trong do co tinh bang radian/giay (rad/s) va t tinh bang giay (s) Gia to'c goc eua vat ran bang

A 0,25 rad/s2 B 0,5 rad/s^ C 0,75 rad/s^ D 1 rad/s^ y

Huang dan gidi:

So sanh v o i p h u o n g trinh co = coo + yt, ta suy ra y = 0,5 rad/s^ => C h p n B

Cau_56. Trong m p t may A - tiit, hai vat nang nol v o i nhau bang spi day khong

CO dan vat qua m p t rong rpc M p t trong hai vat co khoi l u p n g 200 g, vat kia co khoi lupng 205 g Rong rpc eo true quay nam ngang, khong ma sat, co ban kinh

= 10 cm K h i dupe tha t u nghi, nguoi ta thay qua nang hon roi dupe doan duong s = 1,8 m trong khoang thoi gian t = 6 s Gia toe goe y eua rong rpc bang:

A. 0,5 rad/sl B 1 rad/s^ C 2 rad/sl D 3 rad/s^

Huang dan gidi: (.; / r:

Gia toe ciia vat nang a = ^ = 0,lm/s^

t^

Gia toe goe eua rong rpc y = = Irad / s^

R

Chon B

SlilST, M p t vat ran quay quanh mpt tryc co djnh xuyen qua vat Goe quay c})

•^ua vat ran bien thien theo thoi gian t theo phuong trinh cp = 2 + 2t + t^, trong do

^ tinh bang radian (rad) va t tinh bang giay (s) M p t diem tren vat ran va each

trite quay khoang r = 10cm thi co toe dp dai bang bao nhieu vao thoi diem t = Is?

- » ^ 0 4 m / s , B.50m/s C 0,5 m/s D.40m/s

Huong dan giai:

Theo bai ra, ta c6: y = 2 rad/s^, coo = 2rad/s

Van toe goc: co = cp'(t) = 2 + 2t

K h i t = Is thi van toe goe co d p Icjn: w = coo + yt = 4 (rad/s)

K h i do toe do dai eiia diem do la: v = cọr = 0,4m/s => Chon A

Cau 58 M o t banh xe eo dirang kinh 50 em quay nhanh dan deu, trong 4 giay

van toe goe tang t u 120 vong/phiit len 360 vong/ phut Gia toe h u o n g tam cua

diem M 6 vanh banh xe sau k h i tang toe duoe 2 s la

Ạ 137,8m/s2 B 147,8 m M C 157,8 m/s^ D 167,8 m/s^

Huang dan giai:

Ta co: coo = 47:rad/s va co = 127irad/s

co-Q)o 127t-4n „ , 2

y = ^ = = 27trad / s^

t 4

Sau 2s, van toe goe b3ng: co = coo + yt = 47t + 271.2 = STI rad/s

Gia toe h u o n g tam: a,„ = ^ = o)^ | = {Snf ^ = 157,8m / s^ => Chon C

Cau 59 Mot vat ran quay quanh mot true co d i n h xuyen qua vat Goc quay c|)

eiia vat bien thien theo thoi gian t theo phuong trinh cp = 15 + t + t^, trong do c|)

tinh bang radian (rad) va t tinh bSng giay (s) M o t diem tren vat ran va each

true quay khoang r = 10cm thi gia toe toan phan co dp Ion bang bao nhieu vao

thoi diem t = 1 s?

Ạ0,92m/s2 B l , 8 4 m / s l C 2,68 m/s^ D.4,16m/s2

Huong dan giai:

Theo bai ra, ta co: y = 2 rad/s^ cpo = 1 (rad/s)

Van toe goe: co = (p'(t) = 1 + 2t

Khi t = Is thi (0 = coo + yt = 3 (rad/s) K h i do:

Gia toe h u o n g tam: a,,, =cộr = 0,9|m/s^j

Gia toe tiep tuyen: a, = r.y = 0,2|m / s^

Gia toe toan phan cua diem do la: a = ^â, + a\ 0,92 m / s^ => Chon A

Cau 60 M o t banh xe co d u o n g kinh 4 m quay v6i gia toe goe khong doi

3 rad/s^ Gia toe tiep tuyen eiia diem N tren vanh banh xe b3ng

Ạ I m / s 2 B 3m/s2 C.6m/s2 D 9 m / s 2

Huong dan giai:

Gia toe tiep tuyen a,j = Ry = 2.3 = 6 m / s^ => Chgn C

Cty TNHH MTV DWH Khang Vỉt (^jfU 61 M p t banh da dang quay v o i toe dp 3000 vong/phiit t h i bat dau quay

^J^^^^Tdan deu v o i gia toe goe co dp Ion bSng 20,9 rad/s^ Tinh t u luc b3t dau quay ch^m dan deu, hoi sau khoang thoi gian bao lau thi banh da d i m g 1^1?

Ạ 64s B 90s C 15s D 72 s

Huang dan giai:

Toe dp goc: CO = 3000v6ng/phut = lOOn rad/s / ' r

Thoi gian de banh da d u n g lai: t = — = « 1 5 ( s ) Chon C ' Cau 62 M o t banh xe co d u o n g k i n h 4 m quay v o i gia toe goc khong doi 4 rad/s^ thoi gian ban dau to = 0 la liic banh xe bat dau quaỵ Gia toe h u o n g tam ciia mpt diem N tren vanh banh xe 6 thoi diem t = 2 s bang

Ạ84m/s2 B 128m/s2 C 264 m/s^ D 386 m/s^

Huang dan giai:

Ta co: CO = coo + yt = 0 + 4.2 = 8rad/s Gia toe hu(?ng tam a |,, = — = co — = 8 - = 128m / s => Chon B

R 2 2 Cau 63 Banh da ciia mpt dong co t u liic khoi dong den liic dat toe dp goc 140 rad/s phai mat 2,5s Biet banh da quay nhanh dan deụ Goc quay ciia banh da trong khoang thoi gian tren bang

Ạ 175 rad B 350 rad C 70 rad D 56 rad

Huang dan giai:

Gia toe goc cua banh da: y = — = 5 6 ( r a d / s ^ ) Goc banh da quay duoe

At ^ ' trong thoi gian tren: Acp = ^ = 175(rad I => Chon A

2y ^ ' Caii_64.De do gia toe goc ciia mpt chiéc may mai trong giai doan tang toe, mpt

" g u o i dem so vong ciia no quay dupe trong mpt giaỵ Gia su may quay nhanh dan deu va giay dau tien n g u o i ta thay may quay dupe mpt vong H o i giay t h u hai may quay dupe bao nhieu vong?

Ạ 1 vong B 2 vong C 3 vong D 4 vong

Huang dan giai:

Do COQ = 0 nen goequay cp-cpy = ^ y t ^ '

i

Sóvongquay n = — ^ = — yt^ => so vong quay t i I f v o i t^

271 471 Theo de ra, trong Is quay dupe 1 vong nen trong 2s quay dupe 4 vong

i ~ > So vong quay trong giay t h i i 2 la: 4 - 1= 3 vong => Chpn C

M muat gJAt nhanh tiTTRViU 11 12, tap 1 - Nguyen Quang Lac

Cau 65 M o t banh xe c6 d u o n g kinh 50cm quay nhanh dan deu tir trang thai

d u n g yen, sau 4s thi toe dp goc dat 120 vong/phiit Gia toe h u o n g tarn ciia

diem 6 vanh banh xe sau khi tang toe dugc 2s t u trang thai d u n g yen la

Ạ 157,9 m M B 9,86m/s2 C 25,1 m M D 39,4 m/s^

Huang dan gidi:

Toe do goc: (0 = 120 vong/phiit = 4n rad/s

Gia toe goc ciia banh xe: y = — = 7t(rad / s^) aị

At \' '.v

Toe dp goc dat dxxgc sau 2s la: co = COQ + yt = 27i (rad / s)

Gia toe h u o n g tarn cua diem a vanh banh xe la: a = (ộr = 9,86 (m/s^)

Chpn B

Cau 66 M o t banh xe c6 d u o n g kinh 60 em quay nhanh dan deu, trong 3s van

toe goc tang t u 120 vong/ phut len 300 vong/phiit Gia toe tiep tuyen ciia diem

M tai vanh banh xe la

Ạ 0,157im/s2 B.0,3nm/s2 C 0,67tm/s2 D 0,97tm/s2

Huang dan gidi:

Gia toe goc: y = = = 27trad / s

t 3 Gia toe tiep tuyen: a „ = Ry = 0,3.27t = 0,67tm / s^ => Chpn C

Cau 67 M o t eon lac vat ly c6 khoi lupng m = 1,6kg, momen quan tinh

I = 0,4(kg.m^), dao dpng nho tai nai eo gia tóc trong truang g = m/s^ xung

quanh mpt true quay nam ngang v6i khoang each t u true quay den trong tarn

eiia con lac la d = 25 cm Chu k i dao dpng ciia con lac la:

Cau 68 K h i khoang each t u chat diem den true quay tang len 4 Ian thi momen

quan tinh doi v o i true quay do se

Ạ tang 4 Ian B giam41an C tang 16 Ian D g i a m l 6 1 a n

Huong dan gidi:

Ta eo: I = mr^ K h i n = 4r thi = mr^ - m.(4r)^ = 16mr^ = 161 => Chpn C

Cau 69 M p t con lac vat l i c6 momen quan tinh dói voi true quay la 3 kgm^, eo

khoang each t u trpng tam den true quay la 0,2 m, dao dpng tai noi eo gia toe

roi t u do g = 71^ (m/s^) v o i ehu k i rieng la 2,0 s Khoi l u p n g cua eon lac la:

Ạ 10 k g B 15 k g C 2 0 k g D 12,5 kg

=> m = f2n^ _L^-i5(kg) = > C h 9 n B gd

^ m g d V W 6 "

Cau 70 H a i qua cau con lac dac lam ciing hang mpt loai thep, dong chat eo ban

kinh gap 3 Ian rihau RA = 3RB thue lien h§ giiia momen quan tinh cua qua cau dói v o i true quay d i qua tam ciia m o i qua cau la

A - ro runff ehieu cao, duoc lam bang cung mpt

,Z quay erung vai tt„c dac cua mSi hinh r^) cua hai h,.h m nay la

Huong dan giat:

M o m e n quan tinh cua cac h i n h tru Ian lupt la:

Ạ3,0kg.m2 B.3,75kg.m2 C 7,5 kg.m^ D 2,25 kg.m^

Huong dan gidi: , ,

Theo d j n h ly true song song, ta c6:

= 3^ = 81 => Chpn D

37

I = Ic +md2 =^mR2 +mR2 = | m R 2 = 2,25(kg.m^)

=>ChQnD

Cau 73.Tai each dinh A, B, C, D cua mpt hinh vuong canh a = 80cm c6 g3n Ian

luot cac chat diem m j , m2,1113, m4 voi m j = m 3 = 1kg, m 2 = m 4 = 2kg

Momen quan tinh cua h^ 4 chat diem doi vai true quay qua M (trung diem ciia

DC) va vuong goc vai hinh vuong c6 gia trj nao sau day?

Cau 74 Mot qua cau dac, dong chat, khoi luang M , ban kinh R Momen quan

tinh ciia qua cau doi voi true quay each tarn qua cau mpt doan — la

Cau 75 He CO hpc gom mot thanh AB c6 chieu dai I, khoi luong khong dang ke,

dau A ciia thanh duac gan chat diem c6 khoi lugng m va dau B ciia thanh

du(?c gan voi chat diem c6 khoi lug-ng 3m Momen quan tinh ciia h^ doi voi

tryc quay vuong goc voi AB va di qua trung diem ciia thanh la

A 4 m R B 3ml2 C 2 mP D 1 mP

Huang dan gidi: ^

Ta chpn D vi I = I , + = („,^R2 ^ ^^R2 J ^ ^

2) = I m p => Chgn D

Cau 76 Mot thanh manh c6 khoi lugng m = 2 kg, chieu dai 3 m Doi voi true

quay di qua khoi tam va vuong goc vai thanh, momen quan tinh ciia thanh

0aTL^^^^ duong kinh ciia mot vanh banh xe dap la 800 mm, khoi lugng ciia

vanh la 600 g Momen quan tinh ciia chie'c vanh banh xe d^p doi vol true ciia banh xe la t A.0,016kgm2 B 0,037 kgm2 C 0,053 kgm^ D 0,096 kgm^

Huong dan gidi:

TaehgnBvi I = mR^ = 0,6.0,4^ =0,096kgm2 Chon D

C5uJZ8.Mot hinh cau dac khoi lugng m = 5kg, ban kinh R = 0,2m Momen quan

tinh ciia no doi voi true quay di qua tam la

A.0,02kg.m2 B.0,4kg.m2 C 0,06kg.m2 D 0,08kg.m2 '*

Huong dan gidi:

Ap dung cong thiie tinh momen quan tinh ciia vat hinh cau d|ie:

~I = |mR2 =0,08kg.m2 Chon D Cau 79 Mot dia tron dong chat c6 khoi lugng 2kg Momen quan tinh ciia dTa doi voi true quay di qua tam dia I = Ikg.m^ Ban kinh ciia dia la

quay mot doan r theo phuong tiep tuyen voi quy dao chuyen dong ciia diem

N Momen luc tac dung vao vat c6 gia trj 200N.m Khoang each r bang

Huang dan gidi:

M

Ap dung cong thiie M = F.d = F.r => r = — = 2m => Chon C

£iu8X Mot momen luc M = 60 N.m tac dung vao mot banh da eo momen quan t'nh ciia no voi true quay di qua tam la 12kg.m^ Ban dau banh da diing yen, sau khi tac dung momen luc banh da chuyen dong quay quanh true quay eo

^linh di qua tam Sau 15s ke tu khi ehiu momen lye tac dyng, toe dg goe eiia

•^anh da la? I

A 75rad/s B 50 rad/s C 25 rad/s D 150rad/s

Huang dan gidi: ^

Ap dung phuong trinh dong luc hoc vat ran:

M = Iy=>7 = — = — = 5rad / s'^ I

Ma (0 = COQ + yt = 0 + 5.15 = 75rad / s => Chon A ^

Cau 82 Vat rSn quay duoi tac dyng ciia mot luc Ne'u do Ion luc tang 8 laVi

khoang each tu tryc quay den gia cua lye giam 4 Ian thi momen lye

A giam 4 Ian B tang 2 Ian C tang 8 Ian D giam 2 Ian ^

• Huang dan gidi:

Mo men luc: M = F.d

Ne'u do Ion lye tang 6 Ian, khoang each tu true quay den gia cua lye giam 3

Ian thi momen luc se la: M ' = F'.d' - 8F.- = 2F.d = 2M => Chon B

4 Cau 83 Mgt khoi try dac, dong chat, nam ngang, ban kinh R, khoi lugng M, e6

the quay t y do xung quanh true cua no Mpt sgi day qua'n quanh kho'i try vn

M dau ty do ciia day c6 gan mgt vat nho khoi lugng m = — Gia toe ciia vat nho

la (ggi g la gia toe trgng truong)

thai nghi, banh da dat den van toe 480v6ng/phut trong 8s Momen lye tac dyng

Cau 85 Duoi tac dung cua mo men lye c6 do Ion M = 960N.m thi mgt dla mong,

phang, dong chat c6 ban kinh 2m c6 the quay duge xung quanh mgt true di qua

tam va vuong goe voi gia toe 3 rad/s^ Khoi lugng eiia dTa la:

thi chiu tac dyng ciia mgt momen can c6 do Ion bang 12 N.m Bie't momen quan tinh ciia vat ran doi vol true quay la 8 kg.m^ Sau 6s ke tu khi bat dau quay cham dan deu, vat dat toe do goc la

A 8 rad/s B 16 rad/s C 32 rad/s

Huang dan gidi:

D 48 rad/s

Ta c6: y = M = - | = -l,5(rad/s)

o^coo+yt = 25-1,5.6 = 16(rad/s)

=>ChgnB Cau 87 Mgt dTa mong, dong chat quay quanh mgt tryc di qua tam va vuong goc voi mat phSng dTa Tac dung mgt momen lyc 720N.m khong doi khi do dTa chuyen dgng quay voi gia toe goc 4 rad/s^ Momen quan tinh ciia dTa la

A 120kg.m2 B 140kg.m2 C 180 kg.m^ D 360 kg.m^

Huang dan gidi:

• Chgn C Cau 88 Mot dTa tron dac quay quanh true doi xung di qua tam va vuong goc voi mat dTa duoi tac dyng ciia momen lyc khong doi 6 Nm Sau 3s ke tu liic bat dau quay, toe do goe ciia dTa la 36 rad/s Momen quan tinh ciia dTa la

thanh CO g i n hai cha't diem c6 khoi lugng Ian lugt bang m va 2m Toe do dai

ciia hai chat diem co khol luang m la v Momen dong lugng ciia thanh va

hai chat diem doi voi tryc quay co bieu thuc

A — B C —— D 3mlv

3 v V V

Huang dart gidi:

Momen quan tinh cua thanh co hai chat diem m , va m j la:

I = m j l ^ + m 2 l ^ = 3 m l ^ _^ „

:.^|-Momen dong lugng ciia he (thanh va hai chat diem) la:

M = Ira = 31^(0 = 3 m P y = 3mlV => Chgn D Cau 90.Mot vat hinh cau dac dong chat co ban kinh R = I m va momen quan

tinh doi voi true quay co djnh di qua tam hinh cau la 6kgm^ Vat bat dau quay

khi chju tac dung ciia mpt momen lyc 60 N.m doi voi tryc quay Bo qua moi

luc can Tinh thoi gian de tu khi chju tac dung ciia momen luc den liic toe do

goc dat gia tri bang 100 rad/s va khoi lugng ciia vat?

A t = 10s;m = 15kg B t = 15s; m = 20 kg

C t = 25s; m = 30 kg D t = 3 5 s ; m = 40kg

S Huang dan gidi:

f Theo phuong trinh dong luc ciia vat ran quay quanh mpt true:

Cau 91 Mot vat ran co momen quan tinh I = 3,14kg.m2 dang quay deu voi toe

dg gck (OQ = 1 v6ng/s thi chju tac dung ciia momen luc can M DTa quay dugc

10 vong thi dung lai Lay TI^ = 10 Dg Icjn ciia momen lyc can bMng bao nhieu?

A I N m B 21 N.m C 12 N.m D 3 N m

Huang dan gidi:

Goc quay ciia vat ran tu khi chju momen luc can tac dung den khi dimg lai

(^2u 92 Mgt vanh tron khol iugng m, ban kinh R quay cham dan deu quanh true

2^'t^dung ciia momen lyc can Cu sau khoang thoi gian T thi goc quay giam deu A'P- ^9 '^"^ momen lye can dugc xae djnh bSng bieu thiie nao sau day?

mR^Am „ mRAcp „ mR^A(p r^ "\RA(p

Huang dan gidi:

Tga dg goc ciia vat ran dugc xae djnh: (p = (P(,+a)Qt + —yt^

Goc quay dugc sau 2T(S): tp = 2a)oT + —y4t^

Suy ra goe quay dugc trong t (s) thu ba la: Aipj = 93 - (P2 = + ^yt^

Ta thay, chuyen dong ciia vat ran la cham dan deu nen gia toe goc y co gia trj am, sau nhiing khoang thoi gian T, goc quay ciia vat ran giam deu mgt lugng:

A(p = A(p| - A(P2 = A(p2 - A(p3 = = - y t => y = — ^

Ap dung phuong trinh dgng lyc hgc vat ran:

M = Iy = - I ^ = - i ^

2,

Suy ra dg Ion ciia momen can: M = ^ => Chgn C

£au 93 Dugi tac dung eiia momen ngoai lyc M ciia luc F, mgt banh xe bat dau

quay nhanh dan deu, sau 4 giay quay dugc 16 vong Sau do khong tac dung

"lomen M nua thi no quay cham dan deu voi gia toe goc 1 rad/s^ duoi tac dung

Ciia momen lye ma sat eo dg Ion 0,8 Nm Mgmen nggai lyc co dg Ign la

A 1,6 N.m B 2,4N.m

C 0,8(1 + 47T) N.m D 3,27i N.m ; :

Huang dan gidi:

-.^ Khi C O tac dyng ciia momen M : M - M ^ = ly

mm

CtyTNHHMTVDW H KhangVift V§t quay dvtac 16 vong trong 4 giay: cp = ^7*^ = 16.27t = 32n

Suy ra: y = 4n rad/s^

Khi khong c6 tac d u n g ciia momen M thi chi con tac d y n g cua momen lij^

ma sat: M ^ ^ = l y ' = > I = 0,8kg.m^

T u d o ta c6: M = 0,8(1 + 47r)N.m => Chon C

Cau 94 M o t vat ran c6 the quay quanh m o t true co djnh d i qua trpng tam Vat

ran bat dau quay khi chju tac dung ciia m o t luc khong d o i F = 2,4 N tai moj

diem M each true quay mpt doan d = 10 cm va tiep tuyen v a i q u y dao chuyeti

dong cua M Sau khi quay dugc 5 s thi toe do goe cua vat ran dat gia trj bang

30 rad/s Bo qua m o i luc can Chon moc thoi gian t = 0 la liie vat ran bat dau

quay, toa do goc ban dau ciia vat ran bang 0 va chieu d u o n g la chieu quay eua

vat ran Gia su tai thoi diem ti = 10s vat ran khong chju tac d u n g ciia luc F,

Tinh toa dp goc tai thoi diem t2 = 20s?

A (p = 300 rad B (p = 500rad C (p = 900rad D (p = 800rad

Huong dan gidi:

l a CO co = a)o+Yt=:0 + Y t = > y = — = — = b r a d / s

t 5 Mat khac momen lye tac d u n g len vgt r i n duoc xac d j n h : ,,

Cia 95-M9t ^'^ ^^'^^ k e n h u hinh ve: m^ = 1kg; m 2 = 2kg; khoi luong

^^^ng roc m = 4kg; lay g - lOm/s^ Soi day noi hai vat khong dan va khong

M = F.d = I.y =^ I = F.d 2,4.0,1 = 0,04kg.m'

Tai thoi diem t , = 10s, vat ran khong chju tac d u n g cua lue F nen M = 0, suy

ra I.y = 0 => y = 0 Vay vat ran ehuyen dong quay deu v6i toe do goc bang:

A p d u n g eong thuc: co = (0(, + yt = 0 + 6.10 = 60rad / s

De tinh tpa d p goc tai thoi diem t2 = 20s, ta tinh goc quay cpj cua v$t ran

trong qua trinh vat ran quay quanh nhanh dan deu trong khoang thai gian

t, = 10s va goc quay (p2 cua vat ran trong qua trinh vat ran ehuyen dpng qua\

deu trong khoang thai gian t2 - t j = 20 - 1 0 = 10s

Tpa dp goe cua vat tin tai thoi diem t j = 20s

Huang dan gidi:

Chpn chieu d u o n g la chieu ehuyen dpng ciia cae vat

T i ; T2 la luc cang spi day tac dung len vat m j va m j

A p d u n g d j n h luat I I N e w t o n cho ehuyen dpng quay cua rong rpc:

M = ly « ( T 2 - T,) R = 1 mR^y « (T2 - T,) = i mRy (3)

Vi spi day khong dan nen ai = a2 = a

Sg^i day khong truat tren rong rpc nen y = —

Thay vao (1); (2); (3) ta co:

Sau.96.Mpt lue tiep tuyen eo dp Ion 4 N tac d y n g vao vanh ngoai cua m p t banh

^6 CO d u o n g kinh 80em dang quay deu Trong giay cuoi cung truoc khi toe dp cua banh xe bang khong, mpt diem tren mep ngoai cua banh xe d i dupe

|uang d u o n g bang m p t phan t u ehu v i banh xe M o m e n quan tinh ciia banh xe

^ ^ v 6 i trye quay la

A gan b a n g 0,24 kg.m^

C gan bang 0,51 kg.m^

B gan bang 0,43 kg.m^

D gan bang 0,89 kg.m^

Huang dan giai:

T r o n g g i a y c u o i c i i n g t r u d c k h i d u n g quay, goc banh xe q u a y d u g c (p = ^

A p d u n g cong t h u c cp = o)(,t + ^ y t ^ va w = (OQ + yt ta d u g c y = 7t rad/s^

d u n g yen, sau d o tha nhe cho he c h u y e n

d o n g t h i gia toe ciia m o i vat la 9,2m/s^

Sgi day nh? va k h o n g t r u g t tren r o n g

rpc C h o rang sue can tac d u n g len he

chi la luc ma sat t r u g t ciia mat ban len

m , Lay g = lOm/s^ H e so ma sat t r u g t

Huang dan giai:

C h g n chieu d u o n g la ehieu chuyen d o n g ciia cac vat

V i sgi day k h o n g d a n nen 3 ^ = 3 2 = a

Thay vao (1), (2) va (3) r o i g i s i h? p h u o n g t r i n h ta d u g c h# so m a sat g i u a

va ban:

„ = f i M = M = o,08 = ^ C h g n D

^ m , g 10 Cau 98 M o t b a n h xe c h j u tac d u n g ciia m o t m o m e n l u c M i k h o n g d o i T o n g ciia m o m e n M i va m o m e n l u c ma sat co gia t r j bSng 24 N m T r o n g 5s d a u , toe

dp goc ciia banh xe bie'n d o i t u 0 rad/s den 10 rad/s Sau d o m o m e n M i n g u n g

tac d u n g , banh xe q u ay cham d a n va d u n g hlin lai sau 50s Gia s u m o m e n luc

ma sat la k h o n g d o i suot t h o i gian banh xe quay M o m e n l u c M i co gia trj

A M l = 11,3 N m B M l =26,4 N m

C. M l = 33,4 N m D M i = 48,6 N m •

-Huong dan giai:

Ban d a u : M = M , + M ^ ^ = 2 4 ( N m )

Toic d g goc ciia b a n h xe liic co M i : (o = a)(, + yt ^ y = 2r ad / s^ '

M o m e n q u a n t i n h ciia banh xe: I = — ~~2~ ^ ^ ^ k g m ^ j

K h i M l t h o i tac d u n g : w ' = w + y't = 0 - > y ' = - 0 , 2 r a d / s^ ^

Suy ra: M ^ ^ = y ' l = - 0 , 2 1 2 = - 2 , 4 ( N m ) Vay M , = M - M , ^ ^ = 2 6 , 4 ( N m ) C h g n B » " ' Cau 99 M o t dla dac d o n g chat, khoi l u g n g 0,4kg, ban k i n h 20cm, co true q u a y

A d i qua tarn dia va v u o n g goc v o i dTa, da n g d u n g yen Tac d u n g vao dla m o t

momen luc k h o n g d o i 0,16 N m T i n h q u a n g d u o n g ma m g t d i e m tren v a n h dla d i d u g c sau 5s ke t u liic tac d u n g m o m e n luc

A 25m B 50m C 75m D 100m

Huang dan giai:

M o m e n q u a n t i n h ciia dTa: I = ^-mR^ = 8.10"-^ | k g m ^ j ;

Gia to'c goc ciia dTa: y = ^ = 20rad / s^ f / ,

Goc r o n g rge q uay d u g c : cp = i y t ^ = 2 5 0 ( r a d ) , j

Q u a n g d u o n g m a m g t d i e m tren v a n h dTa d i d u g c sau 4s la:

s = R(p = 0,2.250 = 5 0 { m ) C h g n B

Ki thuatgidi nhanh BTTN V^t Li 12, tap 1 - Nguyen Quang L^c

Cau 100. Mot banh da dang quay deu voi toe dp goc 250 rad/s Tac dung nriQt

momen luc ham khong doi 75 N.m vao banh da thi no quay cham dan deu va

dung lai sau 10s Momen quan tinh cua banh da do'i voi true quay c6 gia tri

A 3kg.m2 B 4kg.m^ C 6 kg.m^ D 8 kg.m^

Huang dan gidi:

Ta eo: 7 = — = -25(rad / s^) => I = — = — = Sf kg.m^) ^ Chon A

t \ y -25 ^

Cau 101. Mpt vat c6 momen quan tinh dol voi mot true quay la Skgm^

quay xung quanh true nay voi toe do goc bien doi theo thoi gian voi quy luat

(0 = 3 + 5t(rad/s) Momen lue tac dung vao vat bang

A 5 N m B lONm C 15 Nm D 20 N m !•

• Huang dan gidi:

Theo dau bai ta c6 (o = 3 + 5t => y = 5rad/s^

Ap dung phuong trinh dong luc hoe vat ran: M = ly = 3.5 = 15 N m

=> Chon C

Cau 102. Mot vanh tron dong chat, khoi luong m = 3kg, ban kinh R = 0,6m,

true quay qua tam va vuong goc voi mat phang vanh Ban dau vanh dung yen

thi chju tac dyng boi mot luc F tie'p xiic voi mep ngoai vanh Bo qua mpi ma

sat Sau 4s vanh tron quay duoc mpt goe 48 rad Dp Ion cua luc F la

A 2,4N B.4,9N C 7,6N D 10,8N i

0 Huong dan gidi:

Taco: (p = ^yt^ = 4 8 ( r a d ) ^ y = 6rad/s^ I = m.R^ =l,08(kg.m^) ],

Momen li/c: M = F.R = ly = 1,08.6 = 6,48 (N.m)

Dp Ion ciia luc F la: F = — = 10,8(N) ^ Chpn D '

^ R

Cau 103. Mpt thanh chan duong c6 chieu dai 7,8 m, trpng luang 210 N, trpng

tam G cua thanh each dau ben trai 1,2 m Thanh eo the quay quanh mpt true

nam ngang each dau ben trai 1,5 m De giii thanh nam ngang, can phai tac

dung vao dau ben phai cua thanh mpt luc F la:

<i A F = 10N B F = 15N C F = 20 N D F = 2 5 N

Huang dan gidi:

Ta C O M,, = Mp Pd,, = Fdp hay 210 0,3 = F 6,3 => F = ION

Chpn A

Cau 104. Mpt tarn van nang 240 N dupe bac qua mpt con muong Trpng tam

ciia tarn van each diem tua A 2,4 m va each diem ti^a B 1,2 m Hoi \\fc ma tam

van tac dung len diem tua A la bao nhieu ?

A 2 0 N B.40N C 60 N D 80 N

Huang dan gidi:

Coi diem B la tam quay tam thoi Vi van can bang nen momen trpng lye can bang voi momen ciia lye nang ciia bo muong tai A nen Mp = Mp

=> P.1,2 = F(l,2 + 3,6) F = SON => Chpn D

Theo dinh luat III Niu ton, lye ma tain van tac dyng len diem tua A la SON

cau 105. Mpt thanh dong chat tiet di?n deu, trpng lupng P = 100 N , dai

L = 2,4m Thanh dupe do nam ngang len hai diem tya A va B A nam 6 ben trai, B each dau ben trai 1,6 m Ap lye eua thanh len dau ben trai la

A 1 5 N B.25N C 35 N.q D 45 N

Huang dan gidi: ' C

Trpng tam nSm each diem tya B mpt khoang 1,6 - 1,2 = 0,4 m

Coi B la tam quay tam thoi, ta eo Mp = Mp P.0,4 = F.1,6 =^ F = 25N

=> Luc ma tarn van tac dung len diem tya A la 25N => Chpn B

Cau 106. Mpt thanh OA dong chat, tiet dien deu, c6 khoi lupng 1,6 kg Thanh

CO the quay quanh mpt true eo'djnh theo phuong nam ngang di qua diem O va

vuong goc vdi thanh Dau A cua thanh dupe treo bang spi day c6 khoi lupng khong dang ke Bo qua ma sat d true quay, lay g = 10 m/sl Khi thanh d trang thai can bang theo phuong nam ngang thi day treo thang dung, vay lyc can bang cua day la

£iu 108 Tac dung mpt momen luc M = 0,48 N m len mpt chat diem lam chat

•liem ehuyen dong tren mpt dudng tron vdi gia toe goc khong doi y = 2,4rad/s2

B'et ban kinh dudng tron la 50 cm Khoi lupng ciia cha't diem la

A m = 0,23 kg B m = 0,56 kg

C m = 0,7 kg D m = 0,Skg

Huang dan giai:

Ta co: I = — = — — = 0,2ke.m

y 2,4 ' ^

Matkhac I = mR^ =i>m = ^ = 0,8kg => Chon D

Cau 109 Mot dla mong, phang, dong chat c6 the quay dugc xung quanh mot

true di qua tam va vuong goc voi mat phang dia Tac dung vao dla mot

momen lyc 760 N m khong doi, dia chuyen dong quay quanh true voi gia toc

goe 4 rad/s^ Momen quan tinh ciia dia doi voi true quay do la

A I = 170 kg.m2 B I = 190 kg.m^

C I = 230 kg.m2 D 1 = 380 kg.m2

Huang dan gidi:

Tu phuong trinh eo ban cua chuyen dong quay M = ly

=>I = M = Z60^190kg.m2 ^ C h o n B

Cau 110 Mot dla mong, dong chat, ban kinh 2,5m eo the quay dugc xung

quanh mgt true di qua tam va vuong goc voi mat phang dla Tac dung vao dia

mot momen lire 640 Nm khong doi, dia chuyen dong quay quanh true voi gia

toe goc 4 rad/s^ Khoi lugng cua dia la

Cau 111 Mgt rong rgc eo ban kinh 15 em va momen quan tinh doi voi tryc

quay la I = 0,03kgm^ Ban dau rong rgc dang dung yen, tac dung vao rong rgc

mgt luc khong doi F = 4N tiep tuyen voi vanh ngoai cua no Gia toe goc cua

rong rgc bang

A.8rad/s2 B 12 rad/sl C 20 rad/s^ D 38 rad/s^

Huang dan gidi:

ria 112 Mgt rong rgc co ban kinh 20 cm va momen quan tinh doi voi tryc

yay la I = 0,02 kgm^ Ban dau rong rgc dang dung yen, tac dung vao rong rgc

ffiQt lu^<^ khong doi F = I N tiep tuyen voi vanh ngoai eiia no Sau khi vat ch}u

taC dyng 'yc dugc 4s thi van toe goc cua no la

A 10 rad/s B 20 rad/s C 40 rad/s D 60 rad/s

Huang dan gidi: • t V' — < T

Co M = F R = 1.0,2 = a2N.m v>

M 0,2 i „ , 2

=:> Sau 4s, van toe goc bang co = co„ + yt = 0 +10.4 = 40rad / s => Chgn C

r^u 113 Duong kinh v6 lang ciia mgt chie'e oto la d = 40 cm De xoay dugc v6

lang voi momen luc can la 10 Nm Phai tac dung mgt ngau luc co do Ion eiia tnoi luc tol thieu bang

A ION B 15N C 25N D 30 N

Huang dan gidi:

Muon xoay dugc v6 lang, can phai tac dung mgt momen ngau luc Ian han Momen luc can:

Mp > M^ ^ F.d > M^ => F > 25N -> F^j^ = 25N => Chgn C Cau 114 Mgt vat ran phang mong dang mgt tam giae deu ABC, canh a = 20cm

Nguoi ta tac dung vao mgt ngau luc nam trong mat phang ciia tam giae, cae

lire CO do Ian 8,0 N , dugc dat vao hai dinh A va C, song song voi canh BC

Momen cua ngau lye la

A l,28Nm B l,38Nm C.4,48Nm D.5,58Nm

Huang dan gidi:

Khoang each giira hai luc d = = 0,173m

Mo men eiia ngau luc la: M = F.d = 8 0,173 = 1,38 Nm => Chgn B

SaiLllS Momen ngau luc M = F.d = 8.0,173 = 1,38m Mgt luc tiep tuyen I N tac

dung vao vanh ngoai ciia mgt banh xe co duang kinh 0,5 m Banh xe bat dau quay den thai diem 5 s thi quay dugc vong dau tien Momen quan tinh ciia

^anhxela

A 0,24 kg.m^ B 1 kg.m^ C 0,27 kg.m^ D 1,08 kg.m^

Huong dan gidi: ' • *

Ap dung phuong trinh dong luc hgc vat ran: " •

M = F.R = I y ^ y = ^ (1)

51

Chpn moc thai gian t = 0 tai thoi diem vat ran bat dau quay, tga dp goc baj^

dau <PQ = 0 Chieu d u o n g la chieu quay ciia vat ran

Cty TNHH MTV DWH Khang Vift

A p d u n g cong thuc: (p = (PQ + " o t + ^ y t ^ = ^ y t ^ (2)

Thay (1) vao (2) ta d u o c cp = 1—t^ => I = 1.— 1 2 = i k g m ^ ^ C h p n B

2 1 2 (p Cau 116 M o t vanh tron d o n g chat, khoi l u p n g m = 1 kg, ban ki'nh R = I m , trii(

quay qua tam va v u o n g goc v o l mat phang vanh Ban dau vanh dang diing

yen thi chju tac d u n g boi mot luc F tie'p tuyen v o l mep ngoai vanh Bo qua moi

ma sat Sau 3s vanh tron quay dupe mot goc 72 rad D p Ion ciia luc F la

Chpn moc thoi gian t = 0 tai thoi diem vat ran bat dau quay, tpa dp goc ban

dau (P() = 0 Chpn chieu d u o n g la chieu ^uay cua vat rari

1 2 1 2

(p = (P(j+(0(,t + - y i t =-yjt

2 2 a

A p d u n g cong thuc: (p = (p(, +co^,t + ^ y t ^ = ^ y t ' (2)

Thay (1) vao (2) ta duoc: if, = l,^,t^ =

2 mR 2

mR9 t^ = 8 N ==> Chpn B Cau 117 D u o i tac d u n g cua momen luc, m p t banh xe b5t dau quay nhanh dan

80 deu, sau 8s quay dupe — vong Sau do khong tac d u n g m o m e n luc nua t h i no

T:

quay cham dan deu v o i gia toe goc 2rad/s2 d u a l tac d y n g cua m o m e n Ivrc mn

sat CO dp ion 0,2 N m M o m e n luc eo dp Ion la

A 0,7 N.m B 0,6 N.m C 0,4 N m D 0,3 N m

Huang dan gidi:

C h p n mpc t h o i gian t = 0 tai thoi diem vat ran bat dau quay, tpa d p goc ban

dau cp„ = 0 Chpn chieu d u o n g la chieu quay ciia vat ran

Qua t r i n h dau banh xe chju hai momen luc tac d u n g la m o m e n luc M va

momen can cua luc ma sat M^^ gay ra gia toe goc y, cho vat

A p d u n g p h u o n g trinh dpng luc hpc vat ran: M-M^^^^ = ly^ (1)

A p d u n g cong thuc:

52

2(p 2.27t.n,

>yi=-r-t " t " 8 ' = 5rad / s^ (2) Qua t r i n h sau banh xe chiu m o m e n can cua lye ma sat M ^ g gay ra gia toe y2 cho vat A p d u n g p h u o n g trinh dpng luc hpc vat rMn: - M ^ g = ^^2

M = 0,24 N m Sau k h i quay dupe 5s t h i toe dp goc cua vat ran dat gia trj bang

30 rad/s Bo qua m p i luc can T i n h m o m e n quan tinh ciia vat ran d o i v o l true

A I = 0,04kgm^

C I = 0 , 0 6 k§m2

B I = 0,05kg.m2

D I = 0,07kgm2

Huang dan gidi:

Ta eo: w = COQ + yt => to = 0 + yt co = (OQ + yt

£a!Lll2 M p t banh da c6 m o m e n quan t i n h 15 (kg.m^) quay deu (quanh true eo

^inh) v o i toe d p 3600 vong/phiit M o m e n d p n g l u p n g ciia banh da d o i v d i true

quay CO d p Ion bang:

CSu 120 Mot banh xe dang quay quanh tryc ciia no voi momen dpng Iv-gix^

2 kgmVs thi chju tac dung cua mot momen luc can 8 Nm Thai gian de dT^

dung lai bang

A 0,25 s , B.0,4s C 0,6 s D 0,35 s

Huang dan gidi: " '

Khi dia chju momen can tac dung se chuyen dong cham dan deu va dung

Cau 121 Mot vat ran c6 momen quan tinh 2kg.m2 quay deu 10 vong trong 2s

Momen dpng luong ciia vat rSn c6 dp Ion bang

> A 3,141kg.m2 /s B 62,8kg.m2 /s

^^^^ C 314,lkg.m^/s D 628,23kg.m^/s

Huang dan gidi:

Ap dyng cong thuc L = Iw = 2 i ^ ^ = 62,8kgm^ / s => Chon B

Cau 122 Coi Trai Dat la qua cau dong chat c6 ban kinh R = 6400 km, khoi

lupng M = 6.102" kg Momen dpng lug-ng cua Trai Dat la

A 7,14.1033kgm2/s B 5,14.10^^ kgm^/s

_ C 3,14.1033kgm2/s D I,14.10^3kgm2/s

Huong dan gidi:

Momen quan tinh cua Trai Dat la: I = -MR'^

5 Toe dp goc ciia Trai Dat la: co = ^ , T chu ki quay ciia Trai Dat, T = 24gia

Momen dong lupng ciia Trai Dat la:

2

5

(;3u 123 Mpt nguai c6 khoi lugng m = 60 kg dung 6 mep san quay hinh tron,

duong kinh 2m, c6 khoi lugng M = 120 kg Bo qua ma sat 6 true quay Luc dau

jie dung yen Nguai bat dau chuyen dgng vai van to'c 6 m/s (so vai dat) theo

phuang nam ngang va tiep tuyen voi mep san Chon chieu duong theo chieu chuyen dgng ciia nguai Van toe goc ciia san khi do la:

A. (0 = - 0,75 rad/s B to =-1,5 rad/s. j A f / s

C 0) = - 3 rad/s D to = 6 rad/s

Huang dan gidi:

Van toe goc ciia nguoi so vai dat: co^ = ^ = ^ = 3(rad / s) Momen quan tinh ciia nguai va san so vai tryc quay Ian lugt la:

14 rad/s theo chieu duong Dla thu hai c6 momen quan tinh 6 kg.m^ dang quay theo chieu am vai toe do goc 2 rad/s Tha nhe dla thu hai xuo'ng dla thu nhat, mot thoi gian rat ngan sau do hai dla dinh vao nhau va eimg quay Ket luan nao sau day ve chuyen dgng ciia hf la diing

A He quay voi toe do goc 3 rad/s theo chieu am

B H ^ quay voi toe do goc 4 rad/s theo chieu duong

C He quay vai toe do goc 2 rad/s theo chieu duong '

D Dgng nang quay ciia he khong doi

Huang dan gidi:

Dinh luat bao toan momen dgng lugng:

/ l T \ T

(I, + I j )(0 = IjCOj + 120)2 ~* ^ = I1+I2

Trong do: I1 = 2 kg.m^; I2 = 6kg.m2; coi = 14 rad/s; 0)2 = -2rad/s

2.14 + 6.{-2) Thay so', ta duge: co =

2 + 6 - = 2>0 rad/s => Chgn C

Cau 125 M p t banh da c6 momen quan h'nh doi v o i nxQt tryc quay I = Skg.m^

Do tac d y n g cua momen lye, momen dpng lugfng cua banh da giam deu tit

12 kg.m^/s den 6 kg.mVs trong khoang thoi gian A t = Is M o m e n lyc tac d y n g

va gia toe goc d o i v o i true quay cua banh da la:

A - 6 N m va Zrad/s^ B 6N.m va 2rad/s2

C - 6 N m va - Zrad/s^ D 6N.m va - 2rad/s2

Huang dan gidi:

Chpn chieu dtrang la chieu quay cua banh da: L = Ico

=> coj = ^ = 4rad / s; (1)2 = ^ = 2rad / s

^ y = f V l ^ ^ _2rad / ^ M = ly = - 6 N m =^ Chpn C

At

Cau 126 M o t nguoi c6 kho'i lup-ng m = 50kg d u n g 6 mep mpt san quay hinh

tron, d u o n g k i n h 8m dang quay deu v o i toe dp goc 0,2 rad/s M o m e n quan tinh

cua san doi v o i tryc quay la lOOOkg.m^ Bo qua sue can tac d u n g len h? Liic

t = 0, nguoi do bat dau d i deu ve tarn san v o i toe do khong doi v = Im/s so v a i

san Toe dp cua nguoi do liic t = 2s, so v o i mat dat la

A gan bang 3,76m/s B gan bang 1,16 m/s

C gan bang 6,23m/s D gan bang 7,52 m/s

Huang dan gidi:

^ M o m e n dpng l u p n g cua he ban dau:

LQ = ( i j + 12)0)0 = Ij + mr^ JG)Q = 360khm^ / s Sau 2s n g u o i do se each tam san doan a = 2m

M o m e n dong lugng cua h§ liic nguoi each san a = 2m: L = ^Ij + ma^ jco

M o m e n ngoai lye tac d u n g vao h ^ bang 0 nen momen dong lugng doi v o i

tryc quay bao toan: | l j + ma^ jco = 360

co = — ^ = ?^2_,- = 0,3rad/s

I j + m a ^ 1000 + 50.2^

Van toe ciia nguoi so v o i dat:

V o = V v 2 + c o V =Jl^+(0,3.2)^ « 1 , 1 6 m / s = > C h Q n B

Cau 127 M o t thanh cung manh chieu dai AB = 3m c6 kho^i l u p n g khong dang

ke quay deu xung quanh mpt tryc vuong goc v o i thanh va d i qua diem O eiia

^|hanh voi toe dp goc khong doi to = lOrad/s H a i qua cau kich thude nho c6

Cty TNHH MTV DWH Khang Vift

\i \\6i lu'9'"8 b3ng nhau m^ = 2kg, m j = 4kg dupe gSn vao hai dau thanh Biet

tuong ling la V j = 5m/s va V 2 = 10 m/s M o m e n dpng lupng

ciia h? ^^^^ 1"^y

A lOOkgmVs B 120kgmVs C.140kgmVs D ISOkgmVs

Huang dan gidi:

iChi thanh quay thi toe dp goc ciia 2 qua cau la n h u nhau: li, h la khoang

each t u m i , m2 toi diem O: ^

v, V , 5 10 , „,

a)i=co2=^-L = - r ^ ^ p = -r-=>l2=21i (D

Do // + /2 = AB = 3m (2) ' Z - ^ ' Tu'(1) va (2), suy r a : / i = Im;/2 = 2m

Momen dpng l u p n g ciia h$ doi voi true quay la:

L = ( l i + l 2 ) w = (mi^2 + m2l2)» = (2 + 16).10 = 180kg.m2/s =^ Chpn D Cau 128 M p t thanh n h ^ dai 2 m quay deu trong mat phang ngang xung quanh

tryc thang d u n g d i qua trung diem ciia thanh Hai dau thanh eo hai chat diem

CO khoi l u p n g 2,4 k g va 3,6 kg Van toe ciia m o i chat diem la 6 m/s M o m e n

dpng lupng ciia thanh la

A L = 24kgmVs B L = 36 kgm^/s C L = 48kgm7s D L = 62kgmVs

Huong dan gidi:

Taco: L = I(o = [ m , R j + m2R2)—= ( n i j + m2).Rv = 3 6 k g m ^ / s = > C h p n B Cau 129 M p t dia mai eo momen quan tinh doi v o i true quay etia no la

1/5 kgm/s^ Liic dia d u n g yen, tac d u n g vao dia m p t lye momen khong doi 3Nm M o m e n dpng l u p n g cua dia tai thoi diem t = 15 s bang

=> Momen dpng l u p n g ciia dia L = Ico = 1,5.30 = 45kgm^ / s => Chpn C

£^iU30 M p t dia dac quay quanh tryc dol xung di qua tam va vuong goc voi phang dia Dia chju tac dung ciia mpt momen lye khong doi M = 10 N m

3s ke t u khi dia bat dau quay, van toe goc ciia dia dat 15 rad/s Momen

^9ng lupng ciia dia tai thoi diem t = 3 s bang: I

J l ^ 18 kgmVs B 21 kgmVs C 30 kgmVs D 46 kgmVs

Kt thuat gidi nhanh BTTN Vat Li 12, tap 1 - Nguyen Quang Lac

Gia to'c goc Y = to - CO, '0

Huong dan gidi:

Cau 131 M o t vat r3n c6 momen quan tinh 2kg.m2 quay v o i toe d p goc 10 rad/s

Dong nang quay ciia vat ran la

A.200J B lOOJ C.400J D 20000J

Huang dan gidi:

A p d u n g c o n g thue = ^Ico^ = ^.2.10^ = lOOJ Chpn B

Cau 132 M o t vat r i n eo monmen quan tinh 0,5 kg.m^ doi voi mot true quay cu

djnh Vat ran quay quanh true theo phuong trinh (p = 23 + 30t - 3t^ Trong do (f,

tinh theo rad, con t tinh b5ng s Tai thoi diem t = 4s dpng nang quay cua vat rSn la:

A.3J B 6 J C 9 J D.21J

Huang dan gidi:

Van toe goc: co = (p'{t) = 30 - 6 t (rad/s)

Tai thoi diem t = 4s, van toe goc c6 dp Ion: (o = 30 - 6t = 30 - 6.4 = 6 (rad/s)

= Iko^ = 1.0,5.62 = 9(J) => Chpn C

Cau 133 M o t banh xe eo momen quan tinh 8 kg.m^ doi v o i true quay co djnh

Banh xe d u n g yen thi chju tac d u n g ciia mot momen lye la 32N.m Bo qua moi

lire can Sau 12s ke tit k h i chju tac d u n g ciia momen lye, dpng nang quay ma

banh xe thu dupe la

A 1153J B 4357 J C.9216J D 12321J ; |

Huang dan gidi:

Ta co: Y = y = y = 4(rad / s); co = COQ + Yt = 0 + 4.12 = 48(rad / s)

W j = ijco^ = 1.8.482 = 9216(J) => Chpn C

Cau 134 M o t vat r3n eo momen quan tinh doi v o i true quay eo d i n h la 2kg.m'/

quay deu, trong 1 phut quay dupe 240 vong D p n g nang quay ciia vat la '

r g u 135- M p t vat ran co momen quan tinh 0,5 kg.m^ do! v o i mpt true quay eo

jjjnh Vat ran quay quanh true theo phuong trinh cp = 18 + 40t - St^; trong do cp

f'nh theo rad, con t tinh theo giay Tai thoi diem t = 4s dpng nang quay ciia vat tinh

ran la

Huang dan gidi: '

Van toe goc: co = cp'(t) = 4 0 - 6 t ( m / s ) Tai thoi diem t = 4s van toe goc eo dp Ian: co = 40 - 6.4 = 16 (m/s)

= l l c o ^ = 1.0,5.162 = 64(J) => Chpn C

Cau 136 Cong de tang toe mpt canh quat t u trang thai nghi deh khi co toe dp

goc 160 rad/s la 3200 J Momen quan tinh cua canh quat do doi voi true quay da cho la:

A.0,13kg.m2 B.0,25kg.m2 C 0,38 kg.m^ D 4 , 7 k g m 2

Huong dan gidi:

Cong dupe chuyen hoa thanh dpng nang ciia canh quat Do do: ,

17 J B.48J C.60J D 9 4 J

Huong dan gidi: ' '

f Momen dpng lupng eiia dla la: L = Ico

Dpng nang quay eiia dia la:

W - l l c o 2 - l ( l c o ) c o = 1L.CO = 1.15.8 = 60(1) =^ Chpn C

d 2 2^ ^ 2 2 ^ '

£au 138 Tir trang thai nghi, mpt banh da quay nhanh dan deu voi gia toe goc

30 rad/s2 Tinh dpng nang quay ma banh da dat dupe sau 6s ke tir liie bat dau

quay Biet momen quan tinh ciia banh da doi v o i trye quay ciia no la 4,5 kg.m^

.3452 J B 6531 J C 72900 J D 12000 J

Huang dan gidi:

oe dp goc: CO = Yt = 180 (rad/s) ' ipng nang quay cua banh da: = llco^ = 1.4,5.1802 = 72900(j) Chpn C

K i thuatgidi nhanh BTTN Vat Li 12, tap 1 - Nguyen Quatig Lac

Cau 139 MQt dla tron dong chat kho'i lugng nn = 16kg, ban kinh R = 50cm dang

quay deu voi toe do goc 80 rad/s thi chiu tac dung cua mot momen luc ham CQ

dp Ion M = 20 N m Sau 5,5s ke t u khi ham dpng nang cua dia tron la

A 144 J B.256J C.441 J D.625 J

Huong dan gidi:

Theo dinh ly dong nang: llco^ = M g | ^ ^ML^co^ = M g L ^ co =

3g Momen dong l u g n g dol voi tryc quay khi do: L = Ico = ^ M L ^ ^ -Thay so ta dugc: L » 5,5kg.mVs => Chon C

Cau 142 Hai banh da A va B quay xung quanh true d i qua tarn ciia chiing,

^^j^J^ng quay cua A hang 4 Ian dgng nang quay ciia B , toe do goc ciia A

- — ' • - ° \ / f ^ ^ a n / n i i a n h'nh rtn'i voi truc Quav Qua tam

1 2 1 / \ / 2 \ „xne quay cua A bang 4 lan aong nang qudy c u a 1 ^ , - V

M o m e n quan tinh cua dia la: I = - m R = -.16.(0,5) = 2 kg.m ) dpng " S 4 , ^ ^ ^ ^ ^ ^ ^^^^ ^ , ^^^^ ^^^^

bang 0,2b lan toe u g Gia to'c goc ciia dia: Y = ^ = — ^ =-10 rad / j

Toe dp goc ciia dia sau 5,5s la: co = CDQ + yt = 80 -10.5,5 = 25(rad / s)

Dong nang quay cua dia la: W j = ^Ico^ = ^-2.25^ = 625(j) => Chpn D

Cau 140 M p t rong roc c6 khoi lugng m = lOOg, xem n h u mot dia tron, quay

quanh true ciia no nam ngang M o t sgi day manh, khong dan, khoi lugng

khong dang ke, vat qua rong rgc Hai dau day c6 gan hai vat c6 khoi lugng m

va 2m va tha t u do K h i van toe ciia vat la 2 m/s thi dong nang ciia he la

A 0,7 J B 0,9J C 1,2J D.2,3J

Huang dan gidi:

Dgng nang eiia he: W^^ = VV^i + + W^g

deu va CO the quay trong mat phang thang d u n g quanh dau A Thuoc dugc tha

nh^ t u v i tri nam ngang Lay g = lOm/s^ va bo qua sue can tac d u n g len thuoc

M o m e n dgng l u g n g ciia thuoc doi voi true quay co'djnh nam ngang d i qua A

khi no CO vi tri thang d u n g la:

A gan bang 1,3 kg.m^s B gan bang 3,1 kg.mVs

C gan bang 5,5 kg.mVs D gan bang 7,7 kg.m^s

Huang dan gidi:

M o m e n quan tinh ciia thuoc do'i voi true quay: I = ^ML'^

3 Ggi toe dp goc ciia thuoc t ^ i vj tri thang d u n g la co

cua A va B Ian lugt la IA va IB Ti so ^ la

Huang dan gidi:

Co nang toan phan ciia xe truoc khi di vao v u n g c6 luc can:

= 8 m => Chgn D

61

Cau 144 M o t banh xe co momen quan tinh do'i v6i true quay co' dinh la

kgrn^ quay deu voi toe do 36 vong/phut Dong nang ciia banh xe la

A Wd = 120J B Wa=180J C.Wc = 240J D Wd = 300J

Huang dan gidi:

Ta co: co = 60v6ng/ phiit = = 2jtrad / s

60

=> Dpng nang: W j =U(a^ = ^.15.(27t)^ = 300J => Chpn D

Cau 145 M p t momen luc co dp Ion 3,6Nm tac dpng vao mot banh xe c6

momen quan tinh d o i voi true banh xe la 1,8 kgm^ Banh xe quay nhanh daVi

deu t u trang thai nghi Dpng nang cua banh xe 6 thoi diem t = 5 s la

A W d = 60J B.Wd = 90J C.Wd = 120J D W d = 180J

Huang dan gidi:

Phuong trinh co ban ciia chuyen dpng quay cho gia toe goe :

Cau 146 Banh da co momen quan tinh do'i voi true quay eo d j n h eua no la 0,4

kg.m^ De banh da tang toe t u trang thai d u n g yen den toe dp goe co phai ton

eong 2000J B6 qua ma sat Gia trj eiia at la

A lOOrad/s B 50 rad/s C 200 rad/s D 10 rad/s

Huang dan gidi:

Theo djnh li dpng nang, eong can thue hien bang dp bien thien dpng nang

ciia vat: , ,,

p o n g nang ciia vgt rSn tai thai diem t = 10s la: W = ^Ico^ = 225J

^ Chon B

Cia l ^ ^ - ^'^ dang hinh cau dac dong chat ban kinh R = 0,5 em quay

"^^^xanh true quay d i qua tam voi toe dp goe bang 50 rad/s D p n g nang cua vat

ran bSng 125J Khol lugng ciia vat ran nhan gia trj nao trong cae gia tri sau ?

r a u 149 M p t hinh tru dac, dong chat, ban kinh R = 40em, khoi lupng m = 80kg,

quay quanh true do'i xung cua no t u trang thai nghi K h i vat dat dupe toe d p goc 540 vong/phut thi momen ngoai lue da thue hien mpt eong la (lay = 10) A.5120 J B 7483 J C 9102 J D 10368 J

Huang dan gidi:

Ta C O CO = 600 vong/phut = 1 STT rad/s

Theo dinh ly bien thien dc)ng nang, ta co: - W j , = A Vay A = ^ I c o ^ - 0 = ^ ^ m R V =^.^.80.(0,4)^(I8n)^ =10368J

=> Chpn D Cau ISO Cong de tang toe mpt eanh quat t u trang thai nghi den k h i co toe dp goe 200 rad/s la 3000 J M o m e n quan tinh ciia eanh quat bang

Dp bien thien dpng nang b^ng eong ciia ngpai li^e: -Ico - -ICOQ = A

Do CO,, = 0 nen -Ico^ = A I = ^ = 0,15kgm2 > Chon A

Cau 147 M p t momen lue co dp Ion 3 N m tac dung vao mpt banh xe co momen

quan tinh doi v o i true banh xe la 2 kg m ^ Banh xe quay nhanh dan t u trang

thai nghi Dpng nang cua banh xe 6 thai diem t = 10 s la :

A 300 J B.225J C.525J D.275J

Huang dan gidi:

A p d u n g p h u o n g trinh dpng lue hoe vat r3n: X Q

Van toe goc tai thoi diem t = 10s: CO = COQ H-yt = 0 + 1,5.10 = 15rad/s

£4u 151 M p t san quay hinh tru eo khoi lupng 80 kg va eo ban kinh 1,5m San

''at dau quay nho mpt lue khong doi, nam ngang, eo d p Ion 500 N tac d u n g

^ao san theo phuong tiep tuye'n vc>i mep san Dpng nang ciia san sau 3 s la

A W = 28,lkJ B W = 29,lkJ C W = 50,5kJ D W = 30kJ

Huang dan gidi:

^p d u n g eong thue W = ^Ico^

Ap dyng phuang trinh dpng l\fc hoc vat rin:

Cau i52 Mot vien bi khoi lupng m = 200 g, ban kinh r = 1,5 cm Ian khong truot

theo duang doc chinh ciia mot mat phSng nghieng Lay g = 7C^ « 1 0 Khi bi dat

van toe goc 50 v6ng/s thi dpng nang toan phan ciia bi bang?

A 2,25 J B 3,15 J C.0,9J D 4,05 J

Huang dan gidi:

Momen quan tinh cua vien bi: I = - m R ^

Toe dp goc cua vien bi: co = 50v6ng/giay = = 1007:(rad / s)

Khi vat ran Ian khong trupt, tue la vat ran vua chuyen dpng tjnh tien va vua

chuyen dpng quay quanh true di qua trpng tam cua no Vay dpng nany

toan phan cua vat r i n khi Ian khong trupt gom dpng nang tinh tien va dpng

nang quay

W = llco^ + i-mv^ = l.imR2.„2 ^ i 2

2 2 2 5 2 Mat khae, ta c6 v = toR

^ W = i |mR2.c)2+imv2=^mR2.«2^3,15J

2 5 2 2

=> Chpn B

Cau 153 Mpt momen lire 30 N.m tac dung len mot banh xe c6 khoi lupng 5 kg

va momen quan tinh 2 kg.m^ Neu banh xe quay tu nghi thi cong cua momen

luc thuc hien trong 10s dau la

A 12,5kJ B.22,5kJ C 35,5 kj D 45,5 kj

Huong dan gidi:

Gia toe goc eua banh xe: y = M = ^ = 15^rad / s^ j

Toe dp goc ciia banh xe sau 10s: co = cog + yt = 15.10 = 150(rad / s)

Dpng nang eiia banh xe sau 10s: Wj = -Ico^ = ^.2.150^ = 22500J

64

Cong cua momen lire thuc hien trong khoang thai gian 10s la:

A = Wd - Wdo = 22500 J = 22,5 kJ => Chpn B

Ciu IS"*' Cong de tang toe mpt canh quat tu trang thai nghi de'n khi c6 toe dp

"^^^iorad/s la 4800J Hoi momen quan tinh eua canh quat blng bao nhieu?

^ A 0,124 kg.m^ B 0,243 kg.m^ C 0,375 kg.ml D 0,478 kg.m^

Huang dan gidi:

Theo djnh ly bien thien dpng nang, ta c6:

A = - W , ^ =^Ico2 -ilcog =lW (docoo =0)

Suyra: I = ^ = ^ : ^ = 0,375(kg.m2) ^ Chpn C

^ co^ 160^ ^ '

CM 155 Mpt b? quay hanh li 6 san bay coi nhu dia tron dac, dong chat co khoi

lupng M = 120kg, ban kinh 2m quay quanh mpt tryc di qua tam vai toe dp goc

(0 = 2rad/s Khi dia dang quay, mpt kien hanh li khoi lupng m = 100kg roi thang

dung xuong sat mep eua be quay va gan chat vao b? quay Dp bien thien dpng nang ciia he la:

A.-200J B.-300J C.-500J D.-250J

Huang dan gidi:

Momen dpng lupng eiia h^ truoc liie tha ki^n hanh li la:

L = I,co = —mR^co

^ 2 Momen dpng lupng cua he sau khi tha kien hanh li la:

w, =iico2 = 1 M R V

^ 2 4 Dpng nang eiia h? sau khi tha kien hanh li

W 2 ^ i ( l l + l 2 ) c o ' 2 = i

Dp bien thien dpng nang:

^MR^+mR^

2

' 2 to'^ -^MR^co^ =-300J

=> Chpn B

Cau 156 H a i dia tron cxS momen quan tinh Ii = 3kg.m^ va l 2 = Ikg.m^ dang quay

dong true va cung chieu v a i toe do goc goe a)i = 10 rad/s va goc OK = 20 rad/s

sat a true quay nho khong dang ke Sau do cho hai dia d i n h vao nhau, h# quay

v a i toe dp goc o) Phan ca nang mat d i cua hai dia trong cu va eham tren la

A A W j = 7,7.5] B A W j = 17,5J C AW^ = 27,5J D AW^ = 47,5]

Huong dan gidi:

D p n g nang cua h§ hai dia ban dau: W^Q = ^ I j O j + ^ l 2 « 2

D p n g nang ciia he hai dTa sau k h i dinh vao nhau: WJQ ^ ( i j + l2)w^

Cau 157. M o t h i n h t r u dong chat ban kinh R = 20 cm, kho'i l u a n g m = 100 kg,

quay quanh true d o i x u n g cua no tir trang thai nghi K h i vat dat van toe goc 60

vong/phiit thi ngoai lye da thye hien m p t cong la bao nhieu? (lay Tt^ = 10)

A.40J B.20J C 160J D 80J

Huang dan gidi:

M o m e n quan tinh cua hinh t r u : I = ^ m R ^ = 1.100.0,2^ = 2kg.m^

Toe d p goe cua hinh t r y : o) = 600 vong/phut = 2n (rad/s)

A p d y n g d j n h l i bien thien dpng nang: A W = ^Icaj - l l w j = A

Vat bat dau quay tir trang thai nghi nen dong nang ban dau eiia vat bang khong

Suy ra cong ciia ngoai lye bang:

A = A W = l l o ) ^ = i i c o = 40J => Chpn A

i y j 5 8 : M p t vat ran quay quanh m p t tryc A co d i n h v o i toe d p goc 30 rad/s

j^omen quan tinh ciia vat ran d o i v o i tryc A la 6 kg.m^ M o m e n d p n g l u p n g vat r i n d o i v a i tryc A la

A 2 0 k g m V s B ISOkg.mVs C 500 kg.mVs D 27000 kg.mVs

Huang dan gidi:

Ta CO M o m e n dpng l u p n g cua vat ran d o i v a i tryc A la ' ' ' ^ '

L = I.u) = 6.30 = 180 kg.mVs ^ Chpn B '

0 u l 5 9 : H a i qua cau nho c6 khoi l u p n g Ian lupt la 2,4 k g va 0,6 k g gan 6 hai

dau mpt thanh eung va nh? M o m e n quan tinh eiia h^ do^ v o i tryc quay d i qua trung diem ciia thanh va vuong goc v o i thanh la 0,12 kg.m^ Chieu dai ciia thanh la

A 0,4 m B 0 , 6 m C 0 , 8 m D 0,3 m '

Huang dan gidi:

Momen quan tinh ciia he d o i voi tryc quay d i qua trung diem ciia thanh va vuong goe v o i thanh la

/ ^2

I = (mj +m2)r^ ={"^i +"^2)

=>1 = 2 * I

•v=2 0,12 = 0,4m [ ( m i + m j ) ^(2,4 + 0 , 6 )

=> Chpn A Cau 160; M p t banh xe dang quay deu quanh true A eo'djnh v o i dpng nang la

225 J Bie't momen quan tinh ciia banh xe doi v a i tryc A la 2kg.m^ Toe d p goc ciia banh xe la

A.56,5 rad/s B 30 rad/s C 15 rad/s D 112,5 rad/s

Huong dan gidi:

Ta CO dpng nang W , = l l o ^ =>a) = ^ 2.W

I

2.225

= 15rad/s =:>ChpnC

£ a u 161: M p t dTa tron, phang, dong chat c6 momen quan tinh 8 kg.m^ doi v a i

true A CO d j n h d i qua tam dia va vuong goc v a i be mat dia DTa quay quanh A

Voi g i a toe goc bang 3 rad/s M o m e n lye tac d y n g len dTa doi v o i tryc A c6 d p Ion la

A 24 N m B - N m

3 C 12 N m D - N m 8

Huang dan gidi:

Phuong trinh dpng lye hpc ciia v$t

M = l y = 8.3 = 24N.m ^ Chpn A

67

CH(J 2

D A O D O N G C O I

I H5 THONG H 6 A K I E N THlTC

1 Dao dpng co va dao dpng tuan hoan

Dao dpng la nhung chuyen dpng c6 gioi han trong khong gian dupe lap (j,

l|ip lai xung quanh mpt vj tri can bang

Dao dpng tuan hoan la nhirng dao dpng ma trang thai cua no dupe lap cjj

lap lai trong nhung khoang thai gian bang nhau T Khoang thai gian T dupe

gpi la chu ki ciia dao dpng tuan hoan N h u vay de thyc hi^n mpt dao dpng

tuan hoan phai mat mpt khoang thoi gian T So' dao dpng ma vat thuc hien

dupe trong mpt dan vj thai gian gpi la tan so f Nhu vay:

• Chu ki cua dao dpng tuan hoan la khoang thai gian ngan nha't de trang

thai dao dpng lap lai nhu cu Chu ki thuong ky hi^u bang chir T (do bang

giay: s)

• Tan so' la so' Ian dao dpng (tuc la so' Ian trang thai dao dpng lap lai nhu da)

trong mpt dan vj thoi gian Tan so'thuong ky hieu bang chit f (do bang hec: Hz)

• Moi lien he gii>a chu ki va tan so': ^ = ^

2 Dao dpng dieu hoa

Dao dpng dieu hoa la nhiing dao dpng dupe mo ta boi ham so cosin hoac

sin theo thoi gian: x = Acos(o)t + (p) hoac x = Asin(cot + (p)

Trong do:

• x: li dp, no la dp l^eh cua vat khoi vj tri can bang

• A: bien dp, no la gia tri cue dai cua li dp

• (o: Tan so' goe, tuong ung vdi ehuyen dpng cua vat trong chuyen dpng

tron deu

• T: Chu ki, no la khoang thai gian ngan nha't ma vat thuc hi^n dupe mpt

dao dpng

• f: Tan s6^ no la so'dao dpng ma vat thuc hien dupe trong mpt dan vj thai gian

• cot + (p: pha dao dpng, no xac djnh vj tri cua vat trong chuyen dpng tron

deu tuong ung tai thoi diem t

• (p: pha ban dau, no xac dinh vi tri ban dau ciia vat trong chuyen dpng

tron deu tuong ung vdi thoi diem ban dau t = 0

- ^ 271 „ 1 t 27t , 1 N CO

• M O I lien h?: co = 27if = —; T = - = — = — ; f = — = — = —

Trong do: N la so'dao dpng ma vat thuc hi^n dupe trong thoi gian t

3 toe va gia toe trong dao dpng dieu hoa Z> v^Tdao d*„g dieu hoa voi phu.„g rlnh: x = Acos«o KK, do: phuang trinh vgn toe:

y ^ x' = -coAsin(cot + (p) = v^^^.cos cot + (p + -n

, Van to'c cue dai cua vat c6 gia tri: vmax = Aco khi vat di qua vi tri can bang

, Phuong trinh gia toe:

a = v'= x'=-Aco^ cos(cot + cp) = a^3^.cos(cot + (p + 7t)

• Gia toe eye dai co gia trj: amax = Aco^ = cJVmav khi vat a v i tri bien

4, Moi lien hf giira chuyen dpng tron deu va dao dpng dieu hoa

Mpt dao dpng dieu hoa co the dupe coi nhu hinh chie'u ciia mpt diem chuyen dpng tron deu xuo'ng mpt duang thang nam trong mat phang quy dao

Tu moi lien h^ giCra ehuyen dpng tron deu va dao dpng dieu hoa eho tha'y khi vat dao dpng dieu hoa co phuong trinh x = Acos(cot + cp) thi trong mpt phan tu

chu ki vat di duac quang duang S = A, trong nua chu ki vat di dupe quang duang S = 2A va trong mpt chu ki vat di dupe quang duong S = 4A

5 Con lie 16 xo a) Con lac 16 xo nam ngang

> Cau tao: Con ISc 16 xo nam ngang la mpt co h? gom 16 xo co khoi lupng

khong dang ke, co dp cung k Mpt dau eiia 16 xo dupe g^n vao mpt diem co'

djnh, e6n dau kia dupe gan vao vat co khoi lupng m va co kich thuoc khong

dang ke Vat co the truat tren mpt mat phSng nSm ngang khong co ma sat

^ Cac dai lupng dac tnmg trong dao dpng dieu hoa cua con lac 16 xo

Tan so goc: co = 27if = •

b) Con lie 16 xo thang dung

II Dp gian cua 16 xo khi v^t nSm tgi vi tri can b^ng: Al -mg

Con rkc 16 xo thang dung dao dpng voi tan so goc: co - _k m Al

Tan so:

C h u k i :

6 Nang lugrng trong dao dpng dieu hoa

Mpt con lac 16 xo gom vat c6 kho'i luong m, 16 xo c6 dp cung k, dao dpn

dieu hoa voi phuong trinh: x = Acos(a)t + ip) va c6 van toe: v = -A(osin((Ot + (p)

Khi do:

• The nang ciia 16 xo:

Wt = i kx^ = i kA^ cos^ (cot + (p) = i k A^ ( l + cos (2cot + 2(p))

• Dpng nang ciia vat:

Con 15c don la mpt co h f gom spi day khong gian c6 chieu dai 1, mot dau

dupe treo vao mpt diem co djnh, c6n dau kia dupe treo vao vat c6 khoi lupng

m, CO kich thuae rat nho so voi chieu dai cua spi day

> Cac dai lupng dac trung cho dao dpng dieu hoa ciia con lie doti

> D i e u k i ^ n de con lac dom dao dpng dieu hoa

De eon lac don dao dpng dieu hoa phai thoa man hai dieu kifn sau:

• Dao dpng v o i bien dp rat nho

• Bo qua mpi sue can ciia moi truong

y Nang lupng trong dao dpng dieu hoa ciia con lac dofn

jy^pt con 15c don gom spi day khong gian, co chieu dai 1, vat co kich thuoc ra't 0*^° lupng m dupe kich thich cho dao dpng dieu hoa voi phuong

trinh: S = SQ cos(cot + cp) va co van toe: v = -S()COsin(cot + cp) Khi do:

, The n5ng ciia vat:

W, = I mco^So cos^ (cot + cp) = -mco^Sg ( l + cos(2cot + 2cp))

Dpng nang cua vat:

= ^ mco^S^ sin^ (cot + cp) = -^mw^S^ ( l - eos(2cot + 2(p))

Co n5ng ciia eon lac don: W = W, + W j = ^mco^Sg = const

I day can chii y rang: So = aol, do do co nang ciia con lac dcm dupe tinh theo

bien dp goc co eong thiic: W = ^mco^Sp = ^mco^aQp

Ngoai ra khi eon lac dan dao dpng voi phuong ciia spi day tao voi phuong

th5ng dung mpt goc a bat ki thi the n5ng va dpng nang ciia vat dupe xac dinh

boi cac eong thue:

• The n5ng ciia vat: W, = mgh = m g l ( l - c o s a )

8 Da

Dpng nang ciia v^t: W j = - m v ^

2 ;/

Dao dpng tat dan

• La dao dpng co bien dp giam dan theo thai gian

• Nguyen nhan sinh ra dao dpng t5t dan la do v | t dao dpng trong moi

truong CO sy ton tai ciia luc ma sat

9 Dao dpng duy t r i

• Dao dpng duy tri la dao dpng co bien dp khong thay doi theo thai gian

• De CO dao dpng duy tri thi phai tac dung vao vat (vao con lac) mpt lye

tuan hoan co tan s6'b5ng tan so'dao dpng rieng ciia vat (cua con lac)

10 Dao dpng cuong biic

• La dao dpng chju tac dung ciia mpt lire cuong biie bien thien tuan hoan

• Dao dpng cuang biic co bien dp phu thuoc vao dp chenh l^ch giira tan so

f ciia luc cuong biie va tan so' rieng fg ciia vat Khi tan so f cang gan tan so ^

thi bien dp dao dpng cuong biie cang t5ng Khi f = ^ thi bien dp dao dpng cuong biic dat gia trj eye d^i, liie nay ta noi xay ra hi?n tupng cpng huang

11 Cpng hu6ng

• La hi^n tup'ng bien dp dao dong cuang buc t3ng nhanh dpt ngpt va deit

den mpt gia tri cue dai khi tan so' cua luc cudng buc b^ng tan so dao dpnw

rieng cua vat

Hi^n tuong cpng hupng the hi^n ro khi luc can ciia moi truang nho

12 Tong hgp hai dao dpng dieu hoa cung phuong, cung tan so

> Cach bieu dien mpt dao dpng dieu hoa bang mpt vecto quay:

Cach bieu dien phuong trinh ciia dao dong «

-dieu hoa x = Acos(cot + cp) bang mot vecta quay

dugrc ve tgi thai diem ban dau (Hinh ve) nhu sau:

• Co goc tai goc toa dp ciia tryc Ox ;

• Co dp dai bang bien dp dao dpng, OM = A;

,^ • Hop voi true Ox mpt goc bang pha ban

dau (chpn chieu duang la chieu duang cua

duong tron lupng giae), ^OM,Oxj = cp

Tu do: O M : = A

(OM,Ox) = cp

> Tong hgp hai dao dpng dieu hoa cung phuong, cung tan so bang

phuong phap vecta quay (Phuang phap Frexnen):

Cho hai dao dpng dieu hoa cung phuong, cung tan so', c6 phuong trinh Ian

lupt:

Xj = Ajcos(cot + (pj)

X2 = A2Cos (a)t + (p2)

Phuong trinh li dp tong hpp se la: x = Acos(a)t + (p) i l

Trongdo: A = ^ A ^ + A^ + A1A2 cos((p2 - 9 i )

A , sincpi + A , sinip, tan(p = ^5 ^ ? ^

A J cos(pj + A2 cos(p2

> Dpl?chpha:

Dai lupng Acp = cpj - cpj gpi la dp l^ch pha ciia hai dao dpng Dp l^ch pha A(p

dupe dung lam dai lupng dac trung cho sy khae nhau ve trang thai giiia hai

dao dpng cung tan so' Cy the:

^ > Neu Acp>0 (pj >(P2 : dao dpng 1 som pha han dao dpng 2

P > Neu A<p < 0 -> (pj < 92 : dao dpng 1 t r i pha hon dao dpng 2

^ Cac truang hpp dac bi#t: j^: , Neu Ac}> = 0 hay A(p = 2k7t vdi k = 0, ±1, +2, hai dao dpng cung pha Khi

hai vat dao dpng cung phuong va chuyen dpng cung chieu nen bien dp dao jjpng ^'^^ '""^ ^^^^ ''^"S *°"g bien dp: A = A j + A j

, Neu Acj) = 7T hay A(p = (2k + l)7i voi k = 0, ±1, ±2, hai dao dpng ngupc

pha Khi do hai vat dao dpng ciing phuong va chuyen dpng ngupc chieu

^en bien dp dao dpng tong hpp la nho nha't va bang trj tuy?t doi ciia hi?u hai bien dp: ' - ' ^-

A =|AJ - A2

Neu A(p = ± ^ hay Acp = ± | + 2kn voi k = 0, ±1, ±2, hai dao dpng c6

pha vuong goc (gpi tat la hai dao dpng vuong pha), liic do ne'u vat nay 0 vi tri

can bang thi vat kia 6 vj tri bien hoac ngupc lai nen bien dp dao dpng tong

• Neu dp l?ch pha la bat ky thi bien dp dao dpng tong hpp c6 mpt dp Ion trung gian:

A2 - A , < A < A^ + A2 ' " ' " y " ,

II C A C D A N G B A I T A P V A V I D y M I N H H Q A

Dangl X A C D I N H C A C D A I L l / O N G D A C T R l / N G "

C U A D A O D O N G D I E U H O A

Phuong phap giai:

^ Xac dinh cac dai lupng tu phuang trinh dao dpng dieu hoa I

• Li dp X va pha ban dau cp nhan gia trj tuy y

• Bien dp A, tan so goc w, tan so f va chu ki T luon nhan gia trj duong

^0 do, khi tim cac dai lupng A, to, f, T va (p ta can chuyen phuong trinh dao

(Jpng ve dang phii hpp voi dac diem ciia cac dai lupng do

^ Xac djnh van toe va gia toe E^oi voi loai toan nay ta can sii dung cac kien thiic sau:

• Van toe cue dai va gia toe cue dai cua dao dpng Ian lupt la: ^^i

, v „ _ = A ( o ; _ ^ ^ '

a „ , a x = A c O = C O V „ , ,

Moi lien h^:

muatgtat nnanH ailN vat Li 12, tap I - Nguyen jjuang Lac

( c m / s ^ )

V i 2 Mot vat dao dong dieu hoa c6 dp Ion van toe cue dai la 94,2 cm/s

Lay 7t = 3,14 Toe dp trung binh ciia vat trong mot chu ki dao dpng la:

A 35 cm/s B 45 cm/s C 60 cm/s D 78 cm/s

Huong dan gidi:

s 4A Toe dp trung binh ciia vat trong mpt chu ki dao dpng la: ^ = - =

Tudo: v = ^ ^ ^ ^ - ^ ^ ^ = 60(em/s) => Chon C

H

Vi du 3 Mpt chat diem dao dpng dieu hoa, tai thai diem tj chat diem eo li dp

va van toe: xi = 3cm, V j =15V37i—; tai thoi diem t, chat diem c6 li dp va

s ^ van toe: X j = 3V3cm, V2 - 1 5 7 T — Lay 71^ a 10 Tan so dao dpng ciia chat

2

= 57t(rad/ s]

Q0g2 XAC DINH CAC DAI L l/ O N G DAC T R L / N G T R O N G DAO

^ " " ^ DONG CUA CON LAC L 6 XO

Fhufwig phap giai:

y Con lac 16 xo n i m ngang:

• Dp gi^*^ nam tai vi tri can bang: Al = 0

• Con lac 16 xo nam ngang dao dpng voi tan so'goc: -.^j^

'r- Con 13c 16 xo thang dung:

• Dp gian cua 16 xo khi vat n,

• Con lac 16 xo thMng dung dao dpng voi tan so goc:

• Dp gian cua 16 xo khi vat nam tai vi tri can bang: Al =

co = , — =

m 1 Al Tan so':

Chu ki:

271 27tVm 2 7 I V A 1

CO \ V g Con lac 16 xo nam tren mat phing nghieng, nghieng mpt goc a

• Dp gian cua 16 xo khi vat n3m tai vj tri can bang: