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

530

076

K300T

PGS.TS. N G U Y E N Q U A N G L A C
S. N G U Y E N T H I N H I - T S . C H U V A N L A N H

KI THUAT GIAI NHANH
BAI TAP TRAC NGHIEM

irl*if
TAP!
• D O N G LTJC H O C V A T R A N
. D A OD O N G C O
• SONG C O
• D A O D O N G V A S O N G D I E N TU"
. D O N G DIEN XOAY

CHIEU

• Danh cho hoc sinh Idp 12 chiidng trinh chuan va nang cao
• On tap va nang cao ki nang lam bai
Bien scan theo npi dung va cau true de thi cua bp GDSfDT

BAN D A IH O C QUOC GIA H AN O I


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— ¥ & r N G U Y E N T H I N H l - Tfc>. (Jhtu VAJN £ A m r

Kl THUAT GIAI N A H
HN
•

BAI TAP TRAC NGHIEM

• D O N G L U C H O C VAT RAN
• DAO

DONG

CO

• S6NG CO
• DAO D O N G VA SONG D I £ N T f
. D 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 k i nang lam b^i
• Bien soan theo noi dung va cau triic de thi cua bp GD&DT

THIJ ViFNTiNHBINMTHUAN

DCK]

NHA XUAT BAN DAI H O C Q U O C GIAH A NOI


CHCJ

LOfI N O I D A U

1.
DONG L U C HOC VAT RAN

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 t u cac de thi thu dai
hoc ciia cac truong nhu THPT chuyen Phan Boi Chau, THPT chuyen Dai hpc
Vinh, THPT chuyen DHSP Ha Noi,... va de thi CD - D H cac nam gan day, ke
ca de thi CD- D H nam 2013 vua qua. Mot so'bai tap kho dugc danh dau * de
cac em luu y khi doc. Quyen sach dugc tach thanh hai tap de c6 d i i dung
lugng cho vi^c chuyen tai ngi dung ly thuyet va khoi lugng bai tap day dii,
phong phii.
*

1. Chuyen dpng quay ciia vat ran quanh mpt true co dinh
Su tuong t u gii>a cac dai lugng goc dac trung cho chuyen dgng quay ciia vat
r ^ quanh mgt true co djnh va dai lugng dai dac trung cho chuyen dgng thang:

Tap 1 bao gom:

-

I. H E T H O N G H O A K I E N THLfC
Mot vat ran quay quanh mot true co'djnh thi mgi diem tren vat ran do vach
nen nhOng vong tron trong cac mat phang vuong goc vai true quay, c6 tam

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 .

Chu de 1: Dong luc hgc vat ran;

-

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;

Chuyen dgng quay

(chieu khong doi)

Chu de 2: Dao dgng ca

-

Chuyen dgng thang

(true quay co djnh, chieu quay khong doi)

Tga do: x

Tga do goc: (p

Toe do: v = x'

Toe do goc : ( 0 = cp'

Gia toe: a = v' = x"

Gia toe goc: y = co' = cp"

Chuyen dgng thSng deu:

Chuyen dgng quay deu:

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

0) = hang so; y = 0; (p = cp,, + cot

Chu de 7: Lugng t u anh sang

Chuyen dgng thSng bien doi

Chuyen dgng quay bien doi deu:

-

Chu de 8: Thuyet tuong doi hep;

deu:

-

Chu de 9: Vat ly hat nhan nguyen t u

a = hang so'

-

Chu de 10: T u vi mo den vT mo

V

= vo + at

X

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

= xo + vot + -at^

2

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

v ^ - V o =2a(x-Xo)

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

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

\

• •

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

nang lam trgn ven de thi CD - D H sap toi.
Dau da C O be day kinh nghiem lau nam va da co'gang bien soan quyen sach
tot de phuc vu dgc gia nhung chung toi luon vui long don nhan nhirng y kien
quy bau t u cac thay c6 giao va cac em hgc sinh.
Nhom tac gia

y = hang so'
CO = COQ

+ yt

(p = (P(,+C0(,t + ^yt^

s = r(p,

co^-cog =2y((p-(Po)

V

= rco; at = ry; a„ = rco^

Chii y: Dan vj ciia cac dai lugng 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


Cty TNHH

T r o n g d o d la canh tay d o n cua luc F (khoang each tie t r y c A den gia cua
Ivc F ) .

•

T h a n h d o n g chat, c6 k h o i l u g n g m va c6 tie't d i ^ n n h o so v o i chieu dai 1

1 = -lml2

C h p n ehieu quay cua vat l a m chieu d u o n g , ta c6 q u y uoe:
-

M > 0 k h i F eo tac d u n g l a m vat quay theo ehieu d u o n g .

-

M < 0 k h i F eo tac d u n g l a m vat quay theo ehieu ngupe ehieu d u o n g .

> Mot lien he giita gia toe goc va momen luc
T r u o n g h p p v^t ran la m p t qua cau n h o eo kho'i l u g n g m gSn vao m p t
dau t h a n h rat nh? va dai r. Vat quay tren mat phMng n h a n n a m ngang x u n g
q u a n h m g t true A th^ng d u n g d i qua m p t dau eiia t h a n h d u o i tae d y n g a i a lye
F , t h i m o m e n lye tac d u n g len vat ran nay la:
M = (mr2)y

12

•

V a n h tron d o n g chat eo k h o i l u g n g m , ban k i n h R, t r y c quay A di qua

tarn v a n h va v u o n g goc v o i mat p h a n g v a n h tron: I = m R
•

D i a t r o n m o n g d o n g chat c6 k h o i l u g n g m , eo ban k i n h R, t r y e quay A di
1

qua t a m dia t r o n va v u o n g goc v o i mat dia: I = - m R
•

2

Qua cau dac d o n g chat eo k h o i l u g n g m , eo ban k i n h R, t r y c quay A di
2

(2)

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

qua tam qua cau:

I = - mR

2

o
c. Phuong trinh dpng l y c hpc a i a vat tin quay quanh mpt tryc co d i n h la:

T r u o n g h g p vat ran g o m nhieu chat d i e m c6 k h o i l u o n g Ian l u g t la mi,

mj, ... 6 each true quay A n h u n g khoang n, r\, ... khac n h a u t h i m o m e n lye tae
d y n g len vat ran nay la:

M = ly

(5)

T r o n g do: I la m o m e n quan t i n h ciia vat ran d o i v o i t r y c quay A; M la
m o m e n lye tac d y n g vao vat ran d o i v o i trye quay A; y la gia toe goc ciia vat

(3)

ran t r o n g ehuyen d o n g quay q u a n h true A.
3. Momen dpng lugmg. d i n h luat bao toan momen dpng l u g n g
a. Momen dpng l u g n g L eiia vat rin t r o n g ehuyen d p n g quay q u a n h t r y e la:

b. M o m e n q u a n t i n h
T r o n g p h u o n g t r i n h (3), dai l u g n g Y^mj^
dac t n m g cho m i i e q u a n t i n h
i
cua vat quay va d u g e g o i la m o m e n quan rinh, k y hi$u la I .
M o m e n q u a n t i n h I d o i v o i m o t true la dai l u g n g dac tnmg cho m u c quan
t i n h ciia vat ran t r o n g ehuyen d g n g quay quanh true ay.
(4)
M o m e n q u a n t i n h c6 d o n vj la kg.m^.
> M o m e n quan tir\ ciia m g t vat ran khong chi phy thuoe vao khoi l u g n g a i a
vat ran ma eon p h u thuge vao ea sy phan bo khoi l u g n g xa hay gan true quay.
> D i n h l y ve trye song song: I Q =

Vift

ciia no, t r y c quay A d i qua t r u n g d i e m ciia thanh va v u o n g goc v o i t h a n h :

D o n v j cua m o m e n l y e la N . m .

*

MTVDWirKK^g

+ md^

T r o n g do: d la khoang each tir true quay O den true song song qua t r o n g
tam G ciia vat; lo; IG t u o n g l i n g la m o m e n quan h'nh ciia vat d o i v o i t r y c O va
trye G.
> M o m e n q u a n t i n h ciia m g t so vat ran eo trye quay do'i x i i n g :

L = lo)

(6)

T r o n g do: I la m o m e n quan t i n h ciia vat ran d o i v o i t r y e quay; co la toe dp
goc eiia vat ran t r o n g ehuyen d p n g quay q u a n h tryc.
D o n vj eiia m o m e n d p n g l u g n g la kgmVs.
b. Phuong trinh dpng l y c hpc ciia vat tin

quay quanh mpt tryc dupe viet

duoi dang khac:
AL
M =At

(7)

T r o n g do: M la m o m e n lye tae d y n g vao vat ran; L = Ico la m o m e n d p n g

•trgng ciia vat ran d o i v o i trye quay; AL la dp bien thien m o m e n d p n g l u g n g
ciia vat ran t r o n g t h o i gian At.
c. D i n h luat bao toan momen dpng l u g n g
K h i M = 0 t h i L = L(o = hang so
N e u t o n g eac m o m e n lye tae d u n g len m g t vat ran (hay he vat) d o i v o i m p t
true hang 0 t h i tong m o m e n d p n g l u g n g ciia vat ran (hay h ^ vat) d o i v o i t r y c
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 k h o n g d o i : vgt ran (hay h | v^t) d u n g yen

ho§e quay deu.


Cty TNHH MTV DWH

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

•

T r u o n g h g p I thay d o i t h i co thay d o i : vat ran (hay he vat) c6 I g i a m t h i co

tang, C O I tang t h i co g i a m (Ico = hang so' hay I^co^ = I2CO2).
a. D p n g n a n g W d cua v a t r a n quay q u a n h m p t true eo d i n h l a :
(8)

Vi

1 : M p t b a n h xe quay deu q u a n h true co d j n h v o i tan so goc k h o n g d o i

6000 v o n g / p h i i t . T r o n g 2,5s banh xe quay d u p e m p t goc la
^

1257T rad

B. 250n rad

T r o n g d o : I la m o m e n quan t i n h cua vat ran d o i v o i true quay, co la toe d o
goc ciia vat ran t r o n g chuyen d o n g quay q u a n h true.

C. 500 n rad

D . 750TI r a d .

Huong dan giai:
Ta CO f = 6000 v o n g / p h i i t = 100 v6ng/s.

T u (6) va (8), d p n g nang Wd ciia vat ran quay q u a n h m o t t r y c co' d i n h co the
vie't d u o i d a n g :

Suy ra: CO = 27tf = 2007t (rad/s).
D o do: cp = cot = 20071.2,5 =

VVd=^

(9)

T r o n g do: L , I Ian l u g t la m o m e n d o n g l u g n g va m o m e n q u a n t i n h cua vat
ran d o i v o i true quay. D o n g nang cua vat ran co d o n v i la j u n , k i h i e u J.
quay q u a n h m p t true co d i n h bang t o n g cong thuc hien b o i m o m e n ngoai luc

tac d u n g vao vat. Ta co:
• AW,=llco2-llco?=i(co^-co2) = A

(10)

T r o n g do: I la m o m e n quan t i n h ciia vat ran d o i v o i true quay, coi la.to'c dp
goc liic d a u ciia vat ran, C02 la to'c dp goc liic sau ciia vat ran, A la t o n g cong ciia
cac m o m e n ngoai luc tac d u n g vao vat ran, AWd la d p b i e n t h i e n d p n g nang ciia
vat ran.

Dang 1. B A I T A P L I E N Q U A N D E N C H U Y E N D O N G Q U A Y D E U

(rad) => C h p n C

50m, quay deu v o i toe dp 120 v o n g / p h i i t . Toe d p d a i tai m p t d i e m n a m a
v a n h canh quat bang:
A . 112,6m/s

B. 314 m/s

C. 412 m/s

D . 538 m/s.

Huang dan giai:
in
r — 2
Ta co: co = 120 v o n g / p h i i t = in rad/s; ^ = ^ = 25m .
2
D o do: v = co.r = 4.3,14.25 = 314(m / s)

Chpn B

V i d u 3: M p t vat ran quay q u a n h m p t true co d m h x u y e n qua vat v o i
p h u a n g t r i n h tpa d p goc cp = 5,6 + 4,5t, t r o n g do cj) t i n h bang r a d i a n (rad) va t
t i n h bang giay (s). M p t d i e m tren vat each true quay k h o a n g r = 6em t h i co
toe d p dai bang:
A . 12cm/s

VI D V MINH HQA

SOOTI

V i d u 2: M p t canh quat ciia m a y phat dien chay bang sue gio c6 d u o n g k i n h

b . D i n h l y b i e n t h i e n d p n g n a n g : D o bien thien d o n g n a n g cua m o t vat ran

I I . C A C D A N G B A I T A P vA

=

(vi m 6 i v o n g vat ran quay d u p e m p t goc la 2rc rad).

4. D p n g n a n g ciia v a t r a n q u a y q u a n h m p t true.

W,=llco2

So' v o n g vat ran quay dupe: " = ^

Khattg Viet

B. 18 cm/s

C. 27 cm/s

D . 35 cm/s

Huang dan giai:
T u phucmg t r i n h c = 5,6 + 4,5t ta suy ta: co = cp' = 4,5rad / s
p
Vay V = co.r = 4,5.6 = 2 7 ( c m / s) => C h p n C

CUA VATRAN
P h u o n g p h a p g i a i : V a n d u n g cac kien t h i i c ve chuyen d p n g quay deu ciia
vat ran:
•

Dang 2. B A I T A P L I E N Q U A N D E N C H U Y E N D Q N G Q U A Y B I E N

To'c d p goc: CO bang hang so'.

DOI DEUCUAVAT RAN

•

Gia toe goc: Y = 0.

•

Tpa d p goc ( p h u o n g t r i n h chuyen d p n g ciia vat ran quay deu q u a n h m p t

t r v c c o ' d j n h ) : (P = (PQ + cot

'
'

'

L i e n he giCra to'c d p goc va to'c dp d a i : v = cor
Gia toe h u o n g tarn: a,., = — = a)^r

P h u o n g p h a p g i a i : Sii d u n g cac p h u o n g t r i n h chuyen d p n g quay bien d o i
deu ciia vat ran q u a n h m p t true eo d j n h n h u sau:
co = coo + y t ;

;
1

0 g'v; i , ;

.2

cp = (p(,+coot + - Y t ;
co^-co^ =2y((p-cpy)

^ ^


„"J—

^

^

Trong do c> la toa do goc tai thai diem ban dau t = 0; coo la toe dp goc tai
}o
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„ = — = c r
o
> Thanh phan gia toe tiep tuyen

co dp Ian: a, = — = ry

> Vec to gia toe a dupe xae dinh: a = a„ + a(; ve dp ion: a = -Ja^+a^
V i dy 1: Mpt banh xe quay nhanh dan deu tir trang thai dung yen, sau 4s
banh xe dat van toe goc 24 rad/s. Goc ma banh xe quay dupe trong thai gian
do la:
A.23rad.

B.37rad.

C. 48 rad.

D. 55 rad.

Huong dan giai:
_
,
co-cog 2 4 - 0
^ . , 2
Ta co: y =
=
= 6rad / s
t-to
4
Tu
co^ - co^ = 2yAcp
=>Acp = ^

2y

=^

i ^
2.6

Huong dan giai:

j . w..,^

A p dung cong thuc: co = cO(, + y t , trong do coy = 1 2 r a d / 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 + i Y t ^ =0 + 12.2-i.6.2^ =12rad
ChpnD
V i d u 3: Mpt banh xe co duong kinh 54 cm quay nhanh dan deu, trong 5
giay van toe goc tang t u 180 vong/phiit len 480 vong/ phiit. Gia toe huong
tam ciia diem M a vanh banh xe sau khi tang toe dupe 3,5s la
A. 330,4 m / s l

B. 411,2 mls\. 456,3 m/s^

D. 512,7 m / s l

Huang dan giai:
Ta co: COQ - 67irad / s va co = 16rcrad/s.^
y=

CO-co,)

=

167t-6K

^

, , 2

= 27i:rad / s

Sau 2s, van toe goc bang: co = COQ + yt = 671 +27i,5 = 137trad / s
Gia toe huang tam: a^, = co^R = co^ ^ = (l37r)^

:%

= 456,3m /

Chon C

= 48rad^ChonC

V i d\ 2: Mpt vat ran dang quay deu quanh mpt true co dinh vai toe dp goc
12 rad/s thi chju mpt luc ham tac dung va chuyen dong quay cham dan deu
voi gia toe goc 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 t u khi banh xe chju lire ham tac dung den liic dirng lai va goc
quay trong khoang thai gian do la
A. t = Is; c = 6,7 rad.
p

B. t = 1,5 s; c = 7,5 rad.
p

C. t = 3 s; (p = 11 rad.

D. t = 2 s; c = 12 rad.
p

/

k
Dang 3. B A I TAP LIEN Q U A N DEN M O M E N Q U A N T I N H CUA V A T
R A N , HE V A T R A N
Phuong phap giai: Su dyng cac kien thuc sau: I = " ^ i ^ ^
> Momen quan tinh ciia mpt so vat ran co true quay doi xung:

^

• Thanh dong chat co khol lupng m va co tie't di?n nho so voi chieu dai 1
ciia no, true quay A d i qua trung diem ciia thanh va vuong goc vai thanh:
U-lml^.
^2

;,,


K i thuatgidi

nhatih

BTTN

Vat Li 12, tap 1 - Nguyen

Quanx

Lac

Cty TNHH

• 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 cau dac dong chat c6 khoi luong m, c6 ban kinh R, true quay A di
qua tam qua cau: I =—mR^

; > Momen quan tinh cua he vat ran: I = Ii +12 + ...
i trong do: Ii, I2,... Ian l u ^ t la momen quan tinh cua eae vat ran m j , m^...
V i du 1: Hai qua cau 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
=51211

C.I,

=512

12

D.l2

= 314I,

Huong dan gidi:
Goi D la khoi lu-gng rieng cua; V i va V2 la the tich ciia cac qua cau.
Ta c6:

m^ = D.V^ =
5

B. 0,27 kg.m^.

C. 0,54 kg.m^.

Viet

D. 1,2 kg.m^.

Huang dan gidi:
Theo djnh ly true song song, ta c6:

{'^

) ^ ,:

=> Chgn C

Trong do: d la khoang each vuong goc t u true quay O den true song song
qua trong tam G ciia vat; lo; Ic; tuong ung la momen quan tinh eiia vat doi voi

true O va true G

B.I2

Khattg

I = I c + md^ = | m R 2 + mR^ = | m R 2 = |.4.0,3^ = 0,54(kgm2)

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

A . I i = 314l2

DWH

V i dy 3: Mot dia tron dong chat c6 ban kinh 30 cm, kho'i lugng m = 4kg.
Momen quan tinh ciia dla doi voi mot true quay vuong goc voi mat dla tai
mot diem tren vanh c6 gia tri nao sau day?
A. 0,12 kg.m^.

qua tam dia tron va vuong goc voi mat dla: I = — mR

MTV

D.y

.R^;

=

D.V2 =

^-^^l

5

Dang 4:

,^ v

BAI TAP LIEN Q U A N D E N PHl/ONG TRINH D Q N G

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

Ll/C

D I N H

Phuong phap giai:
• Van dung phuang trinh dong lye hoc ciia vat ran quay quanh mot true
CO djnh M = l y va phuong phap dong lue hoe de giai bai toan chuyen dong
quay ciia vat rSn.
• Khi tinh momen lue, ta ap dung eong thuc M = Fd va luu y rang M c6 the
nhan gia tri duong hoac am, 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

U2J

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

yen thi chiu tac dung boi mot lue F tiep xiic voi mep ngoai vanh. Bo qua moi

V i du 2: Mot 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^.

Huang dan gidi:
Ta c6: I = ^ m l ^ = ^ 5 . 1 , 2 ^ = 0,6kgm2 =^ Chon B

D. 0,12 k g m l

ma sat. Sau 3s vanh tron quay dugc mot goe 36 rad. Do Ion eiia lue F la
A, I N .

B. 2 N .

C. 4N,

D. 8N.

Huang dan gidi:
Taco: {p = | 7 t ^ =36(rad)=>y = 8 r a d / s ^ I = mR^ - 0 , 5 ( k g m ^ j
Momen lue: M = F.R = I7 = 8.0,5 = 4 ( N m )
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^.

Dang 5: BAI TAP LifiN Q U A N D E N D I N H L U A T BAO T O A N
MOMEN D O N G LU'ONG
Phuang phap giai: Su dung cac kien thuc sau:
ô*ã
ã 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; c la toe dp
o
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:
n

#
L = Li + L 2 + . . . +Ln=

Goc ma dia quay dupe: c - -^yt^ = -^.20.5^ = 250(rad).
p
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
CO gia trj
A. M l = 11,3 N.m
C. M l = 33,4 N.m

B. M l =26,4 N.m
D. M i = 48,6 N.m

i=i

Trong do:

Lj=IjCOj

,

• Neu momen luc bang khong thi ap dyng dinh luat bao toan momen
dpng lupng:
Ltnrac = Ls.iu
• Neu momen luc khac khong thi ap dung djnh ly ve dp bien thien mo
men dpng lupng:

^ -M
dt

Vi dy 1: Mpt thanh cung, nh^, manh dai Im, quay xung quanh mpt true
vuong goc vai thanh va di qua tam. GSn vao hai dau thanh hai chat diem c6
kho'i lupng la m, = 2kg va
= 1,5kg. Thanh quay deu quanh tryc, moi qua
cau CO toe dp la 5 m/s. Tinh momen dpng lupng cua he.
A. 3,55 kgm^s

B. 4, 65 kgm^s

Huang dan gidi:

C. 6,75kgm^s

D. 8,75 kgm^s

Huang dan gidi:

Ban dau: M = M j + M^^ = 24(N.m)
Toe dp goc cua moi qua cau:

Toe dp goc ciia banh xe liic CO M i :

=^ =

- lO(rad)

Momen dpng lupng ciia h^:

CO = COQ + yt -> 7 = 2rad / s^

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

Momen quan tinh ciia banh xe:
, M 24
2\
I = - = - = 12(kg.m2)

= ^miR^+m2R^)(o = (mi+m2)R^.a)

= 3,5.0,5h^l0 = 8,75(kg.m2/sj
Khi M l thoi tac dung: co' = to + y't = 0

'

f

t'

y' = -0,2rad / s^

Suy ra: M^^ = y'l =-0,2.12 =-2,4(Nm)
Vay M l = M - M ^ , =26,4(N.m).=>ChpnB

=> Chpn D
Vi dy 2: Mpt nguoi c6 khoi lupng 50kg dung 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 d p goc cua san la bao nhieu?
A . c u n g chieu v a i chieu chay ciia n g u o i v a i toe dg l , 0 5 ( r a d / s)
B. nguoc eiiieu v o i chieu chay eiia n g u a i v o i toe d o - l , 0 5 ( r a d / s)
C. eiing chieu v o i chieu chay eiia n g u o i v o i toe d o 3,05(rad / s)

V i d u 3:. M o t san quay h i n h t r u c6 k h o i l u g n g M = 180kg va ban k i n h
R = 1,2m dang d u n g yen. M o t n g u o i k h o i l u g n g m = 40kg chay tren m a t dat
v a i toe d o 3m/s theo p h u a n g tiep tuyen v d i mep san va nhay len san. Bo qua
ma sat 6 true quay. T i n h toe d o ciia n g u o i do k h i o tren san.
A . 0,52 m/s

B. 0,72m/s

lai chay theo p h u a n g tiep tuye'n eiia san tai M v a i toe d o n h u tren. H o i toe
'

'»

'

'

C. - 0 , 5 2 5 ( r a d / s)

B. 1,425 (rad/s)

L , = 1,(0, = m . R ^ . ^ = m R v j
M o m e n d g n g l u g n g eiia he k h i n g u o i nhay len san:

D . -1,425 (rad/s)

Huang dan gidi:

L2=(li+l2)«2

K h i n g u o i chay q u a n h mep san t h : m o m e n d o n g l u g n g ciia he k h i d o la:

Hay

L | = IjCOj +I2CO2

Do m o m e n d o n g l u g n g duge bao toan, nen: L i = Lo.

Tir d o :

V2

= - ^ ^ ^ i ^ _2m(o^ _

2

CO,

2

D o 0)1, C02 khae dau nen san se quay theo chieu nguge v o i chieu chay ciia
n g u a i v a i toe d o goc: ©2 = = = = - l , 0 5 ( r a d

/ s)

=> C h g n B
b) K h i n g u a i chay den d i e m M t h i : L2 = I,o), +12(02
D o m o m e n d g n g l u g n g d u g e bao toan nen: L2 = Lo. Suy ra:

^=-M._
^2

"
'
50
,
Thay so: CO2 = - - — 0 , =
2.200 '
Chgn C
14

mv.

'

2

2

i
M

40+

1

^

2

Dang 6. B A I T A P

y2y

T R O N G

(0,

8

=

^"^2

4,2

4.R

4.2

m + — M .R.v.
2

^

'

D E N D O N G

N A N G C U A VAT

D O N G

RAN

QUAY

P h u o n g p h a p g i a i : Su d u n g eac kien thuc sau:
• D g n g nang eiia vat ran quay q u a n h m o t true co d j n h : Wd = ^Ico^
• D g n g nang ciia vat ran vua quay vira chuyen d g n g tjnh tien:
2

^
2
+ — mvr-

2

^

v o i V(^ la van toe k h o i tam

mjCOj

v

13

CHUYEN

1
2

m2R^
2

v2

R

= 2^.0,92(m/s)

.180

LIEN QUAN

W J == -ICO
(0,

^

2

Chgn D

r,coj +I2CO2 = 0

Tudo:

=

m+
=

mR2+-MR2

m R , = m + — M .R.v.
2

Suy ra:
+ l2«;= 0 ^

=

Theo d j n h luat bao toan m o m e n d g n g l u g n g , ta eo: L2 = L i

a) Ban dau he d u n g yen nen m o m e n d o n g l u g n g : Lo = 0.

1,0,

. ,

M o m e n d g n g l u g n g ciia n g u o i truoc k h i nhay len san:

do goc cua san k h i d o la bao nhieu?
A. 0,525(rad / s)

D . 0,92m/s

Hu&ng dan gidi:

D . nguge chieu v a i chieu chay eiia n g u o i v o i toe d o - 3 , 0 5 ( r a d / s )
b) N g u o i nay chay dan vao giua san k h i den d i e m M each true quay I m t h i

C. 0,82m/s

V i d u 1 : M o t k h o i cau dac d o n g chat eo khoi l u g n g m = 80 kg, ban k i n h 0,6m.
/
\
= - 0 , 5 2 5 ( r a d / s)

K h o i cau quay q u a n h true d i qua tam ciia no. T i m d g n g nang ciia k h o i cau

k h i toe d o goc ciia khoi cau la 20 rad/s.
A . 1234J

B.2304J

C. 3156J

D . 4758J


Huang dan gidi:

Huong dan gidi:

Do banh xe quay deu, nen tong momen lyc:

Momen quan tinh ciia khoi cau la: I = - m R ^ = -.80.0,6^ = l l , 5 2 ( k g m ^ )
Dgng nang cua khoi cau la: W j = ijco^ =

11,52.20^ = 2304(j) => Chon B

M =M +M ^ =0

M „ , = - M = -60(N.m)
fO-CO(,

0-50

r / ' j / 2 \

Gia toe goc ciia banh xe: 7 = — ^ — =

= -5^rad / s j

V i dy 2: Mot banh da hinh try khoi lugng m = 100kg, ban kinh R = 30cm
chju tac dung ciia mot momen lyc khong doi M = 36 N.m.

, , , , M -60
2
Momen quan tmh: I = — = —r- = 12kg.m
y
b

a) Can bao nhieu thoi gian de tang toe banh da t u trang thai nghi den toe dp
goc bang 12 rad/s.

Cong cua lyc ma sat:
A ^ , = AW, - W , o = - i l o ) ^ - 1 . 1 2 . 5 0 2 =-15000(j) = -15kJ

A. 0,5s .
B. 1,5s
C.2,5s
D. 3,5s
b) Dpng nang ciia banh da a toe dp goc 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^)
I
4,5
V
/
Thoi gian can thiet: t - ^^Z^ =

=> Chpn C
V i 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

= ] 5 ( 3 ) ^ Chpn B

A. 0,6Nm

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

A.40J

D. 3,6Nm

C.80J

B.60J

D. 120J

c) Nang lupng toan phan da truyen cho dia.
A. 80J

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

C. 2,4Nm

b) Dpng nang dia nhan dupe

= i l t o ^ = 1.4,5.122 = 324(J) =^ Chpn C

^ang

B. l,2Nm

B. 120J

Phuong phap giai: Djnh ly ve dpng nang::
AWd = Wd2 - Wdi = ll(co2 - 0)2) = A = MA(p
Trong do: As = rAcp
Chu y: Doi voi cong phat dpng c6 gia trj duong (A > 0), doi voi cong can c6

gia tri am (A < 0 )
V i dy 1: Tac dyng vao banh xe mot momen lyc khong doi M = 60N.m thi
banh xe quay deu voi toe dp goc co = 50rad/s. Thoi tac dung momen lyc M
thi sau 10s banh xe se dung lai. Tim cong ciia lyc ma sat tac dung vao banh
xe ke t u khi thoi tac dung momen lyc M den khi banh xe dung lai.
A. -3kJ
B.-9kJ
C.-15kJ
D. -23kJ

D. 240J

Huang dan gidi:

D Q N G

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

C. 200J

a) Gia toe goc cua dia: y =

=^

= 400(rad / s^)

Momen lyc ma sat tac dyng len dia: M = ly = 6.10"^.400 = 2,4(N.m)
=>ChpnC
b) Dpng nang dia nhan dupe: W j = ^Ico^ = i.6.10"^2002 = 120(j)

•

=> Chpn D
c) Nang lupng de thang c6ng cua lye ma sat can tro ehuyen dpng eua banh da, giir
cho banh da quay voi t6c dp goc khong doi (thanh phan 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 )
=> Chpn D

THUV!ENTiNHBINH25^U^
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.
B.2NvalN

C. l N v a 2 N

D.2Nva2N

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
lugt la:
COJ-COQ

10-0

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'
^gOOvong/phiit. Trong 2,5s banh x e q u a y dupe m p t g o c la
A.

yi

doi

D. SOOTI raD.

rad

>

i

,,

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

(p

= cot = 16071.2,5 = 40071 (rad) => Chpn C

Cau 2. Mpt canh quat

voi toe dp goc khong doi co = lOOrad/s. Toe dp dai ciia

quay

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

= 2(rad/s2j;

Cau 3. Coi Trai Dat la

= -2 r a d / s 2 ) ;

x i e h dao

— I — ^ —r-

Khi thoi tac dyng lyc F, ta c6: M

C. 400 n

goc k h o n g

Huang dan gidi:

Nam. Ban
0-10

_Q)2-C0j

B. SOOn rad

2007Trad

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

a) Xac dinh lyc F va lyc ma sat.
; A. I N v a l N

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

kinh trung

co g i a t r i nao

mpt

qua cau ran quay

quanh tryc co

deu

binh ciia Trai Dat la 6370 km. Van toe dai ciia
sau

A. 435 m/s.

dinh
mpt

Bac -

diem 6

day?

B. 56 m/s.

C. 756 m/s.

D. 463 m/s.

Huang dan gidi:

= Iy„
Ta co: ^ = ~

Trai Dat quay quanh dupe m p t vong het 24h nen:

Do do: F^, =-ImR.y^ =-|.5.0,2.(-2) = 1(N)
Trong giai doan c6 lye F tac dyng: M j - M^^^ =

~ ^ms

CO - — — — * 7,3.10"^ rad / s
24.60.60

= ^Yi

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

Suy ra:

=> Chpn D
( F - F m s ) R = ^ n ^ R ' y i ^ F - F m s = ^ n ^ - Y i = ^•50,2.2 = 1 ( N )

Cau 4. Mpt canh quat ciia may phat d i f n chay bang siie gio co duang kinh

Vay F = F^3 +1 = 1 + 1 = 2 ( N ) ^ Chpn B

khoang 64m, quay deu voi toe dp 120 vong/phiit. Toe dp d a i tai mpt diem nam
o vanh canh

b) Cong ciia lyc ma sat 6 giai doan hai:

A. 88,94 m/s

A„,s2 = W d 2 - W d , = -^Ico2 = - i i m R 2 . c o ?

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

bang:
B. 136,83 m/s

=1.1.5.0,22.102 = - 5 ( j )

Ap dyng djnh ly dong nang cho giai doan mpt, ta c6:
A, + A ^ , = AWj -

quat

C. 382,71 m/s

Huang dan gidi:
Ta co: v = cor, voi co = 120 vong/phiit = 4n rad/s;

Yj = 72

va ti = t2 nen:

; Suy ra: A F = 5 -

Amsi

A m s i = Ams2 = -5

(J)

= 5 + 5= 10 Q). => Chgn C

= ^ = •^^m .

Do do: V = 4.3,14.32 = 401,92 (m/s) ^ Chpn D
QSJIS. Mpt vat ran quay quanh mpt tryc co

Do

D. 401,92 m/s.

trinh tpa dp goc

cp

= 5 + 2,5t, trong do

cp t i n h

djnh

xuyen qua vat voi phuong

bang radian (rad) va t rinh bang

giay

(s). Mpt diem tren vat each true quay khoang r = 4cm t h i co toe dp dai bang
A.5cm/s

B. lOem/s

C.20cm/s

D.25cm/s
iq


Cty TNHH MTV DWH

Huang dan gidi:
Tir phuong trinh < = 5 + 2,5t ta suy ta: co = (p' = 2,5rad/s
p
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 tri 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:

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

Cau 12. Coi Trai Dat la mot vat ran quay deu quanh trye co djnh Bac - Nam.
A. 7,3.10"^rad/s

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
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

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 bi ham lai voi 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.

B. 42 rad/s.

C. 4,7 rad/s.

2

Taco:
D. 0,47 rad/s.

Huang dan gidi:
„

,

Ta co: co =

400.271

, ,

^,

goc trung binh trong thoi gian tang toe cua banh da la
B. 27i (rad/s^)

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:
C. 1 5 r a d / s ^

D.25rad/s^

At

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

Huang dan gidi:
Ap dyng cong thue: y = — =

ChpnB

Cau 14.Mot banh da dupe dua den toe dp 240 vong/phiit trong 4 giay. Gia toe

„

= 42rad / s => Chon B

B. l O r a d / s ^

D. 563 rad.

2

Acp = cp-cpo = ^ ^ ^ ^ =
= 128rad
2y
2.(-4)

A. 7i(rad/s2)

A.2,5rad/s^

C. 350 rad.

Huang dan gidi:

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

y

B. 7,3.10"^rad/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

A. 470 rad/s.

Chpn B

C. 73.10"^rad / s

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

B. 1783m/s2

. ^ ,

Toe dp goe ciia Trai Dat bang.

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

A. n23m/s2

Khang Vift

= 2,5rad / s^ => Chpn A

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^.

2

C. 5,0 rad/sl

D. 7,51 rad/s^.

Huang dan gidi:

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

Taco: y = ^ 1 ^ = ^

t-to
5

= 5 r a d / = ^ Chpn C

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,25rad

B. 2,5rad

C. 5,0rad

D. 8,5 rad


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

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.

, •

T r o n g do: (pg = 0; COQ = 207i(rad / s)

^

'

Goc ma vat quay d u g c t r o n g 1 s cuoi c i m g truoc k h i d u n g l a i la:
^(t=5) ~ ^(1=4) = 2,5rad => C h p n B

i , ,.

;•.

Cau 17. M o t banh xe d a n g quay v o i v a n toe goc 40 rad/s t h i bj h a m lai v o i gia

Thay so ta d u p e cp = 0 + 20n.20 - ^ 7 t . 2 0 ^ = 2007t(rad)

So'vong banh xe quay d u p e la: n = — =

''

' ' ' ' ''

^ ^'

= JOO v o n g => C h p n D

toe goc k h o n g d o i c6 dp I o n 4 rad/s^. T h a i gian tit liic h a m t a i liic b a n h xe d i m g
Cau 2 0 . M p t b a n h da ciia d p n g ea quay n h a n h d a n deu, sau k h i k h o i d p n g

han la
A . 4,7 s.

B.6,9s.

C. 10 s.

D . 17 s.

dupe 2s t h i goc quay ciia banh da la 14 rad. Toe dp goc tai t h o i d i e m d o la:
A . 13 rad/s.

Huang dan gidi:

B. 14 rad/s.

C. 15 rad/s.

D . 16 rad/s.

Huang dan gidi:
Theo cong thiic:

y= "

,•

=> T h o i gian tir liie h a m t a i liic banh xe d u n g
Ap d u n g cong t h i i e cp = (PQ + cogt + i y t ^ , chpn m o c t h a i g i a n liic vat bat d a u

hinla: t = ^

=
y

° : i i ^ = 10s =^ Chpn C
-4

k h o i d p n g va eo tpa d p goc ban dau bang 0, suy ra:
1 2
2(p 2.14 ^
, 2
^ = -7^^ =>y = - ^ =
= 7rad/s
2
t
4

Cau 18. M p t vat ran quay bien d o i deu c6 p h u o n g t r i n h chuyen 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.

Mae khae y = ^

=^=> oi = yy = 7.2 = 14rad / s => C h p n B

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

Cau 2 1 . M o t v a t ran bat dau quay q u a n h true ciia no v o i gia toe goc k h o n g d o i .

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

Sau 5s no quay d u p e m p t goc 50 rad. C h p n moc t h o i g i a n t = 0 tai t h o i d i e m vat

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

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 quay

Huang dan gidi:

ciia vat rSn. Toe d p goe tai t h o i d i e m t = 5s bang:
P h u o n g t r i n h eiia chuyen d p n g quay bien d o i deu eiia vat ran q u a n g t r y c co
djnhcodang:

B. 20 rad/s.

(p = (pQ+a)Qt + i y t ^

D . 80 rad/s.

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 vat ran 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 quay eiia v a t r ^ .

Vay ket l u a n COQ = 5rad / s la sai => C h p n C
Cau 1 9 . M o t banh xe d a n g quay v o i v a n toe goc ban dau 20n (rad/s), t h i bat dau
quay cham dan deu va d u n g lai sau t h o i gian t = 20s. So v o n g banh xe quay
d u p e cho den k h i d u n g hMn la

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

C. 200 v o n g

D . 100 v o n g .

Huang dan gidi:
C h p n moc t h o i gian t = 0 tai thai 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.

'^^^

quay nen toe d p goc ban d a u
1 ^

B. 300 v o n g

C. 50 rad/s.

Huong dan gidi:

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

A . 400 v o n g .

A . 30 rad/s.

2(p

(OQ = 0 =>(p = — y t :=> y = =

2
t^

2.50

,

, , 2

—— = 4rad/s
5^

V i vat quay 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 bang 4rad / s^


Huang dan gidi:

A p dyng cong thiic: 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

Taco:
COQ = 180 vong/phiit = 671 (rad/s); co = 480 vong/phiit = 16Tt (rad/s)
Gia toe goc: y =

a)-cO(.

^=

1671-671

^ /

.

= 27r rad /

7\.

i

=> Chpn B

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

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

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

quay cham dan voi gia toe khong doi b5ng 4,0 rad/s^ quanh true doi xung

khoang thai gian do la

vuong goe vol vong tron. Thai gian va goc quay ke t u Iiic chat diem bat dau

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.

chuyen dpng cham dan deu den liie dung lai Ian lupt la
B. t = 40s; (p = 3600 rad.

C.t = 20s; 9 = 1200 rad.

Huang dan gidi:

A. t = 30s; (p = 1800 rad.

*

D. t = 40s; 9 = 2400 rad.
Huong dan gidi:

A p dung cong thiic: a) = (Oo + yt, trong do COQ =10rad/s, v i vat ran quay

A p dung cong thue: o) = C0(, + yt.

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.

Khi dung lai: co = 0

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

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

toe dp goc ban dau (pg ~ • Chpn chieu duong la chieu quay cua vat ran.
Ap dung cong thue:
(p =

Y
2

= 30(s)
.,2

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 t u thai diem Os den thai diem 10s la

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

A. 45 rad

=> Chpn B

B. 38 rad

C. 75 rad

D. 125 rad.

'

Huang dan gidi:

Cau 23. Banh da cua mpt dpng ca, tir luc khoi dpng den k h i dat toe dp goc
120 rad/s, da quay duac goc bang 240 rad. Bie't banh da quay nhanh dan deu. Thai
gian t u liic bat dau khoi dpng den khi banh da dat toe dp 4800 vong/phiit la:
A. 9,76 s

B. 12,48 s

C. 16,75 s

D. 28,12 s

Huang dan gidi:
2

2

Taco: co^ -co^ = 2 y ( p ^ y = — =
= 3ofrad/s^]
°
' 29 2.240
\
CO' = 4800 (vong/phiit) = 1607T(rad/s)
t =^

t=

y

= 1^.16,75(s)=>ChonC
30
^'

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^

#

Sau ti = 8s taco: 9 , = i y t ? ^ y = ^ = ^
= 2,5f rad / sM
2
t^
8^
^
'
T u 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

Huang dan gidi:
1
2
Ta c6: 9 = — yt^ => y = — = 2 (v6ng/s^).
Toe dp goc sau 12s la: co = COQ + yt = 24 (v6ng/s).

D. 321 vong.
-«
-


.2

„ 2

So'vong quay d u g c sau 12s la: Acp = " ^

=144 (vong).

Ket qua tren cho thay:
-

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

Cau 28. M o t banh da d a n g quay q u a n h true v o i toe do goe 240 vong/phiit thi

=> B d u n g
-

quay eham lai v i c6 m a sat v o i o trye. Sau 1 giay, toe d p ehi con 0,6 Ian toe do
ban d a u , eoi ma sat la k h o n g d o i . 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
60

= 87r(RAD /S), suy ra:

Gia toe goc eiia vat y = - 1 (rad/s^) k h o n g thay d o i theo t h o i gian
=> C d i i n g

-

V i gia toe goc ciia vat k h o n g thay d o i theo t h a i gian nen m o m e n l y e tac

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

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

Cau 3 1 . M p t cai dla d a n g quay v o i toe d p goc 5 rad/s t h i bat d a u quay eham

Huang dan gidi:
Ta eo: COQ =

Toe dp goc ciia vat 00 = - 5 - 1 (rad/s) la h a m so'bae nha't theo t h o i gian

dan deu, sau 5s t h i no d u n g lai. So v o n g ma dia da quay d u p e t r o n g t h a i gian
= 0,6tOo = 4,87t(rad / s ) .

do xap xi bang:
A. 0,85 v o n g

B. 1,99 v o n g

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:

C. 2,15 v o n g

D . 3,39 v o n g

Huang dan gidi:

= O)Q + yt = 87i3,27t.2 = l , 6 7 t ( r a d / s)

=> C h p n D
Cau 29. M o t vat ran quay q u a n h m o t true co'djnh x u y e n qua vat. P h u a n g trinh

(0 -

-5
/
T \
= — = -l|rad/s j

Goc ma dia quay d u p e cho den k h i d u n g lai la:
< = co„t + -^yt^ = 5.5 + ^ . ( - l ) . 5 ^ = - 1 2 , 5 ( r a d )
p

ehuyen d p n g eiia vat cp(t) = 2 + 2t + t ^ , t r o n g 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

C0(,

Gia toe goe eua dTa: y = — p ^

^ ,^

Suy ra so v o n g dTa quay d u p e t r o n g t h o i gian d o la:

n

bang bao n h i e u vao t h o i d i e m t = I s ?
A. 6cm/s

B. 14 cm/s

C. 26 em/s

n =

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 t h o i 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

A. Vat quay eham dan deu
B. Toe d p goc eua v ^ t la h a m so'bae nhat theo t h a i gian

=

*
2.3,14

1,99 v o n g = > C h o n B
^

£ju_32.Mpt b a n h da quay n h a n h dan deu t u t r a n g thai n g h i , v o i gia toe goc
0,57t

rad/s^. De banh da dat toi toe d p goe

247t

rad/s t h i no phai quay bao

nhieu v o n g (ke t u t h a i d i e m ban dau)?
A. 144 v o n g

,

B. 288 vong

C. 342 v o n g

D . 563 v o n g

Huang dan gidi:

Cau 30. M o t vat ran quay q u a n h 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?

2K

T

'

2

2

00^

-

COJ^

T a c o : co - co^ = 2y(p ^ (p = — - — =

CO^

/

, \

— = 5767i(rad)

So v o n g banh da quay dupe la: n = — =

= 288 v o n g => C h p n B

C. Gia toe goc eua vat k h o n g thay d o i theo t h o i gian
D. M o m e n lue tac d y n g len vat k h o n g d o i theo t h o i gian
Huang dan gidi:
Ta eo:
^

co = - 5 - t (rad/s)
y = -l(rad/s2)

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 d p goc 120
rad/s, da quay d u p e goe b^ng 180 rad. Biet banh da quay nhanh d a n deu. T h a i

gian t u liie bat d a u 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

Huong dan gidi:

D. 9,42 s


Huong dan gidi:
Ta c6: COQ = 0 (rad/s); coj = 120 (rad/s); coj = 3600 v o n g / p h i i t = 120Tt (rad)
'0
- en _ 120^

_ (Of

2.180

2cp

1207C-0

-(0

= cOg + yt => t =

-0

40

Y

Ta c6: v = Q)r = (yt)r = (2,4.2,5).3,5 = 21 (m/s) => C h p n B
Cau38.Mot banh xe c6 d u o n g k i n h 2,5m quay v o i gia toe goc k h o n g d o i

= 70(rad/s2)

3,5 r a d M t h a i gian ban dau to = 0 la liic banh xe hk

mpt d i e m N tren vanh banh xe 6 t h o i d i e m t = 4 s bang

A. 21 m/s.

= 9,42(s)

xe dat van toe goe 12 rad/s. Goe ma banh xe quay d u g e t r o n g t h o i gian d o la
A . 9,5 r a d .

B. 18 rad.

C. 36,5 rad.

(o-cop

=

12-0

-(On

2y

lai la
B. 11,2s

C. 13,4s

K h i d u n g lai t h i (o = 0 , s u y r a : t = - ^

12^-0^
2.4

_

= 18rad

= l l , 2 ( s ) => C h p n B

Cau 40. M p t banh xe d a n g q u a y v o i toe d p goc 32 rad/s t h i bi h a m lai v o i m p t

Chc)n B

gia toe goc k h o n g d o i 4 rad/s^. Goe quay dupe t u luc h a m den liic d u n g lai la

A. 72 rad

B. 132 rad

C. 144 rad
2

d i e m 0,4s n h a n gia t r i
B.9,6m/s2

C. 15,8m/s2

D.24,7m/s2

|

Huang dan gidi:
T a c o : a^, = (o^r = ( y t ) ^ = ( 5 . 0 , 4 ) ^ 2 , 4 = 9 , 6 ( m / s ^ )

48t - 2t^ t r o n g d o (p t i n h theo rad, t t i n h bang s. Goc v a t quay d u g e ke tir t h o i
d i e m ban d a u cho den k h i no d u n g lai la
C. 567 rad

^

= 128(rad)

la 4,5 rad/s^. Gia toe tie'p tuyen cua m p t d i e m 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

Cau 42. D o bj m a t dien m p t chie'c may m a i quay cham d a n d e u , biet v a n toe goc

t = 12 (s)
,|

A(p = (p - (po = 315 - 27 = 288 (rad) => C h o n A
Cau 37. M o t b a n h xe c6 d u o n g k i n h 350cm hit dau quay t u n g h i v o i gia toe goc
k h o n g d o i la 2,4 rad/s^. Toe d o dai ciia m p t d i e m tren v a n h banh xe 6 t h a i d i e m
2,5s la
B.2^^

~ ^y.Acp => Aip = — ^ — ^ =

2

T a c o : a , - r.y - 3.4,5 = 1 3 , 5 ( m / s ' J ^ C h p n C

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

A. 14m/s

-^o

2

Cau 41. M o t banh xe eo d u o n g k i n h 3m bat dau quay v o i gia toe goc k h o n g d o i

D . 982 rad

Huang dan gidi:
(o = 4 8 - 4 t = 0

Ap d u n g cong thue:

2

=> C h p n D

Chc)n B

Cau 36. M o t vat ran quay q u a n h m o t true c6' d j n h theo p h u o n g t r i n h cp = 27 +

B. 435 rad

D . 128 r a d

Huang dan gidi:

doi bang 5 rad/s^. Gia toe h u o n g t a m ciia m o t d i e m tren v a n h b a n h xe a t h a i

Taco:

D . 18,9s

Huong dan giai:

Cau 35. M o t b a n h xe c6 d u o n g ki'nh 2,4m bat dau quay v o i gia toe goc k h o n g

A . 288 rad

i.i

=> V a n toe d a i v = (oR = 14.2,5 = 35m/s => C h o n C

A. 5,6s

(0^ - COQ = 2yA(p

A.4,8m/s2

^•

gia toe goe eo d p Ion k h o n g d o i 2,5 rad/s^. T h a i gian t u luc h a m den liic d i r n g
^ i

. . . 2
= 4rad / s''

3

t-tn

(0

D . 49 m/s

Cau 39^ M o t banh xe d a n g quay v o i toe d g goe 28 rad/s t h i b j h a m lai v o i m p t

D . 54 rad.

Huang dan gidi:

A{p =

C. 35 m/s.

V?in toe goe tai t h a i d i e m t = 4s la (o = coo + yt = 0 + 3,5.4 = 14 rad/s

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

Tu

B. 27 m/s.

Huong dan gidi:

Chon D

Ta eo: y =

dau quay. V a n toe d a i eiia

C. 3 5 m / s

ban dau la 360 v o n g / p h u t va gia toe goc la -3n^ r a d / s l So v o n g ma m a y eon c6
the quay d u p e truoe k h i d u n g lai la
A. 12 v o n g

B. 18 v o n g

C. 24 v o n g

D. 36 vong

J

Huang dan gidi:
Ap d u n g cong thue:
(o2-(o2=2y.Acp=^A9 = —

^

= ^ - ^ ^ ^

= 247r(rad)

D. 56m/s
••:^
' v'

—

29

bo v o n g quay: n = —^ =
2n

Huang dan gidi:

= 12 v o n g =?> C h p n A
2n

Cau 43. M o t b a n h xe c6 d u a n g ki'nh 60 cm quay n h a n h d a n d e u t r o n g 2s t h i toe
d p goe tang t u 180 v o n g / p h i i t den 240 v o n g / p h i i t . Gia toe h u o n g t a m ciia d i e m
M tren v a n h banh xe sau 4s la
A . 142m/s2

B. 384m/s2

C. 463 m/s^

D . 600m/s2

Ta eo: coo = 180 v o n g / p h i i t = 6n (rad); coi = 240 v o n g / p h i i t = 87t (rad/s)
coj - COQ _ 87t - 6n
= 7i(rad/s2j
Y=
At
2
((Og

60o|m / s^j =::> C h p n D

+ yt)^ .r = (67t + 71.4)^ .0,6 =

Cau 44. M o t b a n h xe quay n h a n h d a n deu q u a n h m p t true eo d j n h t u t r a n g thai
n g h i . Sau 4s ke t u liic bat dau quay, m p t d i e m each true quay 20 c m c6 gia toe
h u o n g t a m 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„ =
y= ^

=^

= ^f"

= ^

=

^ChonB

C. 8,3 v o n g

D . 12,7 v o n g

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 t u y e n : a, = — = 3,2
^ ^ = -2,5^m / s J
At
Suy ra gia toe goe:

2,5
r

50

(rad/s^j

,

Chpn A

Cau 48. M p t dia t r o n quay n h a n h d a n deu tir trang thai n g h i , sau 5s dat t o i toe

dp goe 10 rad/s. T r o n g 5s d o dTa tron da quay d u p e m p t goe bang
B. 10 rad

C. 25 rad

D . 50 rad

(0^ - C O n

Goe quay d u p e la: A9 = — - — - = 25(rad) => C h p n C
Cau 49. M o t banh xe quay tir liic d u n g yen, sau 2s no dat d u p e toe d p goe
10 rad/s. Gia toe goe t r u n g b i n h va goe quay d u p e t r o n g t h o i g i a n d o Ian l u p t la
A. y = 2 rad/s2; 4) = 4 rad.

A p d u n g cong thue: (o^ - co^ = 2y.A(p => Acp =
2y

B. y = 4 rad/s^; (}) = 8 r a d .

C. y = 3 rad/s^; (j) = 6 r a d .

Gia toe goe cua banh xe: y = — = - 2 , 5 ( r a d / s^).
At
^
/

D . y = 5 rad/s^; cj) = 10 rad
Huang dan gidi:

— = 80(rad)

^
'

Vay, so v o n g quay dupe: n = — = 12,7 v o n g => C h p n D

Gia toe goe t r u n g b i n h ciia vat: Y =

= S^rad / s^

( v o i (oo = 0).

Goe quay d u p e la: Aip = — - — - = 10(rad) => C h p n D

271

Cau 46. M o t xe d u a bat dau chay tren m p t d u o n g d u a h i n h t r o n ban k i n h 256m.
Xe chuyen d p n g n h a n h dan deu, eu sau m o i giay toe dp ciia xe lai tang them
I m / s . Tai v i t r i tren q u y dao ma dp Ion ciia hai gia toe h u o n g t a m va gia toe

£a]i50.Mpt n g u o i d i xe dap k h o i hanh dat d u p e toe d p 18 k m / h t r o n g 25s, biet
d u o n g k i n h ciia banh xe bang 80cm. Gia toe goe t r u n g b i n h ciia l i p xe la
A . y = 0,125 rad/s2.

tie'p t u y e n bang n h a u , toe d p ciia xe la
B. 16m/s

A . Y = 0'05 rad/s2.

A(o
Gia toe eiia vat: y = — = 2(rad / s^) ( v o i COQ = 0)

'
/
At

Huang dan gidi:

A . 8,5m/s

Gia toe goe ciia 6 to tren d u o n g l u p n c6 d p I o n la

Huang dan gidi:

dan d e u . Sau 8s banh xe d u n g lai. So v o n g da quay d u p e eiia banh xe la
B. 6,4 v o n g

= 1 => v = 16m / s => C h p n B

47. M p t 6 to d i vao k h i i c d u o n g l u p n t r o n de chuyen h u o n g . Ban k i n h ciia

A . 5 rad

Cau 45. M o t b a n h xe d a n g quay v a i toe dp goe 20 rad/s t h i hit d a u quay cham
A . 4,6 v o n g

.

X h e o b a i t a , ta c6: a,,, = a , = l | m / s^) => ^

= 20(rad / s)

= 5(rad/s^)

= 1(m /

^ ^ ^ ^ J ^ l u p n la 50m, toe d p 6 to g i a m deu t u 18 m/s x u o n g 10 m/s t r o n g 3,2s.

Huang dan gidi:

Suy ra: a,^, = coj.r =

Gia toe tie'p t u y e n : a^ = ^

C. 24,6 m/s

D . 32 m/s

B. y = 0,25 rad/s^.

C. y = 0,34 rad/s2.

D . y = 0,65 rad/s^


Huang dart gidi:

Q^u 54. M p t v|it r a n d a n g quay q u a n h m p t t r y c c o ' d j n h x u y e n qua v | t v o l toe

Gia toe tie'p t u y e n :

^5 goc 20 rad/s t h i bat d a u quay cham d a n deu va d u n g lai sau 4s. Goc ma vat

Gia toe goe t r u n g b i n h eiia l i p xe bang gia toe goc t r u n g b i n h ciia b a n h xe, ran quay d u p e t r o n g giay cuoi ciing truoc k h i d i m g lai (giay t h u t u t i n h t u liic
bat d a u q u a y c h a m dan) la
nen: y = ^ = a 2 5 ( r a d / s ^ j

A . 1,25 rad

Chpn B

B. 2,5 rad

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

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

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
v o n g quay. Gia toe goc va t h a i g i a n banh xe d u n g lai ke tir liic ngoai l y c d i m g
/

A. y = - — r a d / s 2 , t = llJ4§,, ^
7t

1

B. y =

C. y = - — r a d / s 2 , t = 12,ls

7t

•
>
r a d / s 2 , t = 3,14s

'

Goc ma v a t q u a y d u p e den k h i d u n g l a i : A(p' = —

^
2y

= 40(rad)
^

.

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 )

D . y = - — r a d / s ^ t = 16,14s
n

71

'

40

D . 7,5 r a d

Huang dan gidi:

Cau 51. M o t banh xe nhan d u g c m p t gia toe goc 5 rad/s^ t r o n g 8 giay d u o i tac

tac d p n g la

C. 5 rad

Humtg dan gidi:

Goc vat quay d u p e sau 3s la: Acp =
i

5^ - 20^
2y

-2.(-5)

= 37,5 ( r a d )

Goc vat quay d u p e t r o n g giay t h i i 4 la: 40 - 37,5 = 2,5 (rad) => C h p n B

Toe dp goc eua banh xe sau 8s la: co = yt = 40 (rad/s).
Goc quay eua banh xe ke t u k h i m o m e n ngoai lire thoi tac d u n g :

Cau 55. M p t vat ran quay q u a n h m p t t r y c eo d i n h x u y e n qua vat v o i p h u o n g

cj) = 10 v o n g = 20TT r a d .

trinh toe d p goe: co = 2 + 0,5t, t r o n g do co t i n h bang radian/giay (rad/s) va t t i n h

*
M a t khac, ta c6: - w ^ = 2y,(p -> y, =

bang giay (s). Gia to'c goc eua vat ran bang

2
=
2(p

(rad / s^)
7t ^

'

/

J

Vay t = ^ ^ + 8 = l l , 1 4 ( s ) = > C h o n A
yi

^

bang 1 rad/s^. Tai t h o i d i e m Os t h i banh xe co toe d p goc 3 rad/s. H o i d e n t h o i
d i e m 5s t h i banh xe co toe d p goc b^ng bao nhieu?
B. 4 rad/s

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 t r i n h co = coo + yt, ta suy ra y = 0,5 rad/s^ => C h p n B
Cau_56. T r o n g m p t m a y A - tiit, hai vat nang n o l v o i n h a u b a n g spi day k h o n g

Cau 52. M o t banh da quay n h a n h d a n deu q u a n h true co d j n h v o i gia toe goc

A . 2 rad/s

A . 0,25 rad/s2.

'^

C. 6 rad/s

D . 8 rad/s

CO dan vat qua m p t r o n g rpc. M p t trong hai vat co k h o i l u p n g 200 g, vat kia co
khoi l u p n g 205 g. Rong rpc eo true quay n a m ngang, k h o n g ma sat, co ban k i n h
= 10 c m . K h i d u p e tha t u nghi, n g u o i ta thay qua nang h o n r o i d u p e doan
d u o n g s = 1,8 m t r o n g k h o a n g t h o i gian t = 6 s. Gia toe goe y eua r o n g rpc bang:

Huattg dan gidi:

A. 0,5 rad/sl

B. 1 rad/s^.

A p d u n g cong thuc: co = (oo + yt = 3 + 1.5 = 8 (rad/s) => C h p n D

C. 2 rad/sl

Huang dan gidi:

D . 3 rad/s^
(.; / r:

Cau 53. M o t canh quat d a n g quay v o i toe dp 16 v6ng/s t h i bat d a u quay cham
dan deu va d u n g lai sau t h o i gian 8 giay. Gia toe goe eua canh quat d o co dp
Ion bang bao nhieu?
A.2rad/s2

B. 47i rad/s^

C. 6 rad/s^

Chon B
= I r a d / s^
R
S l i l S T , M p t vat ran quay quanh m p t tryc co d j n h xuyen qua vat. Goe quay c})
Gia toe goe eua r o n g rpc y =

D . 8 n rad/s^

Huang dan gidi:
Toe d p goe ban d a u : coo = 16 v6ng/s = 32TI rad/s.
D p I o n gia toe goe ciia banh xe la: y =
^9

...... .

•^ua vat ran bien thien theo thoi gian t theo p h u o n g t r i n h c = 2 + 2t + t^, trong do
p

= 47c rad / s
At

V
.

Gia toe ciia vat nang a = ^ = 0 , l m / s ^
t^

=> C h p n B
/
—

•i
>

^ tinh bang radian (rad) va t tinh bang giay (s). M p t d i e m tren vat ran va each
trite quay khoang r = 10cm t h i co toe dp dai bang bao nhieu vao t h o i d i e m t = Is?

-»^0.4m/s.

,

B.50m/s.

C. 0,5 m/s.

D.40m/s


Cty TNHH

Huong dan giai:

^J^^^^Tdan deu v o i gia toe goe co d p I o n bSng 20,9 rad/s^. T i n h t u luc b3t d a u

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

quay c h ^ m d a n d e u , h o i sau khoang t h o i gian bao lau t h i b a n h da d i m g 1^1?

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

A . 64s.

B. 90s.

K h i d o toe d o d a i eiia d i e m d o la: v = co.r = 0,4m/s => C h o n A
Cau 58. M o t banh xe eo d i r a n g k i n h 50 em q u a y n h a n h d a n d e u , t r o n g 4 giay
van toe goe tang t u 120 v o n g / p h i i t len 360 v o n g / p h u t . Gia toe h u o n g t a m cua

d i e m M 6 v a n h banh xe sau k h i tang toe d u o e 2 s la
B. 147,8 m M

C. 157,8 m/s^

D . 167,8 m/s^

y=

^ =

Huang dan giai:
Toe d p goc: CO = 3000v6ng/phut = lOOn rad/s.
=

/ '
«15(s)

.. r

Chon C

'

Cau 62. M o t b a n h xe co d u o n g k i n h 4 m q u a y v o i gia toe goc k h o n g d o i 4
ciia m p t d i e m N t r e n v a n h b a n h xe 6 t h o i d i e m t = 2 s bang

„

. , 2

A.84m/s2.

= 27trad / s^

= o)^ | = {Snf

^

B. 128m/s2.

C. 264 m/s^.

D . 386 m/s^

Huang dan giai:

t
4
Sau 2s, v a n toe goe b3ng: co = coo + yt = 47t + 271.2 = STI rad/s
Gia toe h u o n g t a m : a,„ = ^

D . 72 s.

rad/s^ t h o i g i a n b a n d a u to = 0 la liic b a n h xe bat d a u quay. Gia toe h u o n g t a m

Ta co: coo = 47:rad/s va co = 127irad/s.
127t-4n

C. 15s.

T h o i g i a n de banh da d u n g lai: t = —

Huang dan giai:
co-Q)o

Khang Vi?t

(^jfU 6 1 . M p t b a n h da d a n g q u a y v o i toe d p 3000 v o n g / p h i i t t h i bat d a u q u a y

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

A . 137,8m/s2.

MTV DWH

Ta co: CO = coo + yt = 0 + 4.2 = 8rad/s

= 157,8m / s^ => C h o n C

Gia toe hu(?ng t a m a |,, = — = co — = 8 - = 128m / s
R

Cau 59. M o t vat ran quay q u a n h m o t true co d i n h x u y e n qua vat. Goc q u a y c|)

2

=> C h o n B

2

eiia vat bien thien theo t h o i gian t theo p h u o n g t r i n h cp = 15 + t + t^, t r o n g d o c|)

Cau 63. Banh da ciia m p t d o n g co t u liic k h o i d o n g den liic dat toe d p goc 140

t i n h bang radian (rad) va t t i n h bSng giay (s). M o t d i e m tren vat ran va each

rad/s phai mat 2,5s. Biet banh da quay nhanh dan deu. Goc q u a y ciia banh da

true quay k h o a n g r = 10cm t h i gia toe toan phan co d p I o n bang bao n h i e u vao

trong khoang t h o i gian tren bang
A . 175 r a d .
B. 350 rad
C. 70 rad.
Huang dan giai:

t h o i d i e m t = 1 s?
A.0,92m/s2.

B. l , 8 4 m / s l

C. 2,68 m/s^.

D.4,16m/s2

Gia toe goc cua b a n h da: y = — =
At

Huong dan giai:

Theo bai ra, ta co: y = 2 rad/s^ cpo = 1 (rad/s).
V a n toe goe: co = (p'(t) = 1 + 2t

trong t h o i gian tren: Acp =
2y

K h i t = I s t h i (0 = coo + yt = 3 (rad/s). K h i d o :
Gia toe h u o n g t a m : a,,, =co^.r =

dan deu va giay d a u tien n g u o i ta thay m a y quay d u p e m p t v o n g . H o i giay t h u
hai may quay d u p e bao nhieu vong?
m / s^

=> C h o n A

A. 1 vong.

B. 2 v o n g .

C.6m/s2.

Huong dan giai:
Gia toe tiep t u y e n a,j = Ry = 2.3 = 6 m / s^ => C h g n C

C. 3 v o n g .

D. 4 vong

Huang dan giai:

Cau 60. M o t banh xe co d u o n g k i n h 4 m quay v 6 i gia toe goe k h o n g d o i
3 rad/s^. Gia toe tiep t u y e n eiia d i e m N tren vanh banh xe b3ng
B. 3 m / s 2 .

^ = 175(rad I => C h o n A
^
'

" g u o i d e m so v o n g ciia no q u a y d u p e t r o n g m p t giay. Gia s u m a y q u a y n h a n h

Gia toe tiep t u y e n : a, = r.y = 0,2|m / s^ .

A. Im/s2.

5 6 ( r a d / s ^ ) . Goc banh da q u a y d u o e
^
'

Caii_64.De d o gia toe goc ciia m p t chie'c m a y m a i t r o n g giai d o a n tang toe, m p t

0,9|m/s^j

Gia toe toan p h a n cua d i e m d o la: a = ^a^, + a\ 0,92

D . 56 rad

D o COQ = 0 nen g o e q u a y cp-cpy = ^ y t ^

.

'
i

D.9m/s2.
So'vongquay

n =

— ^ = — yt^ => so v o n g q u a y t i I f v o i t^.
271
471

Theo de ra, t r o n g I s quay d u p e 1 v o n g nen t r o n g 2s quay d u p e 4 v o n g .
i ~ > So v o n g q u a y t r o n g giay t h i i 2 la: 4 - 1= 3 v o n g => C h p n C


M

muat

gJAt nhanh

11

tiTTRViU

12, tap

Huang

1 - Nguyen Quang Lac

Cau 65. M o t b a n h xe c6 d u o n g k i n h 50cm quay nhanh dan deu t i r trang thai
d u n g yen, sau 4s t h i toe d p goc dat 120 v o n g / p h i i t . Gia toe h u o n g tarn ciia
d i e m 6 v a n h banh xe sau k h i tang toe dugc
A . 157,9 m M

2s t u trang thai d u n g yen la

B. 9,86m/s2.
Huang

C. 25,1 m M
dan

f2n^

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

gd

VW

k i n h gap 3 Ian rihau R A = 3RB.

gidi:

6"

thue lien h § g i i i a m o m e n q u a n t i n h cua qua

cau do'i v o i true q u a y d i qua t a m ciia m o i qua cau la
A . IA = 68IB

= 7t(rad / s^)

At

^mgd

=> m =

gidi:

Cau 70. H a i qua cau con lac dac l a m c i i n g hang m p t loai thep, d o n g chat eo ban

D . 39,4 m/s^

Toe do goc: (0 = 120 v o n g / p h i i t = 4n rad/s.
Gia toe goc ciia banh xe: y = —

T = 27i

Ta c6:

dan

B. IA = 97IB

ai.

\'

C . I A = 1351B

Huang

'.v

m,=D.V.=D.

Ta eo:

Toe d p goc dat dxxgc sau 2s la: co = C Q + yt = 27i ( r a d / s)
O

dan

D . I A = 2431B

gidi:

471

Gia toe h u o n g tarn cua d i e m a v a n h banh xe la: a = (o^.r = 9,86 (m/s^)
5

Chpn B
Cau 66. M o t banh xe c6 d u o n g k i n h 60 em quay n h a n h dan deu, t r o n g 3s van

R

toe goc tang t u 120 v o n g / p h u t len 300 v o n g / p h i i t . Gia toe tiep t u y e n ciia d i e m
A . 0,157im/s2

B.0,3nm/s2

C. 0,67tm/s2

Huang
Gia toe goc: y =

=

dan

D . 0,97tm/s2

gidi:

,Z

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

3

Gia toe tiep t u y e n : a „ = Ry = 0,3.27t = 0,67tm / s^ => C h p n C

I = 0,4(kg.m^), dao d p n g nho tai n a i eo gia to'c t r o n g t r u a n g g =

m/s^ xung

tinh

Huang
I

Vmgd

= 271

dan

0,4

^1,671^0,25

D.4s'

I^=imirf;l2=im2if

,j

gidi:

= 2(s)

Vi

quan t i n h d o i v o i true quay do se

Huong

C. tang 16 Ian
dan

D. g i a m l 6 1 a n

gidi:

= mr^ - m . ( 4 r ) ^ = 16mr^ = 161 => C h p n C

Cau 69. M p t con lac vat l i c6 m o m e n quan t i n h do'i v o i true quay la 3 kgm^, eo
khoang each t u t r p n g tam den true quay la 0,2 m , dao d p n g tai n o i eo gia toe
r o i t u d o g = 71^ (m/s^) v o i ehu k i rieng la 2,0 s. K h o i l u p n g cua eon lac la:
A . 10 k g

B. 15 k g

,

= 81

it

dan giat:

Tofl^if

mj
m.

^2^

V,

Dodo:

-r =

T~

= 3^ = 81 => C h p n D

Cau 72. M o t d l a t r o n d o n g cha't c6 ban k i n h 50 em, k h o i l u p n g m = 6kg. m o m e n

B. g i a m 4 1 a n

Ta eo: I = mr^. K h i n = 4r t h i

^1

D. ^

=>ChpnB

Cau 68. K h i k h o a n g each t u chat d i e m den true quay tang len 4 Ian t h i m o m e n
A . tang 4 Ian

^ - 2 7

M o m e n quan t i n h cua cac h i n h t r u Ian l u p t la:

eiia con lac la d = 25 cm. C h u k i dao d p n g ciia con lac la:
C.3s

^

Huong

q u a n h m p t true quay n a m ngang v 6 i khoang each t u true quay den t r o n g tarn
B.2s

I1

1

quan

Ta c6: T = 2n,

C.

B.-^ = 9

Cau 67. M o t eon lac vat l y c6 k h o i l u p n g m = 1,6kg, m o m e n

=^ChpnD

r o runff ehieu cao, d u o c l a m b a n g cung m p t

= 27trad / s

t

.A. Is

= 3^=243=>1A=243IB

R

mg-Rg
A-

M tai v a n h banh xe la

^2

C.20kg

D. 12,5 k g

quan t i n h ciia dla d o i v o i m p t true quay v u o n g goc v o i m a t d i a tai m p t d i e m
tren v a n h c6 gia t r j nao sau day?
A.3,0kg.m2.
B.3,75kg.m2.
Huong

C. 7,5 kg.m^.
dan gidi:

D . 2,25 kg.m^
, ,

Theo d j n h l y true song song, ta c6:
37


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

Huang dan gidi:

=>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?
A. I,68kg.m2.

B.2,96kg.m2.

C. 2,88 kg.m^.

D. 3,6 kg.m^

Momen quan tinh ciia h f :

0aTL^^^^

= l l ' ^ " ^ ^ " l,5kgm2 => Chpn B

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
A.0,016kgm2.

B. 0,037 kgm2.

t
D. 0,096 kgm^

C. 0,053 kgm^.

Huong dan gidi:

Huong dan giai:
raf
Ta c6: MC^ = MD^ =
- \ AM2=BM2=a2-h

Ta chon B v i I =

T a e h g n B v i I = mR^ = 0,6.0,4^ =0,096kgm2
5a^

Chon D

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

I2j

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

^ m j . A M ^ +m2.BM^ +m3.CM^ + m , . D M ^ =3,6(kgm^)
=> Chpn D

I = |mR2 =0,08kg.m2

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
3
A. I = — M R 2

13

B. I = — M R 2

21

C. I = ^ M R 2
"

45-

Huang dan giai:
Taco: l = l^ + md^

= - M R 2 + Mf

5

-

B. 3ml2.

C. 2 mP.

Taco I = - m R ^ = > R = — = I m
2
" ^ " " V im

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 d i qua khoi tam va vuong goc vai thanh, momen quan tinh ciia thanh
bang
A.0,75kgm2.

38

B. I,5kgm2.

C. 4 kgm^.

D. 6,5 kgm^

D . R = l,7m

Chgn A

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

^
^

C.R = 2m.

Cau 80. Mot vat chju tac dung mot lye F = lOON vao mpt diem N each true

D . 1 mP

Huang dan gidi:

B. R = l,5m.

Huang dan gidi:

D. I = — M R 2
19

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 d i qua trung diem ciia thanh la
A. 4 m R

-

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
A.R = l m .

• Chon C

.3

Chon D

~-

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

A. 4 m.

B. 3 m.

C. 2 m.

D. 1 m

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 d i 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 t u 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.

Huang dan gidi:
Ap dung phuong trinh dong luc hoc vat ran:

D. 150rad/s
^

.

I

M = Iy=>7 = — = — = 5rad / s'^
Ma (0 = COQ + yt = 0 + 5.15 = 75rad / s => Chon A

^

Huang dan gidi:
Ta c6:

Cau 82. Vat rSn quay duoi tac dyng ciia mot luc. Ne'u do Ion luc tang 8 laVi
khoang each t u 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 t u true quay den gia cua lye giam 3

Ian thi momen luc se la: M ' = F'.d' - 8 F . - = 2F.d = 2 M => 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 t y do ciia day c6 gan mgt vat nho khoi lugng m = — . Gia toe ciia vat nho
C. ^

D. g

Voi I = - M R ^ m = - M , ta duoe:
2
4
1 + J

mR^

g

-I

1MR2

1+2

I = lmR2

^

2

'

21
•m=

640

= 160(kg)

=>ChgnC
^
Cau 86. Mgt vat ran dang quay quanh mgt tryc eo' djnh voi to'c do goc 25 rad/s
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 t u khi bat dau
quay cham dan deu, vat dat toe do goc la
D. 48 rad/s
A. 8 rad/s
B. 16 rad/s
C. 32 rad/s
Huang dan gidi:
Ta c6:

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

=>ChgnB
Cau 87. Mgt dTa mong, dong chat quay quanh mgt tryc d i 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:

g

3

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

la (ggi g la gia toe trgng truong)
A. ^
B. ^

a=

V

3

^ Chgn B

Huang dan gidi:
• Chgn C

-MR2

4

Cau 84. Mot banh da eo momen quan tinh doi voi tryc quay la Skg.m^, tir trang

thai nghi, banh da dat den van toe 480v6ng/phut trong 8s. Momen lye tac dyng
len banh da la
A. 15,6N.m

B.31,4N.m

C. 52,1 N . m

D.63,7N.m

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 N m . Sau 3s ke t u liic bat
dau quay, toe do goe ciia dTa la 36 rad/s. Momen quan tinh ciia dTa la
A. 0,25 kg.m^.

B. 0,5 kg.m^.

CO-co,, 1871-0 „ / , . ')\
y=— ^ =
= 271 rad /
t
8
V
/
M = ly = 5.27t = 31,4 (Nm)
Chgn B
'I
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:

A.960fc^'

B.240Jt^'

C. 160fc^

D.SOkg^

D. 1,25

kg.m2

Huang dan gidi:

Huang dan gidi:
Taco:

C. 0,75 kg.m^.

lia toe goc ciia dia: 7 =

Aco

, , 2'

= 12^rad / s

[omen quan tinh cua dTa: I =

= ^ = 0'5|kg.m^ j

. Chon B

Cau 89. Mot thanh nhe (khoi lugng khong dang ke) dai 21 quay deu trong mat
phang ngang quanh tryc thang dung di qua trung diem ciia thanh. Hai dau
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
hai chat diem doi voi tryc quay co bieu thuc.
.ml
A. —

„ 4mP
B.

3v

^ 5ml
C. ——

V

thanh va

r-, o i
D. 3mlv

Thay so ta dugc M = - I N . m . Suy ra dg ion ciia momen lyc can bang 1 N . m
Chgn A

(^2u 92. Mgt vanh tron khol iugng m, ban kinh R quay cham dan deu quanh true
2 ^ ' t ^ d u n g ciia momen lyc can. Cu sau khoang thoi gian T thi goc quay giam
deu A'P- ^ 9 '^"^

V

Huang dart gidi:

mR^Am

Momen quan tinh cua thanh co hai chat diem m , va m j la:
I = mjl^+m2l^ =3ml^

_ „
^

mRAcp

„

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 t u 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
Huang dan gidi:

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

Huang dan gidi:

I
Chgn moc thoi gian t = t^ sao cho < o = 0 => cp = coot + ^ y t ^
P
2'"
1 2
Goc quay dugc sau z (s) dau ticn: (p = (OQT + —yt = Atp,

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

= ... = - y t => y = — ^

Ap dung phuong trinh dgng lyc hgc vat ran:
M = Iy = - I ^ = -

i

^

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?
D.3N.m.

Huang dan gidi:
Goc quay ciia vat ran t u khi chju momen luc can tac dung den khi dimg lai
la n27t.

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
B. 2,4N.m

C. 0,8(1 + 47T) N.m

47tn

D. 3,27i N.m
Huang dan gidi:

J 2

A p dung phuong trinh dong luc hgc vat ran: M = ly =

^

A. 1,6 N.m

Suy ra: (O^ - to?. = 2yA(p - 2Y.n.2n => y = — ^
i

+ ^yt^

trj am, sau nhiing khoang thoi gian T, goc quay ciia vat ran giam deu mgt

I = - m R 2 = ^ m = - ^ = - ^ = 15kg => Chon A
5
2R2
2.I2

*

^ ,

Ta thay, chuyen dong ciia vat ran la cham dan deu nen gia toe goc y co gia

A(p = A(p| - A(P2 = A(p2 - A(p3

Ap dung cong thuc tinh momen quan tinh ciia vat ran hinh cau:

C. 12 N.m.

•

1
Goc quay dugc sau 2T(S): tp = 2a)oT + —y4t^

Matkhac co = W(, + 7t=> 100 = 0 +10t=> t = 10s

B. 21 N.m.

r^ "\RA(p

lugng:

M = I.7=>y = — = — = 10rad/s2

A. I N . m .

mR^A(p

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

M = Ira = 31^(0 = 3 m P y = 3mlV => Chgn D

f

„

:.^|-

Momen dong lugng ciia he (thanh va hai chat diem) la:

S

momen lye can dugc xae djnh bSng bieu thiie nao sau day?

—
inn

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

mm

;:


CtyTNHHMTVDW

V§t q u a y dvtac 16 v o n g t r o n g 4 giay: cp = ^7*^ = 16.27t = 32n

Cia 95-M9t ^'^

^^'^^

H

KhangVift

k e n h u h i n h ve: m ^ = 1kg; m 2 = 2kg; k h o i l u o n g

Suy ra: y = 4n rad/s^.

^^^ng

K h i k h o n g c6 tac d u n g ciia m o m e n M t h i c h i con tac d y n g cua m o m e n lij^

trugt so v o i r o n g rpc. Ban d a u g i i i cho h# d u n g yen. Bo q u a sue can tac d u n g

roc m = 4kg; l a y g - lOm/s^. Soi day noi hai vat k h o n g d a n va k h o n g

len h?. Toe d p d a i cua m p t d i e m 6 m e p ngoai r o n g rpc vao t h a i d i e m sau k h i

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

tha tv d o he d u p e 2s.

T u d o ta c6: M = 0,8(1 + 47r)N.m => C h o n C
Cau 94. M o t v a t ran c6 the quay quanh m o t true co d j n h d i q u a t r p n g tam. Vat

A . l,5m/s

B.2,5m/s

C. 4m/s

D . 6m/s

Huang dan gidi:

ran bat d a u quay k h i chju tac d u n g ciia m o t l u c k h o n g d o i F = 2,4 N t a i m o j
d i e m M each true quay m p t doan d = 10 c m va tiep t u y e n v a i q u y dao chuyeti

C h p n chieu d u o n g la chieu ehuyen d p n g ciia cae vat

d o n g cua M . Sau k h i quay d u g c 5 s t h i toe d o goe cua v a t r a n d a t gia t r j bang

A p d u n g d j n h luat I I N e w t o n cho m j :

30 rad/s. Bo qua m o i luc can. Chon moc t h o i gian t = 0 la liie v a t ran bat dau
quay, toa d o goc ban dau ciia v a t ran bang 0 va chieu d u o n g la chieu quay eua
vat ran. Gia s u t a i t h o i d i e m t i = 10s vat ran k h o n g chju tac d u n g ciia l u c F,
B. (p = 5 0 0 r a d .

C. (p = 9 0 0 r a d .

D . (p = 8 0 0 r a d .

=^ I =

F.d

2,4.0,1

i

(2)

m 2 " ^ 2 = m2a2

l a C O co = a)o+Yt=:0 + Y t = > y = — = — = b r a d / s
t
5
M a t khac m o m e n l y e tac d u n g len vgt r i n d u o c xac d j n h :

I.y

0),

Ti-Fms = mia,

f 2 + m 2 g = m2a2

Huong dan gidi:

M = F.d =

^i^i

D j n h l u a t N e w t o n cho vat m j :

T i n h toa d p goc tai t h o i d i e m t2 = 20s?
A . (p = 300 rad.

T l + Fms =

.
,,

= 0,04kg.m'

Tai t h o i d i e m t , = 10s, v a t ran k h o n g chju tac d u n g cua lue F nen M = 0, suy
ra I.y = 0 => y = 0. V a y vat ran ehuyen d o n g quay deu v 6 i toe d o goc bang:

T i ; T2 la l u c cang spi day tac d u n g 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 d p n g quay cua r o n g rpc:
M = ly « ( T 2 - T,) R =

1 mR^y

« (T2 - T,) = i mRy

(3)

Vi spi d a y k h o n g dan nen ai = a2 = a.
Sg^i day k h o n g t r u a t tren rong rpc nen y = —

A p d u n g eong thuc: co = (0(, + yt = 0 + 6.10 = 60rad / s
T ^ - m i g = m^a,

De t i n h tpa d p goc tai t h o i d i e m t2 = 20s, ta t i n h goc quay cpj cua v $ t ran
t r o n g q u a t r i n h v a t r a n q u a y q u a n h n h a n h d a n d e u t r o n g k h o a n g t h a i gian

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

t, = 10s va goc quay (p2 cua v a t ran t r o n g qua t r i n h v a t ran ehuyen d p n g qua\

T2-Ti^-ma

deu t r o n g khoang t h a i gian t2 - t j = 20 - 1 0 = 10s .
Tpa d p goe cua v a t tin tai t h o i d i e m t j = 20s
dupe xac d j n h (p = (pj + (pj
Ta co:

=^ChpnC,

44

£

cpi = (Po + (0(,t + - i y t ^ = i . 6 . 1 0 ^ = 300rad
(p2 =a)t = 60.10 = 600rad

Suy ra:

=> a =

cp = (Pi + (P2 = 300 + 600 = 900rad

2(m^-mi)g
2mj +2m2 + m

= 2 m / s^

V a n toe dai cua m p t d i e m 6 m e p ngoai r o n g rpc v a o t h o i d i e m sau k h i tha
*V d o cho he d u p e 2s: v = at = 4 m/s => C h p n C
Sau.96.Mpt lue tiep t u y e n eo d p Ion 4 N tac d y n g v a o v a n h ngoai cua m p t banh
^ 6 C O d u o n g k i n h 80em dang quay deu. T r o n g giay cuoi c u n g t r u o c k h i toe d p
cua banh xe bang k h o n g , m p t d i e m tren m e p 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 q u a n t i n h ciia banh xe
^ ^ v 6 i trye quay la


— ' "-r ~

o

- - A " J * •• ^

„

A . gan bang 0,24 kg.m^

B. gan bang 0,43 kg.m^

V i sgi day k h o n g d a n nen

C. gan bang 0,51 kg.m^

D . gan bang 0,89 kg.m^

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

Huang dan giai:

mi

T r o n g giay cuoi c i i n g trudc k h i d u n g quay, goc banh xe quay d u g c (p = ^
A p d u n g cong thuc cp = o)(,t + ^ y t ^ va w = (OQ + yt ta d u g c y = 7t rad/s^.

3^=32

= a.

va ban:
„ = f i M . = M = o,08

^
m,g
10

=^ChgnD

Cau 98. M o t banh xe chju 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 trj bSng 24 N . m . T r o n g 5s dau, toe

Fd = Iy:

I = f ^ = lM.o,51kgV/s

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 quay cham dan va d u n g hlin lai sau 50s. Gia s u m o m e n luc

=> C h g n C

ma sat la k h o n g d o i suot thoi gian banh xe quay. M o m e n luc M i co gia trj

Cau 97. M o t rong roc c6 k h o l

lugng

m = 2 k g ( H i n h ve). Bie't m j = 2 k g va
1kg,

A. M l = 11,3 N . m
C. M l = 33,4 N . m

m,

B. M l =26,4 N . m
D . M i = 48,6 N . m

ban dau cac vat d u g c g i u

•

-

Huong dan giai:

d u n g yen, sau d o tha nhe cho he chuyen

Ban dau: M = M , + M ^ ^ = 2 4 ( N . m )

d o n g thi 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 rong

Toic d g goc ciia banh xe liic co M i : (o = a)(, + yt ^ y = 2rad / s^

'

rpc. Cho rang sue can tac d u n g len he
M o m e n quan t i n h ciia banh xe: I = — ~~2~

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

^^^kg.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^

^

giua m , va mat ban la
Suy ra: M ^ ^ = y ' l = - 0 , 2 . 1 2 = - 2 , 4 ( N . m )
A . 0,05

B. 0,06

C. 0,07

D.0,08
Vay M , = M - M , ^ ^ = 2 6 , 4 ( N . m )

Huang dan giai:

Chgn B

»" '

Chgn chieu d u o n g la ehieu chuyen d o n g ciia cac vat.

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 quay

Ap d u n g d i n h luat I I N e w t o n cho m , :

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

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

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

T i + Fms = m , a ,
' T,-F^^=m,a,

0)

A . 25m.

B. 50m.

m2 ~T2 = m2a2

f

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

V i sgi day k h o n g dan nen a^ = a j = a.

(3)

Gia to'c goc ciia dTa: y = ^

= 20rad / s^

f/

Goc rong rge quay dugc: cp = i y t ^ = 250(rad)
Q u a n g d u o n g ma 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 )

Sgi day k h o n g t r u g t tren r o n g rge nen y = —
R,

;

(2)

A p d u n g d j n h luat I I N e w t o n cho chuyen d o n g quay cua r o n g rge:
M = ly c:> (T2 - T , ) R = 1 mR2y « ( T 2 - T j ) = 1 mRy

D . 100m.

Huang dan giai:

D j n h luat I I N e w t o n cho vat mi:
f 2 + m2g = m2a2

C. 75m.

Chgn B

,
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