Một số phương pháp giải bài tập trắc nghiệm cơ học 12: Phần 1

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T R A N T R O N G Hl/NG

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12

I

NHA XUJIlT BAN T £ N G H9P THANH PHO HO CHf MINH


cty

P H l / d N G PHAP G I A I BAI TAP T R A C N G H I E M C d H Q C 12

C h i r o n g 1.

I R A N T R Q N G HLfNG

Bai 1.

D O N G LlXC H O C V A T R A N

C H U Y E N DONG Q U A Y C U A VAT RAN
QUANH MOT TRgC C O DjNH

C h j u t r a c h n h i e m xua't b a n

TOM TAT LI T H U Y E T

N G U Y E N T H I T H A N H HUCfNG
B i e n tap

: HAI AU

TNHH MTV DVVH Khang Vl§t

1. T o a do goc
-

\a ban in : H O N G H A I

V i t r i cua vat tai m o i thcJi diem se diTdc xac
dinh bang goc cp giffa mot mat phang dong

T f i n h bay

: Cong ty K H A N G V I E T

P gan vcti vat va mat phang co dinh PQ (ca

Bia

: Cong ty K H A N G V I E T

hai mat phang nay deu chiJa true quay A Z ) .
Goc (p goi la toa do goe cija vat.

NHA XUAT BAN TONG H 0 P TP. HO CHf MINN
NHA SACH TONG H 0 P
62 N g u y e n T h j M i n h K h a i , Q . l
D T : 38225340 - 38296764 - 38247225

.

-

Dcfn vi cua 9 la radian (rad)

-

N e u chon chieu du'dng la chieu quay cua vat thi (p > 0

2. T S c d o g o c
-

Toe do goc la dai lu'dng dac trUng cho mu^c do nhanh, cham cua chuyen
dong quay.

Fax: 84.8.38222726
E m a i l :

Acp

Toe do goc trung binh:

V^ebsite: w w w . n x b h c m . c o n i . v n / w w w . f i d i t o u r . c o m
Toe dp goc ttfc thdi: co =

Tong phdt

hanh

-

d(p
—
dt

D d n vj toe dp goc la rad/s

; •

3. G i a toe g(>c
C O N G T Y T N H H MTV
DjCH Vg VAN HOA KHANG V I E T
Dia chl: 71 Dinh Tien Hoang - P.Da Kao - Q.1 - TP.HCM
Dien thoai; 08. 39115694 - 39105797 - 39111969 - 39111968
Fax: 08. 3911 0880
Email:

-

-•.;», 1/^.

!r\ J.

Gia toe goc la dai liTdng dac trUng cho sir bien thien nhanh hay cham cua
toe dp goc.
Aco

-

Gia toe goc trung binh:

Ytb

-

Gia toe goe tii'e thdi:

Y=

-

D d n vj cua gia toe goe la rad/s^.

Website: www.nhasachkhangvlet.vn

At
dco
dt
' j'

4, Cac phrf

n Ian thuf 1 , S O laong 2 . 0 0 0 cuon,kh6 1 6 x 2 4 c m .
' a i : Chi n h a n h Cty T N H H M T V N X B G I A O T H O N G V A N T A I
Dja c h l : 92 - N a m Ki Kh6i NghTa - Q1 -

Tp.HCM

: P X B S O : 11 68-11 / C X B / 3 7 - 9 7 A r H T P H C M ngay 24/1 0 / 2 0 1 1 .
n xong va nop

ILAJ

c h i e u quy I n a m 201 2.

a. Chuyen dong quay deu Id chuyen dong quay cd tdc do gdc co khdng ddi.
cp = (Po + Mt I, v d i (po la t o a d p g o c b a n d a u .
b. Chuyen

dong quay bien ddi deu la chuyen dong quay cd gia tdc gdc

khdng ddi

^ ^,

y


Phuong phip

CO =

[cp la toa d o g o c v a c luc t

00,, + yt

9 = cpo +
CO

1

coot +

2 - cof) =
-

-

.2

• Goe quay trong th5i gian t: Acp = (p - cpo = co.t

• Doi ddn vi:

2Y((P --(po)

5. Van toe va gia toe cac diem tren vat quay

.

,!.oT,

Goi r la khoang each tijf mot diem tren vat ran tdi true quay.
a. Toe do dai v cd do Idn: V = co.r

b. Gia toe:

.

- Vat ran quay deu: giaV toe cua
m6i diem tren vat ran la gia toe hu^cfng
9
tam CO d o Idn a„= — = co-.r
- Vat ran quay khong deu: gia toe a cua moi diem tren vat ran c6 hai
thanhphan:
+ Gia toe hu^dng tam a„, dac truing cho sir thay ddi ve hu^dng ciia v eo
V

do Idn

2

.r
-+ Gia toe tiep tuyen a, dac tru'ng cho su" thay doi ve dp Idn cua v eo
do Idn a, = r.y
+ Gia toe a cua mot diem tren vat ran
—

= CO

a = a„ +a, co:
* Do Idn:

•;. .

1 vong = 27rrad

+ Neu co.y > 0 thi chuyen dong quay nhanh dan.
+ Neu co.y < 0 thi chuyen dong quay cham dan.

i

fcpo la t o a d 6 g d c v a o l i i c b a n d a u ( t = 0)

g\i\i tap U&c nghigm C o hpc 12 - I r a n Trqng Hang

a = 74+a?

* Hdp vdi ban kinh OM gdc a cho bdi:

BAITAPCdBAN
Dang 1. CHUYEN DONG QUAY DEU

• Lien he giila to'e do quay n va toe do goe co: |co = 27tn
n la toe doquay (v6ng/s)
Vdi
CO la toe dogoc (rad/s)
Phu'cfng trinh chuyen dong quay deu: cp - cp,, + co.t

;•

;

had = — vone
27C
^

'

dp gdc cua banh xe la
A. CO = 113040rad/s B. co = 1884rad/s C. co = 31,4rad/s D. co = 156rad/,s

Giai

Toe dp gdc: co = 27tn, vdi n = 300v/p = 300. -^^^^ = 5 v6ng/s
60s
Vay: co = 271.5 = 31,4 (rad/s). Chpn dap an C. , : r , : , , - r
Vi du 2. Mot banh xe quay deu vdi toe dp gdc CO = 9,42 rad/s.
Trong 20s banh xe quay du'de
A. 30 vong
B. 20 vong
C. 15 vong :
D. 60 vong
Gdc quay: Acp = cp - cpo = co.t = 9,42.20 = 188,4 (rad) = 188,4 (vong)
= 30 (vong)
Chpn dap an A.

271

Dang 2 . CHUYEN DONG QUAY BIEN DOI DEU
Toe dp gdc vao luc t: co = cO(, + y . t
coo la toe dp gdc luc ban dau (I - 0) (rad/s)

y la gia toe gdc (rad/s^)
• Gia toe gdc:

CO-CO,

y=.

Phifdng trmh chuyen dong quay bien doi deu: cp = cpo +coot + - y t '
Vdi cpo la tpa dp gdc ban dau (t = 0)
COQ la toe dp gdc ban dau
'
Gdc quay: Acp = cp - cpQ = cogt + ^ y t '

5


PTTOng phi'ip

hai t.lp trac'ngnigm l^U IHJf 1^ - - r r a n - T T u n g - m m g -

Lien he giffa toe do goc vdi goc quay: co" - cOg = 2yAcp

Acp =

CO

2

2Y

Vi du 1. Mot banh xe quay nhanh dan deu vdi gia toe goe l,57rad/s". Sau 5s ke

M = 0(khi dirng lai)

2

-C0(,

vdi < COQ = 10 rad/s (luc bftt dau ham)
y =-2rad/s

(y < 0 vi quay cham dan)

tir luc bat dau quay banh xe dat toe d6
A. n = 7,85 v6ng/s

B. n = 1,25 v6ng/s

C. n = 2,50 v6ng/s

i

' '^^ * ;

Nen: Acp =

D. n - 12,84 v6ng/s

= 25 (rad) ma 1 rad = — vong
271

2(-2)

1
Vay: Acp = 25. — = 3,98... ~ 4 (vong). Chon dap an B.
271

Giai
(OQ

0-10'

=0

D a n g 3 . T O C D 6 D A I V A G I A T O C C U A MOT D I E M

Toe do goc: co = ©o + yt, vdi y = i,57rad/s^

^ ;>( • ' fv-

TREN VAT R A N QUAY

t = 5s

•

Nen:co = 0 + 1,57.5 = 7,85 (rad/s) ma: lrad/s= — v6ng/s

^ n . ' ^ ^ i v T

Nen: co = 7,85. — = 1,25 (vong/s): ta goi do la toe do banh xe n = 1,25 v6ng/s

Toe do dai eiia diem M each true quay khoiing r:
v

(m/s)

=

CO

',

Ay

. r

(rad/s) ( m )

Gia toe:
+ Neu vat ran quay deu thl gia to'c eua

271

diem M hu'dng tam vdi do Idn:

Chon dap an B.
Vi du 2. Mot banh xe quay nhanh dan deu. Sau 2 phut tijf liie banh xe eo toe do

a„ = — = co .r

120 vong/phiit, banh xe dat toe do 840 vong/phiit. Gia toe goe eua banh xe la
A. y = 0,628 rad/s^
C. y = 1,256 rad/s^
.„./
, •,:„.
•
I
]

+ Neu vat ran quay khong deu thl gia toe

B. y = 0,314 rad/s'
D. y = 0,157 rad/sl
:;

^

, Giai

cua diem M c6 do Idn

rj

Doi ddn vi: 1 vong/phiit = 27t rad/60s = — rad/s
30

+ ar

V

= co^r: gia to'c hu'dng tam
r
a, = r.y gia to'c tiep tuyen

(Oo = 120 vong/phut = 120. — ^4n rad/s
30

\O = 840 vong/phiit = 840. — = 287i rad/s

M

+ Gia toe a hdp vdi ban kinh OM goe a ma: tana =

"I
CO

t = 2 phiit = 120s
!

:

^.

•

^-

,

CO — COn

Gia toe goe: y =

2871 — 471

^- =
t

'

,

, , 1.

„ ^^n /

j ; 2x

(rad/s^) = 0,628 (rad/s")
120

Vi du 1. Mot vat ran dang quay deu vdi toe do 2 v6ng/s thl du'dc tang toe, banh
xe quay nhanh dan deu vdi gia to'c 2rad/s'. Toe do dai cua diem M tren vat
r i n each true quay 10cm. Sau 5s ke ttf lue tang toe la

Chpn dap an A.

A. v = 3,158 m/s

Vi du 3. Mot banh xe dang quay vdi toe do goe lOrad/s thl bj ham va tiep tuc
4

B. v = 5,815 m/s

C. v = 2,256 m/s

Giai

'V'-

quay cham dan deu vdi gia toe CO do Idn 2rad/sl Lay 71 = 3,14.

Toe do goe ban dau (liic t = 0): coo= 27in = 27t.2 = 47i (rad/s)

Cho den khi banh xe dCfng lai, no da quay du'dc xap xi

Toe do goe sau 5s: co = coo + yt = 47i + 2.5

A. 25 vong

B. 4 vong

C. lOOvong
Giai

Co co^ -

COQ

= 2y. Acp

j ^
D. 2 vong

D. v = 4,374 m/s

22,56 (rad/s)

Toe do dai cua diem M : v = co.r = 22,56.0,1 = 2,256 (m/s)
Chon dap an C.

""^
;
^

-

-

/
''''' "
*'
' '

•4


Giai

V i d u 2. M o t t h a n h O A d a i 30cm c6 t h e q u a y t r o n g m a t p h a n g n a m n g a n g xung
q u a n h t r u e t h a n g duTng q u a d a u O. Sau
diTdc g o c

Is ke tCr l u c b a t d a u q u a y , t h a n h q u a y

60°, g i a to'c t i e p tuye'n c u a d a u A c6 do Ictn

A . a, = 0,628 m/s

B . a, = 0,314 m/s

•

C. a,= 1,256 m/s

Giai

•

D . a, = 0,157 m/s

•

-.-is

tana = — =
a„

= - y ma to = y.t (vi coo = 0)

CO"

.r

CO

nen: tana = - ~ - = — ^ => t =
,
= , '
(yt)
y.t
^y.tana
/

= N/3 ~ 1,3 ( S )

,. is ...

G6c q u a y c u a t h a n h : Acp = coot + - y t ^

ChondapanB.
L u c d a u (t = 0) t h a n h b a t d a u q u a y (cOo = 0) nen:

• 2
2A(p
A(p = - y t ^ y = — ^ v d i

A(p:=60" = - r a d

Lf THUYET VA BAI TAP TRAC NGHIEM

^^^Aq

1.1. Chpn cau dung. Toe do goe eua vat rin quay

3
t = ls

A . tinh bang cong thiJc
At
.2
B. tinh bang ddn vj rad/s

3 _27t . . . j , „ 2 ^
N e n : y = - ^ = — (rad/s^)

^ I

C. dae tru'ng cho mu'c do nhanh, cham cua ehuyen dong quay
D. du"dng neu vat quay nhanh dan va am neu vat quay cham dan

Gia toe tiep tuye'n cua dau A : a, - r.y = 0,3. — = 0,628 (m/s^)
•3
ChondapanA.

'

^

-.p ^ V ^ ' :

'

1.2. Chon cau sai. Chuyen dong quay deu c6

n^a/rS-i'f^'

V I du 3. M o t dTa m a i bat dau quay nhanh dan deu tiT nghi. K h i dia quay du-dc
I

goc l,5rad thi mot d i e m tren vanh dTa dat gia toe tiep tuyen la 2m/s^, gia toe

;

cua d i e m do CO do Idn x a p x i bhng

;

A . a - 2,5m/s^

;

B . a = 12,6m/s^

.

D . a = 6,3m/s^

)V'!(3 ff :•:•!; .;',M

""-^

'
;

->^:.2Acp
Y JV •

^7-

Vay ^

(ifh

B. toe do goe khong doi

'

'

"

C. toa do goc du'de tinh bdi: cp = cpo + cot

'
'

"

1.3. Chon cau diing. V d i mot ehieu du'dng bat k i thi
'

- ,. . •

B. vat quay theo ehieu du'dng thi co > 0, vat quay theo chieu a m thi co < 0

r?
T , . a,, =ft> r
a„ CO . 2 ^ . , v
a = Ja;, + a, v d i <^
=> — = — ma co = 2yA(p (vi 03o = 0)
.
_ _
[a, = r y
a,
y

j
i

•

A . toa do goe cp > 0

Giai
;
I

A . gia toe goc la hhng so"

'

D. goe quay ti le vdi thdi gian quay

,

C. a = 5,8m/s^

"

C. vat quay (co y ;^ 0) theo ehieu du'dng thi coy > 0
D. vat quay nhanh dan thi y > 0

-

•

'•

''^

'•••y':i

.'CH-^y-^'Aiy:

: v . ! ^. : . \

1.4. Chon cau diing. K h i vat rjfn quay thi eac d i e m khac nhau tren vat ran (khong
'<

J ft

I

= 2A(p - > a„ = 2A(p.a,

1

> 1*

:

'

:

u

:

'

t

' H '

.

:

,

:

sa?v'

a,

nam tren true quay) co cung

j •,-

,
J

"
uU IV

D o do: a = ^/(2A(p.a,)^+a^ = a, ^(2Acp)^ + 1 = 27(2.1,5)'+ 1 ^ 6 , 3 m / s ^ ' ^ ^ '
,,,,, C h o n d a p a n D

-..^ ;W;;ô.Hf r

f - ã W ' ' . : A -

V i du 4, M o t banh xe dang quay nhanh dan deu v d i gia toe goc Irad/s^ quanh

A . toa dp goe va goe quay

'

C. to'c dp goc va toe dp (dai)

B . goe quay va gia to'c g6c
D . gia toe goe va gia toe (dai)

1.5. M o t vat rKn quay nhanh dan deu tif nghi, to'c dp goc ti le vcjii
A . goc quay

B . binh phu'dng thdi gian

C. Ccin bac hai cua thdi gian

D . can bac hai eua goc quay

I

1-6. Chpn cong thiJc diing

>;•!;. / l u . .

tarn O. Sau thdi gian t ke tiT luc banh xe bat dau quay, d i e m M tren vanh
banh xe c6 vectd gia toe a hdp vdi ban kinh C M goc a = 30°. T h d i gian t xap
x i bang
A. t = l , 7 s
8

dt

At

.(. ;

i

At

• -7. Chpn ehieu diTdng la ehieu quay eua vat ra'n thi
B.t=l,3s

C. t = 2,5s

D . t = 0,9s i r j

A . 0) > 0

B. y > 0

C. co.y > 0

D . co.y < 0


1.8. Chon cau sai khi noi ve chuyen dpng quay cua vat rin

1.18. Canh quat dai 50em quay deu vdi to'c dp 90 vong/phiit. To'c dp dai cua dau

A. Gia to'c goc dac trU'ng cho siT bien thien cua toe dp goc d moi thdi diem.

canh quat la

B. Khi vat ran quay deu thi veetcf van to'c eua mot diem tren vat ran khong

A. v = 18,84 m/s

B. v = 6,58 m/s

C. v = 24,32 m/s

D. v = 12,65 m/s

1.19. Mot dTa mai co ban kinh 20cm bat dau quay nhanh dan deu ttr nghi. Sau
C. Gia toe hu'dng tam dae trU'ng cho siT thay doi ve hifctng eua vectd van toe.

thdi gian lOs ke tu* liie bat dau quay toe dp dai ciia mot diem tren vanh dTa la

D. Gia toe tie'p tuye'n dac trifng cho su" thay doi ve do Idn cua veetcf van to'c.

20m/s. Gia toe gde quay cua dTa bhng

., ., , i ,

1.9. Chon cong thiJc dung
A. a„ = V ^ r

B. a„ =

C. a = r^w'^ +y-

A. y = 5rad/s'

B. y = 8rad/s^

C. y = 18rad/s'

D. y = 1 Orad/s'

1.20. Mot dTa tron ban kinh 30cm bat dau quay nhanh dan deu tCi" nghi vdi gia toe

D. a, = r.co

goc 2rad/s^. Sau 10s thi gia toe ht/dng tarn cua mot diem tren vanh dTa lii

1.10. Vat ran dang quay vcti toe dp 10 vong/phiit. Toe dp goc cua vat rftn luc do la

A. a„ = 60m/s^

B. a„= 120m/s^

C. a„= 80m/s^

D. a„ = lOOm/s^

1.21. Dau kirn giay cua dong ho de ban coi nhu" chuyen dpng tron deu tren
A. Q) = - rad/s
3

B. co = - rad/s
6

C. to = —rad/s

3

D. co = - rad/s
2

du'dng tron ban kinh 3cm. Toe dp dai va gia to'c dai ciia dau kim xa'p xi bang

1.11. DTa mai dat toe dp goc 12,56 rad/s sau 5s ke tij" Itic khdi dpng. DTa mai da
quay dUdc
A. lOvong

B. 20v6ng

C. 2 vong

con 120 vong/phiit. Ke tijT lile ham banh xe se diJng lai sau
B. 25 vong

C. 8 vong

B. v = 0,526cm/s vii a = 0,248em/s-

C. V = 1,224em/s va a = 2,140cm/s'

D. v

2,568em/s va a = 1,634cm/s'

1.22. Coi chuyen dpng ciia cac dau kim giay va kim phiit la cac chuyen dpng

D. 5 vong

1.12. Mot banh xe dang quay vdi toe dp 300 vong/phi'it thl bi ham va sau 6s no
A. 10 vong

A. v = 0,314em/s va a = 0,033cm/s'

D. 50 vong

tron deu tren cac du'dng tron vdi ban kinh eua dau kim giay bang — Ian ciia
6
dau kim phut. Ti so'gia to'c dai ciia dau kim giay va dau kim phiit

la

1.13. Canh quat dang quay vdi toe dp 300 vong/phiit thi li'ie t = 0 canh quat bat
dau quay cham dan deu va sau 5s canh quat con toe dp 180 vong/phiit. Canh
quat se duTng lai vao Itic
A. t = 1 5 s

B. 120

C. 300

D. 360

1.23. Trai Dat coi nhu" hinh eau ban kinh 6400km chuyen dpng tron deu xung

B. t=10s

C . t = 12,5s

D. t = 7,5s

quanh true ctia no vdi thdi gian quay moi vong la 24 gid. To'c dp dai va gia

1.14. Sau thdi gian 10s, toe dp quay cua banh xe tang deu tir 120 vong/phiit len

y

A. 60

toe dai cua mot diem tren xich dap gan bang

ii ,m q .

480 vong/phiit. Biet ban kinh banh xe la 20cm, trong thdi gian nay xe da chay

A. V = 465in/s ; a = 0,0338m/s^

B. v = 465m/s; a = 34m/s^ '

du^c quang du'dng.

C. v = 228m/s ; a - 0,0338m/s'

D. v = 228m/s; a = 34m/s^

A. s = 15,7m

Uj"'-!

B. s = 125,6m

C. s = 31,4m

1.24. Trai Dat eoi nhu" hinh cau ban kinh 6400km chuyen dpng tron deu xung

D. s = 62,8m

1.15. Mot banh xe bat dau quay tu" nghi vdi gia toe goc 2 rad/s'. Biet ban kinh banh

to'c dai cua mot diem tren mat dat d vT dp 60" xa'p xi bang

xe la 50cm. Sau 4s mot diem tren vanh banh xe dii quay dtfdc mot cung dai
g

A. s = 8m

B. s = 4m

C. s = - m

ãô •

D. 16m

n
1.16. Mot dTa mai bat dau quay cham dan deu va dCfng lai sau 10s. Trong 10s
nay dTa quay du"dc 25 vong, lay

A. l,57rad/s^

TC

= 3,14. Dp Idn gia toe goe eua dTa la

B. 3,14rad/s^

C. 6,28rad/s^

D. 12,56rad/s^

1.17. PhiTdng trinh chuyen dpng quay eua vat ran cho bdi cp = 2t^ + 3t - 6, trong
do t tinh bang giay, cp tinh bang rad. Toe dp goc Itic t = 5s la
A. CO = 15rad/s

B. co = 42rad/s

C. co = 23rad/s

quanh true ciia no vdi thdi gian quay moi vong la 24 gid. To'c dp dai va gia
A. V = 465 m/s ; a = 0,034 m/s^

B. v = 465 m/s ; a = 0,017 m/s'

C. v = 232,6 m/s; a - 0,034 m/s^

D. v = 232,6 m/s ; a = 0,017 m/s^

••25. Biet ban kinh banh xe dap la 0,5in. Liic xe chay deu vdi toe dp 18km/h thi

gia to'c dai ciia mot diem tren vanh banh xe la

,

A. 25m/s^

D. 30m/s^

B. 15m/s^

1-26. Mot dTa mai chuyen dpng nhanh dan deu ttr nghi vdi gia toe gde la 2rad/s .
Biet ban kinh dTa la 20cm. Dp Idn gia toe eua mot diem tren vanh dTa sau Is
ke tir luc dTa ba't dau quay la

D. co = 8rad/s

C. 50m/s^


A. a

0,4 yfs m/s^

C. a = 0,4 ^

Cty TIMHH M T V DVVH Khang Viet

B . a = 0,5N/5 m/s^

m/s^

D . a = 0,8 ^

1.8. D a p an B. Sai, vi khi vat ran quay deu thi hu'dng cua vectcf van to'c thay doi

m/s^

1.27. M o t thanh cu'ng O A dai I m co the quay d6 dang trong mat phang nam
ngang quanh mot true qua dau O. Dau A dat du'dc to'c do 2m/s sau k h i quay

nen vectd van toe thay doi (chi co do Idn ciia van to'c la khong d d i ) .
1.9. Dap an C. V i a = ^a^ + af = ^J((a^rf

C. a - 5,5m/s'

B. a = 8,6m/s^

A . a = 12,3m/s^

A sai,

D . a = 9,2m/s'

1.28. M o t dTa compact (CD) bat dau quay nhanh dan deu tiT nghi xung quanh tam
O. K h i quay du'dc goc — r a d thi vectd gia to'c dai a tai d i e m M tren vat ran
6
hdp v<3i ban kinh O M goc a bang

- r^co^ + y^

VI

=

—

B sai, V I a n ^ c o l r
D sai, v l a, = r.y
1.10. D a p an A
1
n = 10 vong/phut = 10 v6ng/60s = — v6ng/s

D.^
2

C.

A.^
6

+ (yrf

.,2

di/dc goc 30° (ban dau duTng yen), luc do gia to'c dai cua dau A xap x i

3

CO = 2jtn = 271. - = — rad/s
6

3

HLfdNG DAN GIAI

l.ll.DapanD

1.1. D a p a n C .
1.2. Dap an A . A sai v i : trong chuyen dong quay deu gia toe goc y = 0
: t i l e v d i thdi gian t. - '

D diing V I goc quay Acp = cp - cpo =

'

•"-

t " '

CO <

1.3. Dap an B

'' ' '

•

-

Acp = - Y . t ^
2^

(vico„ = 0)
co = y.t

A sai, V I neu chon chieu du'cfng ngu^dc v d i ehieu quay cua vat thi cp < 0.
Acp - - c o . t = - . 12,56.5 = 3 l , 4 ( r a d ) =
2
2

C sai, V I vat quay theo chieu du'dng thi co > 0 nhifng neu la chuyen dpng cham
dan thi y < 0, liic do coy < 0.
;
'

l.l2.DapanB

D sai, V I neu chieu du'dng ngu'dc vdi chieu quay thi chuyen dong nhanh dan
CO

y < 0.

)

.

)

1.4. Dap an B

^ = 5 (vong)
271

,
. . . .

'

'

, » .

vi-

,

no = 300 v/ph

'
,

, ,<

= IOT: (rad/s)

120

i

.

300

60

n, = 120 v/ph

A sai, V I cac d i e m khac nhau tren vat r ^ n eo toa do goc cp khae nhau.
C sai, V I toe do (dai) v = co.r; r khae nhau thi v khae nhau.

coo = 27ino = 27t.

C0| = 2Kni = 27i.

= 47i (rad/s^)
60

471-1071

«. . ;

Y=-

^

= - 7 1 (rad/s )

D sai, V I a = -^a^ + a^ , trong do a„ = co^r va a, = yr khae nhau neu r khae nhau,
luc do a khae nhau.

•

0 ' - co^ =2y.Acpz^ A c p - - - ' ^ "

^

2(-7i)

2y

1.5. Dap an D , v d i coo = 0 thi co = yt va co = ^2yAcp .

, ;

V a y toe do goc co ti le vdi can bac hai cua goc quay Acp (va ti le vdi thdi gian t)
1.6. D a p an C, co = - ^ = cp'(t)

'

' ' ' '

dt

:.:

= 5 0 7 t ( r a d ) . ^ = 25(v6ng)
271

113. Dap an C
A p dung: co

coo + yt

d

Trong 5s dau: CO] - coo = yti

(1)

Tuf luc t = 0 de'n khi dij'ng (co = 0): 0 - cOo = yh

(2)

1.7. Dap an A . V i vat quay theo chieu du'dng thi co > 0
cOn = 271.

B sai, V I neu chuyen dong cham dan thi y < 0

12

"

C sai, V I CO > 0 va y < 0 (cham dan) thi co.y < 0

(11.

D sai, V I CO > 0 va y > 0 (nhanh dan) thi coy > 0

(2)

^ 1 - ^ 0

-COn

t,
t.

-COo

coi - co,'0

, vdi

= 107t (rad

/ s)

60

^ 180 ^ ,
,
CO, = 2n.
= 67t (rad/s)
60
ti =5s


PhLfOng p h j p

nen:

giai

b^i t j p trSc nghigm Co hgc

= 5.

12

- Trgn Trgng Hung

Cty TIMHH MTV D W H Khang Vi|t

1.18. Dap an A

= 12,5 (s)

90
CO = 27in = 27:. — = 371 (rad/s);
60

671-1071
1.14. D a p an D
CO <

0

'

(0 - MQ = yt
vdi

2. =

^

Y _^

CO - COQ

^

t

©0 = 2 7 1 . — = 47t(rad/s)

2 © - (OQ

'

03 = 2 7 1 . — = 1671 (rad/s)
60
.„

v = i ^ ^ - ^ = 6 7 T = l 8,84 (m/s)
R
0,5

LL.t = - ( c o + 0)()).t
2
'

.

i . l 9 . Dap an D
CO =

u ' .I'n-'H
<^ ^ ' M "'^ ^'

.

•

•

'

'

> *'

*

S

/

;

." f . - w - ; n > ; - .

''

' \ • •

"••1

= ( y t ) l R = (2.10)'.0,3 = 120 (m/s')
1.21. Dap an A

!

Toe do goc: co = 27tn = 2?:. — = — (rad/s)
60
30
Toe do d a i : v = coR = ^ . 3 « 0,314 (cm/s)

cung d a i : s = R.Acp = 0,5.16 = 8 (m).
1.16. D a p an B

.
'

Gia toe d a i : a = a,, = co^R =

2

A(p = coot + - y t

2
1 2
1 2

=> Acp = -yot' + - y t ' = - - y t ' =:> y =
2
2

y| =3,14(rad/s^)

> o g * i r

Goi k i m giay la so" 1 , k i m phut la so 2.

2A(p
^
t

V d i Acp = 25.271 = 157 (rad) nen y = - 2 .

.3 « 0,033 (cm/s^)

30

1.22. Dap an C

0 = COQ + yt - > COQ = - y t

• ' ;f!<.'"

Taed: "g'^y - " i ^ ^ i _
aphut

= - 3 , 1 4 (rad/s^)

,

Vdi

:

CO2.R2

(27rn2)^R2

n, = 1 v o n g / p h u t
n2 = 1 v 6 n g / 6 0 p h u t

nen

/

ap^a,

5^

= 300

1.23. D d p a n A
•

V d i phiTdng trinh tdng quat: cp = ^ y t ^ + cogt + cpo ta du'dc

—y = 2 - > y = 4 rad / s^
nen v =

. ^fo

B i e u thiJc tinh toe do goc: co = COQ + y.t = 3 + 4t (rad/s) ?

.,2

f

•

O

v = coR = (27rn).R,
vdi n = 1 v6ng/24 g i d =

L i i c t = 5s: CO = 3 + 4.5 = 23 (rad/s)

2

60;

So phiTdng trinh da cho: cp = 2t^ + 3t - 6

COQ = 3 rad/s

V"2

' "R ^
7 \ R2 ;

•'giay

l.lV.DapanC
•

;

':

V d i goc quay d t a m la Acp thi mot d i e m tren vanh banh xe se quay mot

Trong 10s cuoi:

'.;

Toe do k i m giay: n = 1 vdng/60s

• Goc quay: Acp = - y t ^ = - . 2 . 4 ^ = 1 6 (rad)
}
2
2
•

= 100 (rad/s)

a„ = COIR , v d i CO = y.t ( v i coo = 0)

1.15. D a p a n A

;

0,2

1.20. D a p an B

M o i vong quay xe di diTdc: S | = 27I.R = 271.0,2 = 0,471 (m)
'

20
=

,


nen Acp = - ( 1 6 7 t + 471). 10 = IOOTX (rad) = ( v o n g ) = 50 (vong)
2
271
Quang du'dng xe da di du'dc trong 10s: s = 50.0,471 = 62,8 (m)

R

' ^'

co = yt (coo = 0 ) ^ y = ^ = - 1 ^ = 10 (rad/s^)

,
•

V
—

r•

a=

R

86400

v/s

1
271.. ( 6 4 0 0 . 1 0 ' ) a 465 (m/s)
86400
(465)^

J « 0,0338 (m/sO
6400.10

a


Cty T N H H M T V D W H Khang Vigt
Phuong ph^p

giai

bSi t j p Xr&c n g h i g m C o hpc 12 - TrSn Trpng Hung

•

Co co' - COQ = 2y.A(p

1.24. Dap an D
c o ' - 0 = 2y.Acp=^ ^ = - 1 - ^ - ^ = 73
co^ 2.A(p 2 V3

Diem M tren Mat Dat se chuyen dong tron deu tren dUdng tron tam I ban kinh:
r = I.M = R.coscp = 6400.cos60° = 3200 (km)
V = co.r = (27rn).R -

27t.—^1.(3200.10^)
86400

hay tana = N/3 => a = ^

>

1

. ' ) ' „ > ' , . ;

ô 232,6 (m/s)
ã

a=

r

Bal 2. PHl/CJNG TRJNH D p N G Ll/C HQC C U A

(232,6)^
- « 0,017 (m/sO
3200.10-

VAT RAN QUAY QUANH MOT TRgC C O DjNH

1.25. Dap an C

TOM TAT LI THUYET

: I I.

To'c do xe cung la to'c do dai v cua

•

M

Momen cua life F ddi vdi true quay la

= F. d

(N.m)

,

(N) (m)

vdi d la khoang each tCf true quay den gia eua li/e F

1.26. Dap an A

M > 0 ne'u liJc F eo tac dung lam vat quay theo chieu du'dng (thu'dng la
f

a„ = (o^r = (Y.t)^r = (2.1)^0,2 - 0,8 (m/s')

.

•

chieu quay eua vat) va M < 0 neu ngiTdc lai.
2. Momen quan tinh
,
.

a, = y.r = 2.0,2 = 0,4 (m/s')

•

a = 7a^+a? = ^0,8^+0,4^ = 0,4V5 (m/s')

• i . (.

,1 I

Momen quan tinh I doi vdi mot true la dai lu'dng dae trifng cho miJe quan

tinh cua vat ran trong chuyen dong quay quanh vat ay.

1.27. Dap an C
cOo

Gia toe goe: y = "

vdi

2A(p

-0

'

...

(o = - = - = 2(rad/s^)
r 1
A(p = 30" = - r a d
6

nen : y =

n..

1. Momen Wc dO'i vdi true quay

mot diem tren vanh banh xe: v = 18km/h - 5m/s
5^

2
Gia toe dai: a = a,, = —
=
—
=
50(m/s)
R
0,5

b u;'

•

Cong thtfe:

•
•

^
2
m ~: I un'nh
Ddn vi eua I la kg.m
Momen quan tinh cua mot so' vat ran dong chat doi vdi true doi xtfng.

'
1; f; t

2^ - 0 12 ,
2,
— = — (r^^/s )

2 -

a. Thanh C O tie't dien nho so vdi chieu dai/: I = —m./^
12
b. Vanh tron ban kinh R: I = mR'
<
c. DTa tron mone: I = —mR^

,

i " , n O t ' .

.,,

a„ =co2r = 2^1=4(m/s^)
•

Gia toe dai: a = 1 / 3 ^ + ^ vdi

n

nen a = 4^ +

^l2^'

d. K h o i c a u d a c : I = - m R ^
.1 '
•
<
5

3. Phi^ofng tnnh dpng li^c hpc cua vfit ran quay quanh myt tryc co'dinh:
M = I.y

a, = y . r = —.1 = — ( m / s )

« 5 , 5 (m/s')

71

V.
C A C BAI TAP C O BAN

1.28. Dap an B
•

yectdgia toe .a,.hcJp vdi.OM goe a ma:

"M
a

s

D^ng 1. M O M E n L l / C D 6 I VCfl T R ^ C Q U A Y

1

^

\fl

J nruA •

17


Cty TWHHIVrrVDWH Khang Viet

Phoong phap giai bSi tap trSc nghigm Co h o d 2 - Jr^.n Trqng Hung

Giai

' Chon chieu diTdng la chieu quay cua vat thi
+

M > 0 ne'u liTc F c6 tac dung lam vat quay

+

M < 0 neu life F c6 tac dung lam can vat quay

+

M = 0 neu gia cua life F di qua true quay

Momen qudn tinh cua
•

Thanh: I , = — M . / ^ =—.0,9.1^ = 0,075 (kg.m^)
12
12

,
Vs
;

dang xung quanh true qua tam O cua no. Vat qua
•

ranh cua rong roc mot doan day khong dan roi tac
yF2

dung vao hai dau day hai life cCing hifdng thang diTng
/

G

= 0,2. 1 ' ' = 0,05 (kg.m')
v2y

Bi: I2 = m.r = m.

Vi du: Mot rong roc ban kinh 10cm c6 the quay de

m

IL

He (thanh va bi): I = I , + 12 = 0,075 + 0,05 = 0,125 (kg.m^)

Chon dap an B

-s,.,;,„.

V i du 2: Trai Da't coi nhiT mot khoi caU dac c6 ban kinh 6400km, kho'i lUdng

xuong dirdi vdi cac do Idn F, = ION, Fj = 6N (Hinh
ve). Momen life tac dung vao rong roc.

rieng la 5,5. lO-* kg/ml Momen quan tinh cua Trai Daft do'i vdi true quay xa'p xi

A. l , 6 N . m

A . I = 4,5.10"kg.m^

B. I = 9,9.10" kg.m

C. 1 = 4,5.10" kg.m^

D . I = 9,9.10" kg.m

B.0,4N.m

D. 4N.m

C. 16N.m
Giai

Vi F, > F2 nen rong roc se quay theo chieu cua lire Fj , vi vay lUc Fj se c6
momen life Mj > 0 con lUc Fj eo momen life M2 < 0 vdi:

Giai

2
Momen quan tinh cua hinh cau dac: I = - m R ^ ,

M , = F , . R = 10.0,1 = 1 (N.m)
vdim = V . D = - T T R ^ D
3

M2 = - F 2 R =-6.0,1 =-0,6 (N.m)

;/ ?

•

•

Momen Itfe tac dung vao rong roc la: M = M , + M2 = 1 + (-0,6) = 0,4 (N.m)
Chon dap an B
a.

^
D a n g 2 . MOMEN QUAN TINH

Cong thiJc tinh momen quan tinh cua:

-

Cha't diem: I = m.r^

-

Thanh: 1= —ml^
12

-

Vanh tron: I = m.R^

-

1
9
DTa tron: I = - m R ^
2

nen I = —
5 3

15

= —.7c.(6400.10^)^5,5.10^ = 9,8898... x l O " « 9,9.lO" (kg.m') .-

...

Chon dap an D
Dang 3 . P H l / O N Q T R I N H D O N Q L l / C HQC CUA V A T R A N Q U A Y
PhUdng trinh dong life hoc cua vat ran quay quanh mot true c6' dinh la:
M = I.Y
vdi :

•

• Jivsov

,

• M la to'ng cac momen Itfc tac dung len vat ran (ddn vi la N.m)

9

b.

Khoi cau dac: I = - m R ^
Momen quan tinh luon luon la so' du^dng

c.

Momen quan tinh eo tinh cong

• I la momen quan tinh cua vat ran doi vdi true quay (ddn vi la kg.m')
• y la gia to'e goe quay cua vat ran (ddn vi la rad/s')
Vi du 1. Mot dTa tron dong nha't cd ban kinh R = 50em, khoi lUdng m = 1kg. DTa

Vi du 1: Thanh manh dai Im, dong chat va tiet dien deu, khoi \\idng 900g, mot

chiu tac dung cua liTe cd phiTdng tiep tuyen vdi vanh dTa, do Idn F = 1,5N. Bo

dau gan, vdi vien bi nho (coi nhU chat diem) kho'i lUdng 200g. Momen quan

qua lye can tac dung len dTa. DTa quay xung quanh true di qua tam vdi gia toe

tinh cua he (thanh va bi) doi vdi true quay qua khoi tam va vuong goe vdi

goe

thanh la

A. Y = 3rad/s'

IN

B. 7 = 6rad/s'

3.1

C. 1 = 0,175 kg.m^

D. I = 0,250 kg.m^

D. y = 8rad/s'

Giai

= 0,125 kg.m'

A. I = 0,275 kg.m^

C. y = 5rad/s'

Phu'dng trinh dong liTc hoc: M = I.y
19

Phiiang phdp giil b i l t j p tr5c nghigm Co h g c 1 2 - Jr&n Trgng Hifng

M=F.R

M

=> Y = — vdi <
I
^
'

at

:

F.R
net! Y = ImR^
. ,
2

1

Cty TIMHH MTV DVVH Khang Vigt

2F

2.1,5

mR

1.0,5

T

2

•

luc dTa dCfng lai: co = 0 nen:

= 6 (rad/s^).

, .

Chon dap an B

vdi

Vi du 2. Mot banh xe c6 momen quan tinh doi vdi true quay eo dinh la 5 kg.ml

loiV/.

i •

^

-K.

C. 2 vong

D. 25 vong

Giai

.

.

;...it.t

M,

.

,

, . 2 ,

•

•

v/s = lOn rad/s, ta duUc:

^ 2,571^

t:

-.5

*

'

•,

kinh R quay de dang xung quanh mot true nam ngang qua tarn

'

O. Mot doan day nhe khong eo dan du'dc vat qua ranh rong

'''^

•

rpc. Mot dau day du'dc treo vat nang khoi lu'dng m, dau kia
ni

du'dc keo bang liTc F lam vat nang m di len. Lay gia toe rdi tiT
[dau - VI banh xe chuyen dong cham dan]
CO

Ap dung: co^ - COQ =

2yA(f>

;

-COo

=> Acp =

*r

: ° I l l ^ = 12,5(rad)
2(-4)

2Y
12.5

';

A. a =

f " "^S

D

„ _ P+

m

(vong)« 2 (vong)

'Tig

m+

•

I

I

tao nen chuyen dpng quay cua rong rpc nen:

A. 1 vong

B. 2 vong

C. 3 vong

D. 4 vong

, I^i.

Rong rpc chiu tac dung hai liTc tiep tuye'n vdi

Biet he so ma sat giffa dp liTc Q va vanh dia la
;^

-J).)

R

(I)

rong roe la siJc cang T va liTc keo F. Hai liTc nay

den khi diTng lai dia quay di/dc xap xl

ITU-

ni\ut fpii

dia nhiThinh ve vdi dp Idn Q = lOON lam cho dia quay cham dan roi diTng lai.
= 0,5. Ke tijf liic bi ham cho

F-mg

US,,;

Gpi T la siJc cdng day treo vat nang m va a la gia
T - m g = ma =?'T = m(g + a)

•

D. a =

m+

toe chuyen dong cua vat, ta c6:

V I du 3 . Mot dTa mai c6 bdn kinh R = 50cm, khoi lifdng M = 10kg dang quay vdfi
toe dp 300 vong/phiit thi bi ham bang dp liTc Q hu^dng vao tam O ep len vanh

c a ^ F-mg

Giai

iiiUbiii

Chon dap an C

si)

do cua vat la g. Gia toe chuyen dpng cua vat m la

271

[

>; j -

:,{!..:•[

(rad) =271
^ ^ ( v o n g ) « 3,925 (vong) ^ 4 (vong)

'''^

'"'-^ '''''

-20

5

Vi du 4. Mot rong roc la mot dTa tron c6 momen quan tinh I , ban

-

Gia toe goc cua banh xe sau khi ehiu tac dung cua momen life can:

= 300 v/ph =

cogMR
=> Acp = - — =
2y 2
4|.iQ
. . . . . , , , : . M R . !.u

Chpn dap an D

life can c6 do Idn 20N.m. Banh xe diTng lai sau khi quay them diTdc xap xi
B. 4 vong

COo

= CO^)
'Q-Q^^
4.0,5.100

Banh xe dang quay deu vdi toe do goc 10 rad/s thi chiu tac dung cua momen
A. 12,5 vong

-COQ = 2y^.(^

M = ( F - T ) R = I.y=>y =

•

T.
m

(F-T)R
I

;

Gia toe tiep tuyen cua rong rpc la: a, = R.y =

(F-T)R'
I

•

Ap life Q tao ra life ma sat (Fms) tiep xuc vdi vanh dTa c6 dp Idn:

rpc: a = a, =

Momen life ham: M = -Fms-R = -jaQ.R
Theo phiTdng trinh dpng liTc hpc cua vat ran quay:
M = I.Y => Y = -

vdi I = IMR^ nen

Y=

=
- MR'
2

MR

Theo phiTdng trinh cua chuyen dpng quay: co^ - (OQ = 2yA(p
20

(2)

I

( l ) v a (2) cho: a = :^:^^BlgliOR2

(c6 dafu - VI momen nay can chuyen dpng)
:>": •

Chu y rang gia toe a cua vat nang m cung la gia toe tiep tuyen a, cua rong
(F-T).R^

F,„s = ^Q
•

•

a. — - = F - mg - ma
R^

a( m +•
R'

= F - mg

Chpn dap an C
21'


Phuang phap giai bai t$p trSc n g h i g m C o hqc 12 - Jrin

Cty T N H H M T V D V V H K r . i i g Vigt

Trpng Hung

Vi d u 5. Rong roc la mot vanh tron c6 momen quan tinh I ,
ban kinh R. Vat qua rong roc la doan day nhe khong co
dan, hai dau day treo hai vat nang m, va

m2

ma m; >

rrij

nhu" hinh ve. Lay g la gia toe rdi tU" do. Tha cho hai vat
_

B. a =

I
mj + m 2

(m,

C A U H O I V A B A I TAP TRAC N G H I E M

31112

chuyen dpng. Gia toe chuyen dong eua cdc vat la

2.1. Dai li/dng nao sau day luon luon la so' dU'cJng?
+m2)g

A. Momen life

B. Momen quan tinh

C. Gia toe goe

H—2

:

D. Toe do goc

2.2. Momen liTc co ddn vi la
m, - m-

C. a =

n-','ji-.v"*

A.N

D. a =

Giai
•

Vat mi di xuong: m i g - T i = mia => T| = mi(g - a)

•

Vatmjdilen:
+ a)

(2)

A. vSn tiep tuc quay nhanh dan deu

B. quay cham dan deu

C. dufng yen

D. quay deu

B. I = 0,002kg.m' C. I = 0,02kg.m'

D. I = 0,004kg.m'

2.5. Biet momen quan tinh cua thanh dai /, khoi lu'dng m doi vdi true quay di qua

, M = ( T , - T 2 ) . R = I.y

niig

Gia toe tiep tuyen cua rong roc la a, = Ry => y = — = — , vay:
R
R
M = (T,-T2).R = I R

mot dau thanh nhif hinh ve diTdc tinh bdi eong thtJe: I =

IiTdng 50g. Momen quan tinh cua thanh do'i vdi

( m i - m 2 ) g = a(mi+ m 2 + ^ )

^TI''^

Mot thanh OA dai 50em, khoi liTdng 200g
phan bo' deu. Dau A co gan vien bi nho khoi

(3)

(1), (2) (3) cho: m,(g - a) - m2(g + a) = I. —
\-. .
R
'

,

A. I = 0,04 kg.m'

tuyen T| va T2 lam cho rong roc quay nen: , ,

'

vao vat thi no

cua dTa do'i vdi true quay di qua tam la

Rong roc chiu tac dung cua hai life tiep

'

" D. kg.m

2.4. Mot dTa tron co ban kinh R = 20cm, khoi lUdng m - lOOg. Momen quan tinh

- m 2 g + T2 = m2a => T2 = m2(g

•

C. N.m

2.3. Mot vat dang chuyen dong quay nhanh dan deu. Sau do thoi tac dung life

(m,+ m2)g +

•

B. N/m

O

true quay di qua dau O va vuong gdc vdi
thanh xa'p xi bang
(mi - m 2 ) g
a=
I
m,+ m, + - V

A. I = 0,029kg.m'

B. I = 0,017kg.m' C. I = 0,013kg.m' D. I = 0,023kg.m'

2.6. Trai Dat coi nhU hinh cau dac co khoi liTdng rieng trung binh la 5520 kg/m^
v i ban kinh trung binh 6400km. Momen quan tinh cua Trai Dat doi vdi true

Ghi nhd:
Do'i vdi rong roc: a =

quay cua no xa'p xi bang
F.-F2
mi +

XX\^

H

IT

R^

A . I = 4,5.10"kg.m'

B. I = 9 , 9 . I 0 " k g . m \

C. I = 6,8.10'' kg.m'

D. I = 2,8.1 O^'kg.m'

*' '

'

2.7. Mot dTa tron ban kinh 20cm khoi lu'dng 1kg dang quay vdi toe do 120

1. Neu hai dau day c6 treo hai vat nang thi: Fi = mig; F2 = m2g

vong/phiit thi bj liTc ham tiep xuc vdi vanh dTa cd do Idn 1,57N. DTa dijrng lai

2. Ne'u nipt dau day la vat nSng m con dau kia keo bang krc F thl:

sau thdi gian

F-me

A. t = 0,6s

. . . i ' -

B.t=l,Os

C. t = l , 2 s

D. t = 0,8s

2.8. Mot thanh manh chieu dai / khoi liTdng phan bo deu cd the quay xung quanh
mot true nam ngang qua dau O. Biet momen quan tinh cua thanh doi vdi true


Phuong phAp giii bit t j p t r i e nghigm Co hqc 12 - T r j n Trgng Hung

O la ^ m ^ ^ (m

Cty TNHH MTV DVVH Khang ViQt

kho'i lUdng cua thanh). Tha thanh liic no dang nam ngang.

mg

A. a =

m +

Lay gia to'c rdi tiT do la g. Gia toe goc cua thanh liic vuTa tha

B. a =

R"

mg

mg

C. a =

I

D. a =

mgR

mR^ + 1

R^

2 14 Rong roc la mot dTa tron kho'i lu'dng 600g. M o t doan day
21

21

3/

v

3/

nhe khong dan vat qua rong roc, hai vat nang khoi lu'dng

2.9. M o t thanh manh O A kho'i lifdng phan bo'deu c6 the quay de dang xung quanh

Ian Wdt mi - 300g, m2 = 200g treo d hai dau day nhu' hinh

dau O. Biet momen quan tinh cua thanh doi vdi dau O la I = - m / ^ vdi m la

ve. L a y g = 9,8 m/s^. Luc dau giff eho hai vat ngang nhau
roi tha nhe. Sau 2s hai vat da each nhau (tinh theo phUdng

khoi lu-dng va / la chieu dai cua thanh. Lay g = 9,8m/sl Thanh du-dc tha nhe
liic thanh dang nam ngang. Gia toe dai eua dau thanh A liic vCfa tha la
A. 9,8 m/s^

B . 4,9 m/s'

C. 14,7 m/s^

A. 4,5m

D . 18,4 m/s^

thanh c6 the quay de dang xung quanh true qua dau O tiong mat phang nhm
ngang. B i e t momen quan tinh cua thanh doi vdi dau O tinh bang cong thilc
I = ^ m / ' . L i i c thanh dang nam yen ta tac dung vao dau A mot life F c6 do
Idn ION va vuong goc vdi thanh. Toe do dai cua dau A li'ie thanh q u e l difdc

A . 9,4 m/s

, ,

= ... . ,

B . 25,7 m/s

, ,

, ,
D . 12,5 m/s

lOrad/s thi bi ham l a i . Life ham c6 do Idn 2N, ep len vanh banh xe va hu'dng
ve true quay. Life ma sat giiJa life ep va vanh banh xe la 0,2. Sau thdi gian 5s
banh xe dijfng l a i . K h o i lifdng banh xe
B . 0,2kg

D . 2,5m

G

true quay la 0,025kg.m'. M o t doan day nhe khong dan
quan quanh ranh rong roc, mot dau day treo vat nang kho'i
lifdng lOOg. la'y g = 9,8 m/s^. Tha vat chuyen dong, gia toe

m

goe quay eua rong roe la
A. 4,9 rad/s'

B. 6,4 rad/s'

C. 9,8

rad

D. 3,5

tinh doi vdi true quay la

khong dan, hai dau day mang hai vat nang kho'i lu'dng Ian
lu'dt 500g va 200g nhu' hinh ve; lay g = lOm/sl Luc dau giif
hai vat diJng yen. Tha nhe eho hai vat chuyen dong, sau 0,5s
mot diem tren vanh rong roe da quay vdi toe do goe.

C. 1,0kg

D . 0,8kg

A. 15,0 rad/s

B. 6,4 rad/s

2.12. M o t dia mai quay nhanh dan deu tif nghi. B i e t rhng liic nay dTa ehiu tac
dung dong thdi cua momen phat dong va momen can. K h i dTa quay du'dc goe

C. 2,7 rad/s

D. 7,5 rad/s

HadNGDANGIAI

2.1. Dap an B .

'

60" thl momen phat dong thoi tac dung, dTa quay cham dan deu roi difng lai
sau khi quay them du'dc goe 30". Dp Idn momen phat dong M va momen can
M ' ( M va M ' deu du'dng) lien he vdi nhau bang bieu thi'fc

,

Momen quan tinh I = ^ m j r j ^

luon luon la so difdng.

i

,!(!"|

^
2-2. Dap an C.

A. M = 0 , 5 M '

B.M=1,5M'

C. M = 2 , 0 M '

D. M = 2 , 5 M '

2.13. M o t rong roc c6 momen qudn tinh doi vdi true quay la I ,

ban kinh R. Tren ranh rong roc c6 quan mot doan day nhe
khong dan, dau day c6 treo vat nang m nhu"hinh ve.

V d i F ddn vi la N ; d ddn vi la m nen M cd ddn vj la N . m
m*

2-3. Dap an

j ,
,

,

Cong thife tinh momen l i f c l a : M = F.d

Vl_y

Tha eho vat chuyen dong. Goi g la gia toe rdi tif do.
Gia toe ehuyen dong cua vat la

rad

0,012 kg.m', ban kinh 20em. Vat qua rong roc day nhe

2.11. M o t banh xe eo dang vanh tron ban kinh 50em dang quay vdi toe dp goc

A. 0,4kg

^^ • '

I ' c . 6,4m

B . 9,8m

2.16. M o t rong roc c6 momen quan

C. 4,3 m/s

•

2.15- Rdng roc c6 ban kinh 50cm, momen quan tinh doi vdi

2.10. M o t thanh manh O A dai / = 50em, khoi lu'dng m = 200g phan bo deu tren

goc 60° xa'p X I bang

('n ImX)

thangdtfng)

Mn\

D.

'

'

'
M

•

Luc thoi tac dung life (F = 0) nen M = F.d = 0

•

Hdn niJa tru'de do vat dang quay nen sau do vat quay deu.

y=

„

y =o


PhLfOng ph&p giJi b^i t j p t r S c n g h i $ m C o h p c 12 - I r a n T i u n y

Mmig

CtyTNHH

2.4. D a p an B.

M T V L ' V H Khang

•

Luc thanh vCfa m d i tha, momen lye tac dung vao thanh l a : M = mg. —

•

M
Gia toe cua thanh liic m d i tha: 7 = ~

Vi?t

I = i m R ^ =i.0,1.(0,2)^ = 0 , 0 0 2 (kg.m')
2.5. Dap an A.

;,

•

M o m e n qudn tinh cua thanh: I j =^m,./^

•

M o m e n quan tinh cua b i : h = m 2 .

=

m.

I

0,2

H-m-

.1'

=

•

3g
+ 0,05 .(0,5)^ = 0 , 0 2 9 1 6 6 . . . ^ 0,029 (kg.m^

Vay:

1 = -.

3

.D.R^

=

-F.R
imR^
2

•

Gia toe dai cua dau A: a = ^/a^ + a^

- . 7 C R \

15

=

-.71.(6,4.10'^)

15

.5,52.10-^

2/
Vay: a =

0^ +

4F

fM = -F.R

v2y

2.10. Dap an D.
•

I = -m.R'
2

M o m e n li/c tac dung vao dau thanh A: M = F . /

•

.
,
u
u
M
F./
3F
Gia toe goc cua thanh: y - — =
= —
,^
'm/2
"^^

•

Sau khi quay diTdc gdc A(p = 6 0 " = " ' " ^ d thi thanh dat toe dp gdc co ma:

mR

0)^ = 2v.Aq) (vi coo = 0)

©o.m.R

.t ^ t =
"
m.R
2F
V d i ooo = 120 v/phut = 2 v/s = 4n rad/s
COQ

:

•

/6F
co = J2y.A(p = J — . A c p
V m/

Toe do dai 6 dau thanh A:
,
6F./ ^
6.10.0,5 71
, T^ , , ,
v = co/= J
ãA(p=,
. - ô 1 2 , 5 (m/s)
m
V 0,2
3

'

^•ll.DapanA.

2.8. Dap an A.
•

•

Life tac dung vao thanh la trong li/c

Gia toe gdc cua banh xe sau k h i ham: y =

F,

-COo

Q

mg dat tai trong tarn G cua thanh
cdch true quay O ^ .

0<

^ .

2F

N e n : t = ' " - ' - " ' ^ = 0 , 8 (s)
2.1,57

mg

2

Luc dTa dtfng l a i (w = 0):
0 =

G

(xem cau 2.8)

a„ = — = 0 (liic vifa tha v = 0)

Co: w = coo + y.t
2F

11

Vdi

2.7. Dap an D.
M
M = I.y ->• Y = — v d i

—

' 2 /

.D

= 9,9258... X 1 0 " « 9 , 9 . 1 0 " (kg.m^)

Nen: y =

Y =

•

2.6. D a p an B.

3

2

Gia toe cua thanh luc vCfa tha la:

3

I = -.m.R^ v d i m = V.D =
5

-m/
3

2.9. Dap an C.

V a y momen quan tinh cua thanh c6 gdn bi la:
I=I,+l2

51

mg.

mg

M o m e n lu'c ham:

M = Ly = mR^

-COn

o

M = -F„,.R = -MQ.R

26

2*,


Phaong ph^p g i i l bai t$p trie nghi^m Co hqc 12 - TrSn Trgng Hifng

=:> m R \

t

=

,.QR ^ m = i i O l =
R.coo
0,5.10

= 0,4 (kg)

n .,V^

2.12 D a p an B .
•

Life CO momen phat dpng:

+

co^ = 2y. Acp -> y = — —
2A(p

,

\

"*

•

,

Luc do Chung each nhau: d = 2s = a.t^ = 1,225.2^ = 4,5 (m)
: , ; i r f . ,c;jy o u - ; ! h . d l

2.15. D a p an C

,.,

^ , , f

'

Llic chi CO momen can:
+

Sau thdi gian t m o i vat di du'dc quang du'Sng s (vat mi di xuo'ng, vat m2 di len)

; '

1 2
vdi: s = - a . t ;

.

2A(p

ri

0 - 0 ) ^ = 2 7 ' . A c p ' ^ 7' = -

—
2A(p'

' m g - T = ma = m.R7

V!i^

T.R^Iy

^'^^ A . A b ; ; i ^ ^ ^ f i ! > 3 6 n K D ^
,^
]

'

,

V

— + mR
R

mg =

mg

0,1.9,8

mR.-i
R

0,1.0,5.°^
0,5

= 9,8 (rad/s^) A I '
mg

2.16. i 5 a p a n D
•

(1) va ( 2 ) c h o :
M-M'
— =

" '

A(p'

M
o

'

'

' " '

'

A(p'

r+l =

Acp

-M'

"

M'

M
Acp'
<=>—: = ' +
Acp
M'

Acp

' :h

Gia toe cua cac vat eung la gia toe tiep tuyen cua vanh rong roc:
(mi-m2)g

30"
— 7 7 = 1 . J !.\
60°
^''

m i + m-) H — r R^
(m, -m',)g
co = yt = - A _ ]
l^°-j..i

M = 1,5M'
2.13. Dap an A

,

•

D o i v(3i v a t m : m g - T = ma

(1)

•

Doi vdir6ngroc:T.R = Iv= I .
1
R

(1)

va

a
(2)

cho:

mg - I . - y

'

a =

^

(mi-m2)g
.Ml

(mi + m 2 ) . R +
R
(0,5-0,2)

=

( 0 , 5 + 0,2).0,2+

0,012-'^

ã , u'J

uuZ

ô

Bai 3. M O M E N D O N G

LUONG.

D ! N H L U A T BAO T O A N M O M E N D O N G

L J ^ N G

T O M T A T LI T H U Y E T

I
m + —2

10

R^

2

-

M o m e n dong lu'dng cua vat r^n d6'i true quay la [ L = Leo

-

D d n vi cua momen dong lU'dng la: kg.mVs

2- Dinh luat bao toan momen dong lif(/ng
N J u M = 0 thi L = hang so]

2.14. Dap an A

2

^

1- Momen do ng lif<;ng

I

Trong tru'dng hdp nay: F; = mg; F2 = 0; irii = m; 012 = 0 nen a = —

n . , . m , . i ,

1112

™g
vt/Jii'

A

R^

A p dung nhanh cong thu'c tong quat: a =

ni,

= 7,5 (rad/s)

mg
= ma

(mi+m2)R + ~

v_-^ '

(2)

>-T = I . —
R2

a, _

^. ^, ,

~

V a t CO I khong doi thi no khong quay hoSc quay deu

-

V a t CO I thay doi thi Ijco, = IjWa

,

*
29


Cty TMIIIi MTV DVVH Khang Viet

huong ph^p giai bjii tgp trSc nghigm Co h9c12 - TrSn Trgng HUng

trong d6 M va / la kho'i lu'dng va chieu dai cua thanh.

BAI TAP C d B A N

M o m e n dong lu'dng cua thanh luc dang quay la

Dang 1. M O M E H D O ^ Q LUOriQ
Cong thifc: L - ICQ. Ddn vi cua I la kg.m^; oo la rad/s; L la kg.m^/s
/i du 1. Trai D a t coi nhiT hinh cau dac c6 ban kinh 6400km, khoi liTdng rieng
5 , 5 . 1 0 \ g W quay deu xung quanh true cua no v d i chu k i 24h. M o m e n dong
lUcfng ciia Trai Da't xap XI bang

A. 0,2kgm^/s

B.2,6.10'\g.m'/s

C. 7,2.10"kg.m^/s

D. 7,2.10'^kg.m'/s

•

I la momen qudn tinh cua thanh va bi d A d o i v d i true quay (con momen

'
1 =

M
— + m .1'
3

-M/2 +m/^

13

T6c dp goc quay cua thanh: co =

I=^.m.R2=-.V.D.R^= V
5
5
5 3

15

Vay L =

ô!iT

271

f

M
ã+m

I

M
+m

0,6

+ 0,3 .1.0,2 = 0,1 (kgm'/s)

Chon dap an C

CO =

D a n g 2 . D I N H L U A T B A O T O A N M O M E N DOING L U p N G

271

.TiR-'.D. ^

15

= — . 7 1 ( 6 , 4 . 1 . 5,5.1 O l -

T

Neu M = 0 thi L = hang so

24.3600

15

= 7 , 1 8 8 . . . x l 0,33" « 7-,72^. 1in33
0''(n
k g . m 2' / s )
ChpndapanC

'

'

Vi du 2. M o t banh xe bat dau quay tiT nghi xung quanh true cua no di/di tac dung
cua momen liTc 0,5N.m thi sau 10s banh xe c6 momen dong lu'dng
C. 4 kgmVs

B. 8kgm7s

A. 5kgm^/s

D. 3kgm7s

,, ;

•

I khong d o i : vat khong quay hoac quay deu.

•

I thay d o i : I.co = hang so".

; ; ,
- v . , M.;

V i du 1. M o t ngu'di dufng d tam cua mat ban xoay, hai tay cam hai qua ta ciing
kho'i lu'dng mo = 2kg. L u c dau hai tay ngu'di nay dang ngang, hai qua ta each
true quay r = 50cm va cho ghe quay vdi toe do U i = 3 vdng/s, sau do ngu'di
nay xep tay l a i sat ngu'di. Cho rang momen quan tinh cua ngu'di va mat ban

Giai
Co 7 =

D . 2,0kg.m^/s

M o m e n dong lu'dng cua thanh: L = I.co, v d i :

M o m e n dong lu'dng L = I.co v d i :

nen: L =

C. 0,lkg.mVs

Giai

quan tinh cua bi d O bang 0)

A. 2,6.10"kg.m^/s

.

B . l,Okgm^/s

do'i v d i true quay khong doi va bang IQ - 2kgm^. Toe dp quay cua mat ban luc

M

xep tay l a i la

I

A. n2 = 4,5v6ng/s

,
B . 1x2 = 6,0v6ng/s

M

•

.

nft''*f,f'

C. n 2 = 1,5v6ng/s D . na = 0

Giai

(0=y.t= -j-.t

M
M o m e n dong liTdng: L = I.o) = I . y .t = M . t = 0,5.10 = 5(kg.m /s)

Ngu'di - mat ban va hai qua ta la mot he k i n . V i trpng life cua he (la ngoai
life tac dung len he) eCing c6 phu'dng thang diJug nhU' true quay nen momen
I, =Io+2mor'

Chon dap an A
V i du 3. M o t thanh O A dai 20cm dong chat, tiet dien deu khoi lifdng 600g. H a i

ngoai life bhng 0, do do:

I|COi = I2CO2,

vdi

coi = 27ini

dau O va A C O gan hai vien bi nho cung khoi liTdng 300g. Cho thanh quay deu
CO2 =27m2

trong mat phang nam ngang xung quanh mot true thang duTng d i qua dau O.
To'c do quay cua dau A la Im/s.

V a y (lo + 2mor^).27rn, = Io.27in2 =^ n2 = ^"^^"^Q*"

n,=

2 + 2.2.0,5" „
.3

Diet momen quan tinh cua thanh d o i v d i
1

true quay tinh bang cong thiJc I = -Ml
30

2
,

= 4,5 (v6ng/s)

ill?' fh'

Chpn dap an A
31


^huong phAp giSi

bai t^p

trie nghigm Co h9c12 - Iran Irgng Hang

M

Vi d u 2. Thanh cUng O A dai / khoi lifdng M va bi nho khoi liTdng m = — cle

M o m e n ngoai liTc tac dung len he bang 0 nen
L = I,=lm,Rf

dang trifcJt tren thanh. Thanh c6 the quay trong mat phang nam ngang xung
quanh true thang diJng di qua dau O (hinh ve). Diet momen quan tinh cua

IQCOQ = Ico,

1 = 1, + I 2 = ^ m , R f + i ( 2 m , ) ( 2 R , ) 2 = 9 1 ,

vdi

thanh doi vdi true quay la I = ^ M . / ^ .

CO, = 27cn,; CO2 = 27rn2

(m)
Luc dau bi 6 A, truyen cho thanh quay deu vdi toe do 10 vong/s. De thanh quay
vdi toe do 18 v6ng/s thi can di chuyen nhe nhang bi den each true quay khoang

-4
'

3
'•'

. . :A n

r

-

•o--'

4

= ^ ^ = 26 (vong/phut)

Chon dap an C
C A U HOI T R A C N G H I E M V A BAI TAP

5 '

,-:••••.:>.

••

Ngoai lire tae dung vao thanh (gom trong life cua thanh va bi) deu cung
phifdng thang diJng vdi true quay nen momen ngoai life bang 0, do do:

IiCOi = I2CO2, v d i

^

3.1. Chon eong thiJc diing

' Giai

I, = i M / ^ +m/^ =
'
3

V a y : I|27ini = 9I|.27in2 => n2

A. L = ly

B.M =L

dco

C. M = L .

"dT

dco

D. M = d(I.Y)
dt

dT

3.2. Ddn vi cua momen dong lu'dng la

M

A . N.m

T " " 3,

B . kg.m^

C. kg.mVs

D . kg.mVs^

3.3. N e u long cae momen ngoai liTe tae dung len vat bang 0 thi
A. L = 0

I , = i M / 2 + m . x ^ = ^ ( / ^ + x2)

B . vatdiJng yen

C. vat quay deu

D . L = hangso

3.4. N e u tong momen ngoai liTc tae dung len vat ran (tu-c ed I khong ddi) triet
tieu thi vat CO

coi =27tni;c02 =27^2
.

A.y = 0

V a y ^ / ^ 2 7 r n , = ^ ( / ^ + x^).27m2
3

3

18

X

=

D . co = hang s o V 0)

th^ng diJng di qua dau ngdn chan) v d i hai tay luc dau xep sat ngu'di. N e u

-

9

ngirdi ay tiJ tCr dang tay ra thi ho
I

Chon dap an B

A . lap tu-c dijfng l a i

V i d u 3 . Hai dTa tron D , , D2 c6 khoi lifdng
va ban kinh Ian liTdt m, =

C. 00 = 0

3.5. Ngu'di mua ba le dang quay ngu-di tren dau ngdn chan cai (quanh mot true
>

nn

B . 7 = hang so

Ri =

• i' '

C. quay nhanh dan
D

^

'

'

,- a

1 >•

B . van quay nhuTcu
D . quay cham dan

ii;
j -

" t ' rv/

3.6. M o t vien bi nho k h o i li/dng lOOg quay deu 10 vong trong 2 giay va each true
quay I m . M o m e n dong lu'dng eua bi la

dong true quay nhiT hinh ve. Luc dau dia

—

Di quay v d i toe do n, = 234 vong/p con

62^^

dia D2 ddrng yen. M a sat 5 true quay

" ' ' ^ ^

khongdangke.

A . n2 = 117 vong/phiitB. n2 = 58,5 vong/phut
D. n2 = 29,25 vong/phut

C. n2 = 26 vong/phut
Giai

32

B . 6,28kg.m^/s

C. 3,14kg.m^/s

D . 4,85kg.m^/s

3.7. M o t ngirdi khoi lu'dng 60kg dang difng tren M a t D a t d vT do 45°. Coi Trai
B a t la hinh eau ban kinh 6400km va tiT quay quanh true cua no v d i thdi gian
" l o i vong quay la 24 g i d . M o m e n dong lu'dng eua ngu'di d o i vdi true quay cua

Sau do cho hai dTa ch6ng l e n nhau thi he hai dia cung quay v d i toe do

La'y hai dTa l a m m o t he k i n .

]1

A . l,57kg.m^/s

Trai Da'txa'p X I bang
A. 89315,6kg.m-/s

B . 17863Ikg.m'/s C. 89,3kg.m'/s

D . 178,6kg.m'/s

^•8. M o t vat ran bi(t dau quay nhanh dan deu tCr nghi vao liie t = 0. V a o liic t,
momen dong lu'dng ciia vat la L ; thi vao liie t2 = 2t| momen dong lu'dng cua
vat la
33


Udl

1

i-zu i i y i ^

ic

~

iiuit

W ~ r n r n n i w i v uv^^T^^a^g^^V^gt

riyiiy

A. ^
B. 2L,
C. ^
D. 4L,
2
4
.9. Mot vat ran bat dau quay diTdi tac dung cua momen life c6 do Idn 0,1 N . m thi
CO momen dong luTdng la Ikg.m^/s sau thdi gian
A. 10s

B. Is

,

3.15. Mot van dpng vien triTpt bSng dang du'ng yen va quay, neu hp dang tay ra thi
A. quay cham lai VI momen quan tinh giam
B. quay cham lai VI momen quan tinh tang

,

C. 20s

D. 5s

C. quay nhanh hdn vi momen quan tinh giam
'

D. quay nhanh hdn VI momen quan tinh tang.

.10. Mot dTa tr6n ban kinh 20cm dang quay nhanh dan deu du'di tac dung cua

HLfdNG D A N GIAI

liTc tie'p xuc vdi vanh dia. Trong thdi gian 2s, momen dong lu"cfng cua dia tang
3.1. Dap an B

them 5kg.m^/s. Dp Idn life tac dung vao vanh dTa la
A. 25N

B. 15,6N

C. 5,8N

'

3.2. Dap an C

D. 12,5N

.11. Mot thanh ciJng dai Im, kho'i lufdng 600g phan bo deu tren thanh, hai dau

3.3. D a p a n D

^^

CO g^n hai bi nho, khoi lifdng moi bi la lOOg. Thanh quay deu quanh true di

3.4. Dap an A

'

qua trung diem va vuong goc vdi thanh, toe dp moi bi la lOm/s. Momen dpng
B. 2kgm^/s

C. 5kgm^/s

D. 20kgmVs

m

,
'

'

^,
'

m

_

,

f

C d M = 1 . ^ = 0 viI^Ozz^ ^ ^ 0
dt
dt

lu'dng cua he thanh va hai bi la
A. 3kgmVs

'

'

'

hayy = 0

(chij y: y = 0 thi CO = 0 hoae co = hang so)

4^

.12. Mot ngiTdi khoi lu'dng m (coi nhif cha't diem) dang diJng d mep san hinh

3.5. Dap an D. VT trpng life cua ngiTdi song song vdi true quay nen tong momen

ngoai lirebangkhong, dod6:I,cO|

trdn nam ngang khoi luTdng M = 4m c6 the quay de dang xung quanh true

=l2C02OC02=

i-co,

1 •* •

thang diJng. Liie dau ngiTdi va san dilng yen. Ne'u ngu'di ay chay deu quanh
Khi tir tir dang tay ra thi I2 tang dan nen © 2 giam dan: ngiCdi ay quay cham dan

mep san vdi toe dp goc coo thi san

3.6. Dap an C

A. van diJng yen
B. quay deu vdi toe dp goe 0,5cOo theo chieu ngiTdc vdi ehieu chay cua ngiTdi

L = Leo = (mR^).27tn vdi n = ^ = 5 (v6ng/s)

C. quay deu vdi toe dp goc 0,5coo theo cting ehieu chay cua ngu'di
D. quay deu vdi toe dp goc

4CL)O

= (0,1.1 ').27t.5 = 7t = 3,14 (kg.m^/s)

theo ehieu ngiTdc vdi ehieu chay cua ngu'di

.13. Hai dTa tron D, va D2 bKng dong, c6 cung dp day nhu'ng ban kinh Ri = 2R2

3.7. Dap an A

true thang du'ng. Luc dau hai dTa rdi nhau va dang quay cung chieu vdi

•

Ngu'di each true quay khoang: r = M H = Rcoscp

cae toe dp n i = 2 vong/s va nz = 4 vong/s thi sau do hai dTa dinh nhau va ciing

•

Momen quan tinh cua ngu'di do'i vdi true quay:

CLing

quay vdi toe dp
A. 8/3v5ng/s

I = mr^ = m(Reos(p)^
B. 12/5 v6ng/s

C. 36/17 v6ng/s

D. 20/9 v6ng/s

.14. Hai dTa tron D i , D2 c6 khoi liTdng va ban kinh Ian liTdt m i = m2, R, =

•
c6

cung true quay thang dufng. Luc dau hai dTa rdi nhau va quay ngiTdc chieu
nhau vdi cae toe dp coi = 4rad/s, 0)2 = 8rad/s sau do du'de tha nhe nhang cho
hai dTa dinh nhau, chung ciing quay vdi toe dp
A. 5,6rad/sva ngu'dc ehieu quay cua D | ^ ^ . ' ^
B. 5,6 rad/s va eijng chieu quay cua P |
i'
C. 4,0 rad/s va ngiTde ehieu quay cua D i
D. 4,0rad/s va ciing chieu quay cua Di

'

Momen dpng lu'dng eua ngiTdi:
L = 1(0 = m(Reos(p)l — = 60(6400.eos45°)l
24.3600

-89315,6 (kgm^/s)

3.8. Dap an B
cjLi=Ico.=ly.t,

L2 = 1(02 = ly.tj

- = - ^ = 2 =:^L2 = 2L,.

L1

^1

3.9. Dap an A
M
L = 1.(0, vdi CO = yt = — . t n e n L = I . — . t = M . t = ^ t = — = — = 10(s)
I
I
M 0,1
35


Cty TMh

3.10. D a p an D
Co

I|CO| + I2CO2 = ( I | + I 2 ) . C 0

L , =Ico, =I(cOo + y t i )

M
. A L = L2 - L , = I.Y(t2 - t,) = I-Y-At = I . y .At = M . A t
AL
R.At

= 12,5(N)

0,2.2

3.11.Dap a n B

Co

L'(he)
, . , =—Ml^
12
V

V

N e n : L = I.co =
'

U2

=2(kgm^/s)

M

+ 2 . m (-]
.2.

m

.

I,=

im,R?;l2=^m2Rh^m,(2R,)2=4I,

•

Theo dinh luat bao toan momen dong lu'dng:
I|CO, + I2CO2 = ( I | + l2)C0 = ^ CO = - ! — !

I,+l2

T2^"2"

2v

1-

CO

I , . n , +I2.n2
16I,.2 + l2.4
36 ^ .
,^
=> n = ——
— -=
=
— = — (vong/s)
I,+I2
I6I2+I2
17
3.14. D a p an A

L2 =IC02 =I(COo +Yt2)

V d i M = F.R nen: A L = F.R.At =^ F =

' DVVH Khang Vi§t

Chon chieu du-dng la chieu quay cua dTa D , t h i : co, = 4rad/s; CO2 = -8rad/s
7

'2,

2v

(M

/

U2

— =

h

ni

.2v./ =

'2,

f0,6
[ 12

_i

nen : co =

0,0 .2.10.1
2 J

I,.4 + 4.Ii(-8)
• = -5,6(rad/s)
I,+41,

Da'u " - " chu-ng to khi dinh nhau hai dTa cung quay ngU'dc chieu vdi D , , toe
do quay la 5,6 rad/s.

"i

3.12. D a p a n B

^ ^

T o n g momen ngoai life tac dung l e n he bang

3.15. Dap a n B

,,

Co IjCOi =

khi dang tay ra thi

I2CO2,

,„
I2

'

> I , (tang) =^ CO2 < co, (giam)

khong V I ngoai li/c (la trong liTc cua ngu'di va
san) song song vdi true quay cua san nen:

Bai 4 . D Q N G N A N G C U A VAT R A N

L , = L2,

Q U A Y Q U A N H MOT TRgC CO DjNH

L j = 0 (luc dau he diJng yen)
L2 = I s a n - ® + Ingirai-'^0 -

U

V a y : 0 = mR\2(o + coo) ^ co =

j
COn

•

'

' "

* ''^"P^'^W*^'

'•

^

^ •.nyirf::^'A-'\

Co I , = ^mjRJ^ =^(s,.d.D).R^ vdi si = TtR?

)•

• DinhluatbaotoandongliTdng

vdi:

I la momen quan tinh cua vat (kg.m^)
CO la toe do goc quay cua vat (rad/s)
W,, :Jun.

Chiiy:
•

^

,',

.',

N e u vat ran viTa chuyen dong tinh tien vufa ehuyen dong quay (nhiT banh
xe) thi dong nang cua vat ran la: W,, = —Ico^ + — m v "

= ^ . T i . R f .d.D (d: do day; D : khoi lUdng rieng)
Ti/dng tif: I2 = ^ . n . R j . d . D VI R, = 2R2

TOM TAT LI THUYET

Dong nang cua vat ran quay quanh mot true co djnh W , =-.I.co2

dafu " - " chiJng to san quay ngU'dc chieu chay cua ngUcJi v d i toe do
3.13. D a p an C

;

.m + (m.R^).o)o =mR^(2oo + ©o)

Trong do^ V la to'e do cua khoi tam trong chuyen dong tjnh tien (ciing la to'c
do cua vat)

I i = 2\l2 = I6I2.
•

D i n h l i dong nang:

•A(ngoai lire) ~

(sail)

(dSii)

Li+L2 = L

36

37


^hifong ph^p giai bai tjp UJc nghigm Co hQc12 - Tran Trgng Hung

V i d u 4. Banh da la mot dia tron c6 khoi lu'dng 100kg ban kinh 50cm. L a y TT^ = 10.

BAI TAP C d BAN
V i d u 1. M o t vat ran quay quanh mot true c6 dinh. Goi I va L Ian lu'dt la momen
quan tinh va momen dong lifdng cua vat doi vdi true quay do thi dong nang
cua vat la
A.

W ,=

B. W<,=

2L'I

C.

21

Cty TIMHH MTV DVVH Khang Viet

—

2L

D. Wd =

2^
2L

De banh da dat du^dc to'c do 120 vong/phut tuT nghi trong thdi gian 10s thi cong
sua't trung binh cua dong cd cung cap cho banh da la
A. 25W

Co

Dinh l i dong nang:

vdi

21

21

Vi d u 2 . Coi banh xe liJ-a nhiT mot dia tron dong chat. 6 ciing thcfi d i e m banh xe
dang chuyen dong, giiTa dong nang. tinh tien W j („> va dong nang quay W j (q,
l i e n he bang bieu thtjfc

A(ngoaito,

= -W

= W d ( s , „ , ) - W < , « , i t u ) = -Im^ -0

1
life)

~

i-mR^
.2

(27m)' = mR'.Ttln^ = 100.(0,5)^ 10.2' = 1000 (J)

A(ngoaiivrc)Chinh la c o n g c u a dong c d nen c o n g suat dong l a :

P =A . i ^ = ,00(W)
t
10
Chon dap an D .

A. W,(,o = W,(q)

V i du 5. M o t qua cau du^dc tha Ian khong tru^dt tiT trang thai nghi d A cua mat

D. Wd,„) = 4 W c l ( q )

C . W a „ „ = 2W<,(q,

phang nghieng vdi do cao A H = h (hinh ve).

Giai
•

D . lOOW

I = -mR^
2
(n = 120 vong/phiit = 2 v6ng/s)
co = 27in

nen A(ngoai

Chon dap an B

C. SOW
Gi^i

Giai
W^_^ 1

B . 200W

Bie't momen quan tinh cua qua cau la I = "•nR^

Wd(„)= ^ m v ^

trong do m va R la khoi lu'dng va ban kinh. Toe

do khoi tarn qua cau khi Ian den B la
B . v = 7 ^

I=-mR'
2
v
co = —
R

nenWd(q, = - . I m R ^
2

hay : Wc („) = 2Wd (q)

' '

/ \
v

1

2 1
Chon moc the nang S B .
C d n a n g d A : E A = mgh

Chon dap an C.
V i d u 3, M o t vien bi c6 hinh cau dac khoi lu^dng m ISn khong triTdt vcti toe do V .
C. 0,5mV^

D . mV^

Giai
D o n g nang cua vien bi liic dang Ian:
(2
W<, = W<,(,„ + Wd,q,= ^ m V 2 + l l c o 2 = ^ m V 2 + ^ - - m R ^

l5

Chon dap an A

D.v=,|-.gh

Giai

'

D o n g nang cua vien bi la
A. 0 , 7 m V '
B. 0,2mV'

C. V2ih

)

= 0,7mV^

1
Cd nang S B : E B = - m v ^ + -Ico^ = i m v ^ + - - m R
2
2

2
2 5

vRy

7
2
= —mv
10

Theo dinh luat bao toan cd nang: E A = EBC:> mgh = — rnv^ =:> v = ^ y g h
Chon dap an A .
4.1. D

C A U HOI VA BAI TAP TRAC NGHIEM
ai liTdng khong phu thuoc vao khoi lu'dng eiia vat la

^ - m o m e n quan tinh

B . dong nang

^- momen lire

D . momen dong lu'dng

39


Ciy f r j i l i l M i V DVVH Khang Vigt

Phuong ph^p giSi b^i tjp trie nghi^m Co hqc 12 - TrSn Trpng HtJng

4.2. M o t vat ran quay quanh true c6' dinh. M o m e n dong lifdng t i n g 2 Ian thi dong
f

nang quay
A. tang 2 Ian
4.3.

vf,

,

,

4.10.

Thanh O A dai / dong chat tiet dien deu c6 the quay dS dang xung quanh

true quay qua dau O.

B. giam21an

C. tang 4 Ian

D . g i a m 4 Ian

M o t vat ran dang quay quanh true eo djnh v d i momen dong lu'dng la

Luc

dau thanh diJng yen 6 vj t r i thang diirng. M o m e n

O

quan tinh eua thanh do'i v d i true quay O la I = - m / ,

1 kgm^/s va dong nang la 2J. M o m e n quan tinh eua vat la
A. 0,25kg.m'

D. l , 5 k g . m '

C. l,Okg.m'

B. 0,5kg.m^

4.4. M o t rong roc c6 ban kinh 20em, momen quan tinh 4 . 1 0 ' \ g . m ^ de dang quay
xung quanh mot true c d dinh qua tam eua no. Doan day manh quan quanh
rong roc, dau kia treo vat nang lOOg (hinh ve).

4.5.

A. 2,50J

B. 1,25J

C. 3,75J

D . 12,5J

A. V,,

^j„. J
-

m

B . 2,6.10" J

C.4,8.10''j

D.4,8.10'-'j

tren mat phang nghieng nay thi van tdc ban dau eua bi la
B . VSm/s

D . Vl5m/s

M o t hinh tru dac lan khong tru'dt. Biet momen quan tinh cua hinh tru do'i vdi

true quay la I - ^ m R ^ , trong do m la khoi lu'dng va R la ban kinh cua tiet dien

B . 12J

C. W„„ = 4W,(q)

D. W(,o = W,q,

dung mot life 2 N t i e p xiic v d i vanh dia k h i dTa diJng y e n . Sau 6s ke tif luc bat
^'^^'^ ' . - i ^

dau quay, dong nang eua dTa la
. )

B . 9J

W

,«,

! C . 72J

i

,: ^

D . 36J

A. P = 4 0 W

- 10. Cong sua't trung binh eua quat

B . P = 80W

nam

ngang den va vao tu'dng thang dilng. To'c do kho'i tam cua qua cau ngay

Nhiet lu'dng toa ra trong thdi gian va cham la
B . Q = 40J

A. lOs .

B . 20s

C. 15s

D . 30s

M o m e n quan tinh: I = J^mjif

E>6ng n a n g W j =

= 125J

2

M o m e n dong lu'dng: L = Ico

B . Wa = 250J
'

iW+lmv^
2

D o n g nang ciia banh xe la

•

C. Wa = 375J

• •

D . W,, = 500J

D . Q = 7J

4 1 . Dap an C

M o t banh xe (coi nhu' dTa tron) kho'i lu'dng M = 20kg Ian khong tru'dt tren
mat phang ngang v d i toe do eua khoi tam la v = 18km/h.

C. Q - 1 6 J

HLfdNG D A N GIAI

M = 5000kg dang diJng y e n . M o t dong cd cong suat trung blnh P = lOkW lam
= 10. Banh da dat toe do n = 120 vong/phut sau thdi gian

D . P = 60W

trurde va sau khi va cham vao tu'dng la V i = 5m/s va V2 = 3m/s.

A. Q = 56J

banh da quay. L a y

C. P = 1 6 0 W

4.14. M o t qua cau dac kho'i lu'dng M = 5kg lan khong trufdt tren mat san nhan

M o t banh da coi nhu' dTa sat dong chat c6 ban kinh R = I m va khoi lu^dng

•

D . 3J

4.13. Cac canh quat may tao thanh mot vat ran cd momen quan tinh do'i vdi true
(0 = 120 vong/phut. La'y

B.W„„=-W,„

M o t dTa tron ban kinh 10cm, khoi lu'dng 4kg c6 true quay d tarn dTa. Tac

A.

C. 6J

quay la I = 2kg.m'. Sau 2s ke tiT liie dong dien canh quat quay v d i toe do

A. W,„) = 2W (q)

A. 18J

hinh tru. Dong nang cua hinh tru la 18J. Dong nang quay cua hinh tru la
A.9J

CO lien he

40

C. V6 m/s

M o t cai ong thanh mong dong chat va tiet dien deu Ian khong tru'dt. Biet

d eCing m o t thdi d i e m giffa dong nang tjnh tien W(„) va dong nang quay W(q)

4.9.

D. v„,„ = 7 6 ^

4.11. M o t mat phang nghieng hdp vdi phu'dng nam ngang gdc a - 30°. L a y g =

4.12.

kinh eiia tiet dien.

4.8.

C. v„,i„ - 7 3 ^

V /

A. N/lOm/s

momen quan tinh eua 6'ng la I = M R ^ trong do M la khoi lu'dng va R la ban

4.7.

3g

B. v,„,„ =

lOm/s^. D e vien bi cd the lan (khong tru'dt) du'dc do d a i s - 1,4m tif du'di len

D o n g nang quay eua T r a i Dat xap x i

4.6.

3g
21

Coi T r a i D a t nhu" hinh cau dac c6 khoi lu'dng 6.10^^kg tif quay xung quanh

A . 2,6.10'"'J

Ox thi ta can truyen cho dau A eiia thanh mot van to'c
v theo phu'dng nam ngang c6 do Idn to'i thieu

true eua no v d i thdi gian moi vong quay la 24 gid.

'

^ ^ -> V

rdi t i / do. D e thanh c6 the quay den vi tri nam ngang

' :

La'y g - l O m / s l Thii nhe cho vat nang chuyen dong
tijf nghi. Sau Is dong nang quay eua rong roc la

trong do m la kho'i lu'dng cua thanh. L a y g la gia toe

n b i :5 M • .

-


Phjgng phap giai bai t j p trSc nghijnn Co hQc12 - Jr&n Trpng Hung

Cty TNHH MTV DVVH Khang Vi?t

Ba dai lifdng tren deu phu thupc kho'i lifdng m .

4.8. E>ap an B

M o m e n lufc: M = F.d khong phu thuoc nn
4.2. D a p an C

Angoni lire = W d (sa„) - Wrf

(jSu),

vdi

A„go„i i^c

'

I = i m R ^ =^.5000.1^ =2500(kg.m2)

Co W d = — ( v i d u 1)
21
L tang 2 Ian

VayP.t=^Ico'-0^t=^,vdi

4.3. D a p an A

iff

*

2500.(47t)'

nent =

2Wd

2.2

= 20 (s)

2.10'

= 0,25 (kg.m^)

1 =

21

CO = 27i.n = 27:.2 = 4n (rad / s )
P = 10^W

Wd tang 4 Ian.

Co W , =

chiuh la cong cua dpng cd = P . t

4.9. Dap an C

4.4. D a p an B
mg

• A p dung cong thiJc: a -

(xem Phan ghi nhd - trang 22 - bai 2)

+ - M . V ^ , vdi

W d = Wd(quay) + W d (,i„h lie'n) = 1^^^

m +

^

R

-

mg
^ . t=

co = yt =

I

0,1.10

/.,

— .l=25(rad/s)
Wd=

1
= ^Ico^ = ^ . 4 . 1 0 " - \ 2 5 2 = 1,25 (J)

-1(0

2

\

-MR^

2,„2
= - -MR
2 5

^^271^'

^.6.10^^ ( 6 , 4 . 1 0 ' y
5

« 2,6.10^' (J)

V

+ iMv^= -Mv^+-Mv^= - M v ^
2
4
2
4

= 18 km/h = 5 m/s

s ,

Vay W d = - . 2 0 . 5 ^ = 3 7 5 (J)
4

4.5. D a p an A
Wd=

- .

vRy
vdi

D o n g nang quay:

27C

24.3600

\

''

'

Lay moc the nang tai v i tri kho'i tam Go cua thanh luc dau.
Theo dinh luat bao toan cd nang:
O

^1(0^ + 0 =

+ m g ^ > mg.^

Go ^^mmm^mmmp.

J

W,„)= ^ M V ^

2

I = im/2

W<„:.il.(02

lo)^ > mg./, vdi <

=:i(MR2)

Vay:W,o=W„)
-> V> 7 ^

, =M . _ ^ . - ^ = ^
I

,l^j,2

mR

= ,0(rad/s^)

4.0,1

2

3

V
CO = —
/

2

4.7. D a p an D

/, v '

4.10. Dap an C

Wd.^u = W , , „

4.6. D a p an D

i

nen:

V

co = —
R

^ _ j T i ^

a

I = lmR2
2

^

v,.,i„ =

, nen:

1 ,2

- m l

3

V^

>mg./

V

,'

73^7

^ • J l - D a p an A
Lay moc the nang t ai vi tri ban dau.
Theo dinh luat bao toan cd nang:

CO = Y t = 10.6 = 60 (rad/s)
W , = -.Ico^ = - I m R ^
2
42

.(0^ = - . 4 . 0 , 1 ^ 6 0 ^ = 3 6 (J)
4

2

ICOQ

+ ^ m v p = mgh , vdi h = s.sina
43


CtyTNHH MTV DVVH Khang Vi$t

Phuong phap giai bai tap trSc nghi^m Co hgc 12 - Iran Trpng Hung

vcti

1 =- m R>2
5

Bai
B

,
1
nen: —
2 5

5. T O N G

KET CHUCING

T O M T A T Lf

+ —mvo = mgs.sina

R

I:

D Q N G

Ll/C

HQC

VAT

RAN

THUYET

1 Td'c do goc va gia toe gdc trong chuyen dyng quay cua vat ran

R
^

a Toe do goc: co = — . Ddn vi co la rad/s
dt

-I-_^=:gs.sin a

5

2

10
.
<=> V o = J y g s . s i n a =

— .10.1,4.- = V l O (m/s)
7
2

b Gia toe goc: y = — . Ddn vj y la rad/s^
dt
2. Phrfcfng trinh dong Irfc hpc cua chuyen dong quay bien doi deu
1 2
(p = (Po+coot + 2- y t

4.12. Dap an C
Dong nang tinh tie'n: W(„) = - m v "

C0 =

CO0

+ Yt

:, . . ••:

co^- COQ =2yA(p
Dong nang quay: W(q) = ^Ico^ = ^

2

R

= —niv^
4

•

Vay: W(,„=2W,q,
Dong nang cua hinh tru: W,, = W(„) + W(q) ^ 3W(q)

.,.,„.

quay nhanh dan ncu: (oy > 0

,,

. ,

rj

•

quay cham dan neu: coy < 0

^ ^

•

quay deu neu y = 0

.. .j,

a. Van toe:

V

Theo dinh li dong nang, cong lam canh quat quay: A = - l o ) ^ - 0

•

.

?f,i

= co.r

•

vdi (0 = 120 vong/phut = 2 v6ng/s = 4n rad/s, nen: P = •^•^^'^^ = 80 (W)
2.2
"

vdi an= — = co .r

,

a, la gia toe tiep tuyen dac tru'ng cho sif thay ddi ve dp Idn cua v , vdi

a, =r.y

4. Phufofng trinh dong lijfc hoc cua vat ran quay quanh mot true
a. Momen liTc dd'i vdi true quay: M = F.d. Ddn vi cua M la N.m

Dong nang cua qua cau lan khong tru"cJt:
(2
1
W.i= - I ( o " + - m v ' = - - m R '
215

.

a„ la do Idn gia toe hadng tarn dac tru'ng cho sir thay ddi ve hifdng cua
V,

Cong sua't trung binh cua quat: P = — =
t
2.t

1 2

7

2

•

M > 0 ne'u vat quay theo chieu du'dng (qui U'dc).

•

M < 0 ne'u vat quay theo chieu am.

+ —mv = — m v
2
10
Dp giam dong nang cua qua cau ngay tru'dc va sau khi cham vao tu-dng

b. Momen quan tinh: I = ^ m j . r ^ . Ddn vi cua I la kg.m^

chinh la phan nhiet nang da toa ra trong thcJi gian va cham:

c- PhiTdng trinh dong life hoe: M = I.y

Q = I AW, I =

. ,

b. Gia toe: a = ^a^ +af

4.13. Dap an B

•

,

3. V$n t6c va gia tOc cua mpt diem tren vat ran quay ^

<^W,,>=iw,=i.l8 = 6(J)

4.14. Dap an A

,,

m( vf - v^) = ^ . 5 ( 5 ^ - 3^) = 56(J)

i

'

^- Momen dong lifdng
^- Momen dong lu'dng cua vat ran ddi vdi true quay: L = I.co
E)dn vi cua L la kg.mVs
b- Djnh luat bao loan momen dong lu'dng: Ne'u M = 0 thi L = hang so

44

•

I khong ddi: vat quay deu hoac du'ng yen

•

I

thay ddi:

IiCOi =

' '

I2CO2

45


6. Dong n a n g ciia vat r a n quay:

-

—I
Bcfn vi

la J.

CAU HOI VA BAI TAP TRAC NGHIEM

5.1. Cac ngoi sao diTdc coi nhu"cac khoi cau bang khi tu" quay quanh minh ma khong
chju tac dung cua ngoai life va c6 the tich co dan. To'c dp goc cua ngoi sao
A.khongddi
,
B.tangdan
C. giam dan
D. liic tang, liic giam
5.2. Mot vien bi dang hinh cau dac ban kinh 10cm kho'i liTcJng 1kg Ian khong
trUdt vdi toe do 5m/s. Dong nang cua vien bi la
A. 12,5J
B.5J

C. 17,5J
D. 20J
5.3. Banh xe hinh vanh tron ban kinh 50cm chju tac dung cua hai liTc tao thanh
ngau life, moi li/c ed do Idn ION tiep xiic vcti vanh banh xe. Momen dpng
lu^dng cua banh xe sau 10s ke tuf luc bat dau quay la
A. 12,5kgm^/s
B. lOOkgm^/s
C. SOkgmVs
D. 37,5kgmVs
5.4. Mot vat ran quay quanh mot true co dinh vdi toe do goc khong doi. Mot
diem baft ki co dinh tren vat ran khong nam tren true quay co
A. gia toe tiep tuyen bang khong va vectcf gia toe hu-dng tam thay doi
B. gia toe tiep tuyen bang khong va vectd gia toe hiTdng tam khong doi
C. gia toe tiep tuyen va gia toe hUctng tam khong doi va khac khong
D. vectd gia toe (toan phan) khong doi
5.5. Phu-dng trinh chuyen dong quay cua vat ran quanh mot true co dinh la:
(p = 2t^ + 3t - 6, trong do t tinh bang giay, cp tinh bang rad.
Toe do dai ciia mot diem tren vat ran caehnruc quay 10cm liic t = 5s la
A. 5,2m/s
B. 4,6m/s
C. 9,2m/s
D. 2,3m/s
5.6. Sau thcii gian 10s toe do quay cua banh xe tang deu tiT 120 vong/phiit len
480 vong/phut. Biet ban kinh banh xe la 20cm. Quang du'cfng banh xe da chav
diTdc trong thdi gian noi tren la
A. 31,4m
B. 62,8m
C. 45,5m
D. 82,6m
5.7. Mot dia mai chuyen dong nhanh dan deu vdi gia toe goc y = 2 rad/sl Biet

ban kinh R = 20cm. Do Idn gia toe dai ciia mot diem tren vanh dla sau Is ke
tijf luc bat dau quay xap xi
A. 0,8m/s^
B. 0,4m/s^
C. 0,89m/s^
D. 0,55m/s^
5.8. Mot vat ran quay nhanh dan deu xung quanh true qua O tren vat ay. La)'
- = 0,318. Khi dia quay du^dc goc 60° tiT nghi thi vectd gia toe a tai diem M
co" dinh tren vat ran da hdp vdi ban kinh OM goc 9 xap xi bang
A. 9 = 45,8°
B. 9 = 25,5°
C. 9 = 64,3°
D. 9 = 18,5°
46

5.9. Thanh manh OA dki I = 50cm, kho'i lu'dng m = 50g co the quay de dang xung
quanh true qua dau O trong mat phang nam ngang. Luc thanh nam yen, tac
dung li/c F CO do Idn F = ION vuong goc vdi thanh. Liic thanh quet dufdc goc
60°, toe do dai cua dau A xap XI bang
A. v = 22,5m/s
B. v = 45,7m/s
C. v = 18,6m/s
D. v = 34,4m/s
5.10. Thanh OA dong cha't, tiet dien deu co the quay d i dang xung quanh dau O
trong mat phang thang difng. Biet momen quan tinh ciia thanh do'i vdi dau
quay O la I = ^ m / ^ , trong do m va / la kho'i lu'dng va ehieu dai cua thanh.
Thanh dUde tha nhe liic no dang nam ngang. Biet gia to'c rdi tiT do la g. Gia
toe (dai) cua dau A liic vtra tha
A.O

B. ^
C. 2g
D. ^
2
^
2
5.11. Tac dung len mep ciia dia tron dang dilng yen mot liTc tiep tuyen vdi dia
ed do Idn khong doi thi
A. dia quay deu
B. gia toe gde ciia dia bang khong
«f ?
C. to'c do gde cua dia ti le thuan vdi thdi gian quay
D. gde quay ciia dia ti le thuan vdi thdi gian quay
5.12. Mot dia tron dong eha't khoi lu'dng 4kg, ban kinh 10cm dang quay deu
quanh mot true vuong gde vdi mat dia va di qua tam vdi to'c do 60 vong/phiit
thi bi ham bdi mot liTc tiep xtie vdi mep dia. DTa quay eham dan deu va dCfng
lai sau khi quay them dUdc 10 vong nifa. Do Idn li/c ham la
A. 3,6N
B.0,72N
C. 0,0628N
D. 6,28N
5.13. Mot dTa tron ed kho'i lu'dng 2mo ban kinh R dang quay quanh true thang
diJng qua tam vdi toe do 3 vong/s. DTa tron thi? hai eiing true quay vdi dTa
trirdc CO kho'i lu'dng mo va ban kinh R diTde dat nhe nhang len dTa tru'de, hai
dTa Cling quay vdi toe do
A. 6 v6ng/s
B. l,5vdng/s
C. 4,5 v6ng/s
D. 2 vong/s
5-14. Mot vat ran dang quay nhanh dan deu quanh mot true co dinh (bo qua li/c

can) du'di tae dung cua ngoai liTc. Luc t = 0 ngoai liTc triet tieu, ke tiJT dd trd di
vat ran
A. van quay nhanh dan do quan tinh
B. duTng lai
C. quay eham dan roi duTng lai
D. quay deu
'
47


-

Cty TNHH MTV DVVH Khang Vigt

Phuong
phjp giai
bai tap trSc nghiSm Cd hpc
I fanMirpng
HUngban kinh R = lOcm c6 the quay
5.15. Rong
roc
hinh dia tron khoi liTdng
= 3kg,

C. M p i d i e m tren vat ran dang quay c6 cung td^c do goc va gia td^c goc (triT
cac d i e m nam tren true quay)

de dang xung quanh true O qua tarn. V a t day nhe khong dan qua rong roc,
mot dau treo vat m = 500g, dau kia keo bang liTc F ~ 8,2N (hinh ve).

D . K h i vat ran quay thi mot d i e m tren vat ran (khong nam tren true quay) se

L a y g = l O m / s l K e tCr liic bat dau keo, sau thdi gian

ve nen q u i dao tron c6 tam nam tren true quay.
5.22. M o t banh da c6 khdi lu'dng m = 20kg, ban kinh R = 50cm dang quay vdi tdc

At = 1,253 « J— (s) rong roc quay difdc

dp 0) = 120 vong/phut thi bj ham lai nhd mot ap life Q vuong goc v d i vanh
A. n = 2 vong

B . n = 3 vong

C. n = 1 vong

D. n = 4v6ng

banh da nhu" hinh ve.
.

'

5.16. Chpn cau sai
A . Chuyen dong quay cham dan, gia toe goc y c6 the am hay du'dng.

\

I O

^'^--'f<^

B . Q = 12,56N

C. Q = 376,82N

D . Q = 125,60N

5.23. M o t banh xe (coi nhu" vanh tron) kho'i lu'dng m = 200g Ian khong tru'dt tren
mat du'dng nam ngang. Trong khi chuyen dpng banh xe xem nhu' chiu tac

D . Thanh phan gia tdc hu^dng tarn dac triTng cho su" thay doi ve hiTdng cua

dung mot li/c tiep tuyen vdi vanh cd dp Idn khong ddi F = ION. Sau 2s ke tiT

vectP van toe.

liic bat dau chuyen dpng banh xe da di du'dc

5.17. M o t dia tron ban kinh 10cm quay nhanh dan deu vdi gia toe goc 100 rad/sl
D p Idn gia toe ciia mot d i e m tren vanh dia sau 0,1s ke tiT liic bat dau quay la
B . a = 1073m/s^ C. a = 1 0 ^ m / s ^

A. s = 1 0 0 m

B . tdc dp dai khong ddi

C. gia tdc tiep tuyen khong ddi

D . gia tdc hu^dng tam khong d d i

5.19. Canh quat may dai 0,5m. D a u canh quat dat toe dp lOm/s sau 5s ke tu" luc

C. 8 vong

D . 5 vong

B. D d i vdi true quay nhat dinh, momen quan tinh cua mot he vat bang tong
momen quan tinh cua cac vat trong he do.

ay cang Idn thi sir thay ddi tdc dp goc cua vat cang Idn.

momen dpng lu'dng cua vat r ^ n ddi vdi true quay do khong ddi thi vat
quay deu hoac diTng yen.
5-25. X e t mot he thdng gom:
-

I

A . lOrad/s

B . 5 rad/s - >

'

C. 20rad/s

D . 50rad/s

;

M

Rong rpc la mot dTa tron kho'i lirpng m = 1kg cd the
quay de dang xung quanh true qua tam O

:

;;

»

<

D. D d i vdi vat ran cd momen quan tinh khong ddi doi vdi true quay, neu

day treo vat nang. Tha nhe vat thi no se chuyen dpng thang bien ddi deu va

diCdng noi tren la

»

C. M o m e n lire tac dung vao vat ran khong d d i , momen quan tinh cua vat ran

5.20. Rong rpc c6 ban kinh 10cm diTpc quan bang doan day nhe khong dan, dau

sau 0,5s vat di du^pc 25cm. Tdc dp goc cua rong rpc khi vat nang di hdt quang

D . s = 150m

vat ran xa hay gan true quay.

bat dau quay nhanh dan deu tiT nghi. Canh quat da quay du-pc gan
B . 25 vong

C. s = 200m

A. M o m e n quan tinh cua vat ran phu thupc vao sir phan b d khdi lu'dng tren

D . a = 20m/s^

A . tdc dp goc khong ddi

B . s = 50m

5.24. Chpn cau sai

5.18. V a t r ^ n quay bien ddi deu thi mot d i e m c d dinh tren vat ay eo dp Idn

5.21. Chpn cau sai

thdi gian t = 10s. M a sat trUdt giiTa dp IiTc Q

A. Q = 15,70N

true quay.

A . 50 vong

/

Dp Idn ap IiTc Q la

dpng lu'dng cung bang 0.

A. a=10m/s^

Banh da quay cham dan deu va diTng lai sau

^

vk bdnh da la 0,5. L a y 7t = 3,14.

B . N e u tong cac momen life tac dung len mot vat ran bang 0 thi tong momen

C. D p Ictn momen quan tinh phu thupc vao sir phan bo khoi liTpng xa hay gan

^

' " I

A . K h i vat ran quay deu thi gia tdc goc bang khong
B . Gia tdc goc cua mot dTa tron dang quay quanh mot true ti le thuan vdi tdnt^
momen ngoai life, ti le nghich vdi khdi lUpng va ban kinh cua dia

-

D a y A B khong co dan va nhe Vc^t qua rong rpc

~

Lire keo F tac dung vao dau B de keo vat nang di len v d i F = 25N. L a y g
= lOm/s'.

S'Jc cSng day d phia treo vat nang M 1^
^ • T = 24N

B. T = 6N

C.T=16N

D. T = 1 2 N
49