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PGS.TS.
NGUYEN QUANG
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S.
NGUYEN THI NHI
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CHU VAN
LANH
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BAI
TAP
TRAC
NGHIEM
irl*
if
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DONG
CO
•
SONG
CO
•

cua bp
GDSfDT
BAN
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fi
—¥&rNGUYENTHI
NHl
-
Tfc>.
(Jhtu
VAJN
£Amr
Kl
THUAT
GIAI
NHANH
•
BAI TAP TRAC NGHIEM
• DONG LUC HOC VAT RAN
• DAO DONG CO
• S6NG CO
• DAO DONG VA SONG DI£N Tf
. D6NG DI$N XOAY CHIEU
•
Danh
cho hpc
sinh
Idp 12
chUcfng
trinh

giiip
cac em hoc sinh lop 12 va cac em dang on luyen de thi
CD - DH h^ thong hoa kien thuc ly thuyet va
luy^n
tap
each
tra loi cau hoi
trac
nghiem. Kien thuc ly thuyet duoc he thong hoa
theo
chuan chuang
trinh.
Bai
tap
trac
nghiem dugc phan thanh cac dang phu h^p vai npi dung ly thuyet va
mot
so'each
giai dac bi?t dugc cap nhat mot
each
kip thai tu cac de thi thu dai
hoc ciia cac truong nhu THPT chuyen Phan Boi Chau, THPT chuyen Dai hpc
Vinh,
THPT chuyen DHSP Ha
Noi,
va de thi CD - DH cac nam gan day, ke
ca de thi CD- DH nam 2013 vua qua. Mot
so'bai
tap kho dugc danh dau * de
cac em luu y khi doc. Quyen

virng
chac
va luyen dugc
each
giai bai tap, cac em khong
nen chi dgc quyen
sach
nay bang mat nhu doc tieu thuyet ma nen c6 gia'y but
de ghi lai nhOng dieu tam dac va
tinh
toan cac dai lugng vat ly ma bai tap yeu
cau
theo
ggi y huong dan giai da cho. Lam dugc nhu vay, cac em cam
chac
kha
nang lam
trgn
ven de thi CD - DH sap toi.
Dau da CO be day
kinh
nghiem lau nam va da
co'gang
bien
soan
quyen
sach
tot
de phuc vu dgc gia nhung chung toi luon vui long don nhan nhirng y kien
quy bau tu cac thay c6 giao va cac em hgc sinh.

quanh mgt true co djnh va dai lugng dai dac trung cho chuyen dgng thang:
Chuyen
dgng
thang
(chieu khong doi)
Chuyen
dgng
quay
(true quay co djnh, chieu quay khong doi)
Tga do: x
Toe do: v = x'
Gia toe: a = v' = x"
Tga do goc: (p
Toe do goc : (0 = cp'
Gia toe goc: y =
co'
= cp"
Chuyen dgng thSng deu:
V
=
hang
so; a = 0; x = xo + vt
Chuyen dgng quay deu:
0)
= hang so; y = 0;
(p
=
cp,,
+ cot
Chuyen dgng thSng bien doi

(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
Trong
do d la canh tay don cua luc F (khoang
each
tie tryc A den gia cua
Ivc
F).
Don
vj cua momen lye la N.m.
Chpn ehieu quay cua vat lam chieu duong, ta c6 quy uoe:

tinh
Trong
phuong
trinh
(3), dai lugng Y^mj^ dac tnmg cho miie quan
tinh
i
cua vat quay va
duge
goi la momen quan
rinh,
ky
hi$u
la
I.
Momen
quan
tinh
I doi voi mot true la dai lugng dac
tnmg
cho muc quan
tinh
ciia vat ran trong ehuyen dgng quay quanh true ay.
(4)
Momen
quan
tinh
c6 don vj la kg.m^.
> Momen quan
tir\

no, tryc quay A di qua trung diem ciia thanh va vuong goc voi thanh:
1
=
-lml2
12
• Vanh
tron
dong chat eo khoi lugng m, ban
kinh
R, tryc quay A di qua
tarn
vanh va vuong goc voi mat phang vanh
tron:
I = mR
• Dia
tron
mong dong chat c6 khoi lugng m, eo ban
kinh
R, trye quay A di
1
2
qua tam dia
tron
va vuong goc voi mat dia: I = - mR
• Qua cau dac dong chat eo khoi lugng m, eo ban
kinh
R, tryc quay A di
2 2
qua tam qua cau: I = - mR
o

dpng lugng L eiia vat rin trong ehuyen dpng quay quanh trye la:
L
= lo) (6)
Trong
do: I la momen quan
tinh
ciia vat ran doi voi trye quay; co la toe dp
goc eiia vat ran trong ehuyen dpng quay quanh tryc.
Don
vj eiia mo men dpng lugng la kgmVs.
b.
Phuong
trinh
dpng lyc hpc
ciia
vat tin quay
quanh
mpt
tryc
dupe viet
duoi
dang
khac:
AL
M
=
-
At
(7)
Trong

tang,
CO
I tang thi co giam (Ico = hang so' hay I^co^ = I2CO2).
4. Dpng nang ciia vat ran quay quanh mpt true.
a. Dpng nang Wd cua vat ran quay quanh mpt true eo
dinh
la:
W,=llco2
(8)
Trong
do: I la momen quan
tinh
cua vat ran doi voi true quay, co la toe do
goc ciia vat ran trong chuyen dong quay quanh true.
Tu
(6) va (8), dpng nang Wd ciia vat ran quay quanh mot tryc co'
dinh
co the
vie't
duoi
dang:
VVd=^
(9)
Trong
do: L, I Ian
lugt
la momen dong lugng va momen quan
tinh
cua vat
ran

CAC
DANG
BAI TAP vA VI DV
MINH
HQA
Dang
1. BAI TAP
LIEN
QUAN
DEN
CHUYEN
DONG
QUAY
DEU
CUA
VAT RAN
Phuong phap
giai:
Van dung cac kien thiic ve chuyen dpng quay deu ciia
vat
ran:
• To'c dp goc:
CO
bang hang so'.
• Gia toe goc: Y = 0. '
• Tpa dp goc (phuong
trinh
chuyen dpng ciia vat ran quay deu quanh mpt
trvcco'djnh):
(P

CO
f =
6000
vong/phiit = 100 v6ng/s.
Suy ra:
CO
= 27tf =
2007t
(rad/s).
Do do:
cp
= cot =
20071.2,5
= SOOTI (rad) => Chpn C
Vi
du 2: Mpt canh quat ciia may phat dien
chay
bang sue gio c6 duong
kinh
50m, quay deu voi toe dp 120 vong/phiit. Toe dp dai tai mpt diem nam a
vanh
canh quat bang:
A.
112,6m/s
B. 314 m/s C. 412 m/s D. 538 m/s.
Huang
dan
giai:
in rad/s; r = — = 2
2

/ s
Vay V = co.r = 4,5.6 =
27(cm
/ s) => Chpn C
Dang
2. BAI TAP
LIEN
QUAN
DEN
CHUYEN
DQNG
QUAY
BIEN
DOI
DEU CUA VAT RAN
Phuong phap
giai:
Sii dung cac phuong
trinh
chuyen dpng quay bien doi
deu
ciia vat ran quanh mpt true eo
djnh
nhu sau:
co
= coo +yt; ;
1
.2
cp
=

thai gian thi chuyen dpng quay la cham dan (y < 0).
> Khi khong de y den chieu quay ciia vat ma vat chuyen dpng quay nhanh
dan
deu thi co va y cung dau (coy > 0), chuyen dpng quay cham dan deu thi co
va y
khac
dau (coy < 0).
v^
,
> Thanh phan gia toe phap tuyen a„ co dp Ian: a„ = — =
co
r
> Thanh phan gia toe tiep tuyen co dp Ian: a, = — = ry
> Vec to gia toe a dupe xae
dinh:
a = a„ + a(; ve dp ion: a =
-Ja^+a^
Vi
dy 1: Mpt banh xe quay nhanh dan deu tir trang thai dung yen, sau 4s
banh xe dat van toe goc 24 rad/s. Goc ma banh xe quay dupe trong thai gian
do
la:
A.23rad.
B.37rad.
C. 48 rad. D. 55 rad.
Huong
dan
giai:
_ ,
co-cog

A.
t = Is;
cp
= 6,7 rad. B. t = 1,5 s;
cp
= 7,5 rad.
C. t = 3 s;
(p
= 11 rad. D. t = 2 s;
cp
= 12 rad.
Huong
dan
giai:
j . w ,^
Ap
dung cong thuc:
co
=
cO(,
+yt,
trong do
coy
=12rad/s,
vi banh xe quay
ch|m dan deu nen y = -6rad / s^.
Do do phuang
trinh
van toe goc la:
CO

giay van toe goc tang tu 180 vong/phiit len 480 vong/
phiit.
Gia toe huong
tam
ciia diem M a vanh banh xe sau khi tang toe dupe 3,5s la
A.
330,4
m/sl B. 411,2 mls\.
456,3
m/s^ D. 512,7 m/sl
Huang
dan
giai:
Ta co:
COQ
-
67irad
/ s va
co
=
16rcrad/s.^
CO-co,)
167t-6K
^ , , 2
y
= = =
27i:rad
/ s
Sau 2s, van toe goc bang:
co

ciia
mpt so vat ran co true
quay
doi xung: ^
• Thanh dong
chat
co
khol
lupng
m va co tie't di?n nho so voi chieu dai 1
ciia no, true quay
A
di qua
trung
diem
ciia
thanh va vuong goc vai thanh:
U-lml^.
^2 ;,,
TI
Ki
thuatgidi
nhatih
BTTN Vat Li 12, tap 1 -
Nguyen
Quanx
Lac
• Vanh tron dong
chat
c6 khoi lu^ng m, ban

qua trong tam G ciia vat;
lo;
Ic;
tuong ung la momen quan
tinh
eiia vat doi voi
true O va true G
; > Momen quan
tinh
cua he vat ran: I =
Ii
+12 +
i
trong do:
Ii,
I2,
Ian lu^t la momen quan
tinh
cua eae vat ran mj, m^
Vi
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

0,6kgm2
=^ Chon B
Cty TNHH MTV DWH
Khattg
Viet
Vi
dy 3: Mot dia tron dong
chat
c6 ban
kinh
30 cm, kho'i
lugng
m = 4kg.
Momen quan
tinh
ciia dla doi voi mot true quay vuong goc voi mat dla tai
mot diem tren vanh c6 gia tri nao sau
day?
A.
0,12 kg.m^. B. 0,27 kg.m^. C. 0,54 kg.m^. D. 1,2 kg.m^.
Huang
dan
gidi:
Theo
djnh ly true
song
song,
ta c6: {'^ )
^
,:

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).
Vi
du 1: Mot vanh tron dong
chat,
khoi lugng m = 2kg, ban
kinh
R = 0,5m,
true quay qua tam va vuong goc voi mat phang vanh. Ban dau vanh dung
yen thi chiu tac dung boi mot lue F tiep xiic voi mep ngoai vanh. Bo qua moi
ma sat. Sau 3s vanh tron quay dugc mot goe 36 rad. Do Ion eiia lue F la
A,

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^. #

Mi
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
Mi
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
Mi
CO gia trj
A.
Ml
=
11,3
N.m
B.
Ml
=26,4
N.m
C. Ml
=
33,4

=
2rad / s^
Momen
quan
tinh
ciia
banh xe:
,
M 24 2\
I
=
-
=
-
=
12(kg.m2)
Khi
Ml
thoi
tac dung:
co'
=
to
+
y't
=
0
y'
=
-0,2rad / s^

cua vat ran trong chuyen dpng quay quanh true la:
L
=
I{o
Trong
do: I la momen quan
tinh
cua vat ran doi vai true quay;
co
la toe dp
goc
ciia
vat ran trong chuyen dpng quay quanh true.
•
Tinh
Momen dpng lupng cua
h^
vat ran doi vai tryc quay theo cong thuc:
n
L
=
Li
+L2+
+Ln=
i=i
Trong
do:
Lj=IjCOj
,
•

Toe dp goc cua moi qua cau:
=
^
=
- lO(rad)
Momen
dpng lupng
ciia
h^:
L
= Lj + L2 =
IiCOj
+
I2CO2
= (ij +12 )to
=
^miR^+m2R^)(o = (mi+m2)R^.a) ' f
=
3,5.0,5h^l0
=
8,75(kg.m2/sj
t '
=>
Chpn D
Vi
dy 2: Mpt nguoi c6
khoi
lupng 50kg dung 6 mep mpt san quay hlnh tron
CO
khoi

/ s) D.
-1,425
(rad/s)
Huang
dan
gidi:
a) Ban dau he dung yen nen momen dong lugng: Lo = 0.
Khi
nguoi chay quanh mep san th: momen dong lugng ciia he khi do la:
L| = IjCOj
+I2CO2
Do
momen dong lugng duge bao toan, nen: Li =
Lo.
Suy ra:
1,0, +
l2«;=
0 ^ = =
-^^^i^
_2m(o^
_ CO,
2 2
Do
0)1,
C02
khae dau nen san se quay theo chieu nguge voi chieu chay ciia
nguai
vai toe do goc: ©2
====-l,05(rad
/ s)

hinh
tru c6
khoi
lugng M = 180kg va ban
kinh
R = 1,2m dang dung yen. Mot nguoi
khoi
lugng m = 40kg chay tren mat dat
vai
toe do 3m/s theo phuang tiep tuyen vdi mep san va nhay len san. Bo qua
ma sat 6 true quay.
Tinh
toe do ciia nguoi do khi o tren san.
A.
0,52 m/s B.
0,72m/s
C.
0,82m/s
D.
0,92m/s
Hu&ng
dan
gidi:
. ,
Momen
dgng lugng ciia nguoi truoc khi nhay len san:
L,
= 1,(0, = m.R^.^ = mRvj
Momen
dgng lugng eiia he khi nguoi nhay len san:

13 ^ '
Chgn
D
Dang
6. BAI TAP LIEN QUAN DEN DONG
NANG
CUA VAT RAN
TRONG CHUYEN DONG QUAY
Phuong phap
giai:
Su dung eac kien thuc sau:
• Dgng nang eiia vat ran quay quanh mot true co
djnh:
Wd = ^Ico^
• Dgng nang ciia vat ran vua quay
vira
chuyen dgng
tjnh
tien:
WJ= -
2
voi
V(^
la van toe
khoi
tam
1
2 ^ 2
WJ = -ICO + —
mvr-

ciia
khoi
cau
la:
I
= -mR^ =
80.0,6^
= ll,52(kgm^)
Dgng
nang
cua
khoi
cau la: Wj
= ijco^
= 11,52.20^
=
2304(j)
=> Chon
B
Vi
dy 2:
Mot banh
da
hinh
try
khoi
lugng
m =
100kg,
ban

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 =
— = —
=

^ang 7. BAI TAP
LIEN
QUAN DEN
DINH
LY
BIEN
THIEN
DQNG
NANG
CUA VAT RAN
QUAY
Phuong phap
giai:
Djnh
ly ve
dpng nang::
AWd
=
Wd2
-
Wdi
=
ll(co2
-
0)2) =
A
=
MA(p
Trong
do:

deu voi toe dp goc
co
=
50rad/s.
Thoi
tac
dung momen
lyc M
thi
sau 10s
banh
xe se
dung lai. Tim cong ciia
lyc ma sat tac
dung
vao
banh
xe
ke
tu khi
thoi
tac
dung momen lyc
M
den khi banh
xe
dung lai.
A.
-3kJ B 9kJ C 15kJ
D.

quan
tmh:
I
=
— =
—r- = 12kg.m
y
b
Cong
cua
lyc ma
sat:
A^,
= AW,
-W,o =-ilo)^-1.12.502 =-15000(j)
=
-15kJ
=>
Chpn
C
Vi
du
2.
Mot banh
da
dupe lam quay quanh mot tryc thang dung voi
toe
dp
goc khong doi
200

la 6.10"^
kg.m^.
Xae
djnh:
a)
Momen lye
ma sat tac
dung len dia
A.
0,6Nm
B.
l,2Nm
C.
2,4Nm
D.
3,6Nm
b) Dpng nang dia nhan dupe
A.40J
B.60J
C.80J D. 120J
c)
Nang
lupng
toan phan
da
truyen
cho
dia.
A.
80J B. 120J C.

=>
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

lai sau 5s. Gia su luc ma sat la khong doi trong suo't qua
trinh
banh xe quay. Bo qua ma sat 6 tryc quay.
a) Xac
dinh
lyc F va lyc ma sat.
; A.
INvalN
B.2NvalN C.
lNva2N
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
=
2(rad/s2j;
_Q)2-C0j 0-10
yi
—I—

^•50,2.2
= 1(N)
Vay F =
F^3
+1 =
1
+1 =
2(N)
^ Chpn B
b) Cong ciia lyc ma sat 6 giai doan hai:
A„,s2
=Wd2
-Wd,
=
-^Ico2
=-iimR2.co?
=1.1.5.0,22.102
=-5(j)
Ap
dyng
djnh
ly dong nang cho giai doan mpt, ta c6:
A,
+
A^,
= AWj - - W,o = llco^ = lla)2 = 5(j)
Do Yj = 72 va ti = t2 nen:
Amsi
= Ams2 = -5 (J)
; Suy ra: AF = 5 -

vong/phiit
= 80 v6ng/s. ,,
Suy ra: co = 27if = 160::
(rad/s).
Do do: (p = cot =
16071.2,5
=
40071
(rad) => Chpn C
Cau 2.
Mpt
canh quat quay voi toe dp goc khong
doi
co
= lOOrad/s. Toe dp dai ciia
mpt
diem 6 tren canh quat va
each
true quay ciia canh quat mpt doan
25em
la
A.
12,5m/s
B.
25m/s
C.27,5m/s
D.35,8m/s.
Huang
dan
gidi:

- ——— *
7,3.10"^
rad
/ s
24.60.60
Suy ra van toe dai ciia mpt diem a xieh dao la: v = rco =
463m
/ s
=>
Chpn D
Cau 4. Mpt canh quat ciia may phat
difn
chay bang siie gio co duang
kinh
khoang 64m, quay deu voi toe dp 120
vong/phiit.
Toe dp
dai
tai mpt diem nam
o vanh canh quat bang:
A.
88,94
m/s B.
136,83
m/s C.
382,71
m/s D.
401,92
m/s.
Huang

C.20cm/s
D.25cm/s
iq
Huang
dan gidi:
Tir
phuong
trinh
<p
= 5 + 2,5t ta suy ta:
co
=
(p'
=
2,5rad/s
Vay V
= co.r = 2,5.4 = 10 (cm/s)
=>
Chpn B
Cau 6. Tren mot dia dong chat nam ngang quay deu quanh true doi xung c6
mgt
vat nam
each
tam dla 20cm. He so ma sat nghi giua vat va mat dTa
^n=
0,5.
De vat khong bi vang ra
khoi
dTa thi gia tri eua toe do goe khong duoc Ion hon
A.

toe eiia mpt diem 6 vanh canh quat bang
A.
n23m/s2 B. 1783m/s2 C. 2738 m/s^ D. 3412 m/s^.
Huong
dan gidi:
Vi
vat ran quay voi toe do goe khong doi nen vat ran quay deu. Gia toe goe
cua mot diem thuoe vat ran eiing ehinh la gia toe goc
ciia
vat ran.
Taco: a = a,^, = co^r = 74^.0,5 = 2738(m / s^) ^ Chon C
Cau 8. Mot dTa CD quay deu voi toe do quay 400 vong/phiit trong mot 6 doc
cua may vi
tinh.
Toe do goe cua dTa CD do
tinh
theo
rad/s
la
A.
470
rad/s.
B. 42
rad/s.
C. 4,7
rad/s.
D. 0,47
rad/s.
Huang
dan gidi:

B. 90
rad/s.
C. 80
rad/s.
D. 70
rad/s.
Huang
dan gidi:
Ap
dung eong thue: v =
cot=i>co
= - = — = lOOrad / s => Chon A
20
Cty
TNHH
MTV DWH
Khang Vift
Cau 11.Mot vat rSn quay deu voi toe dp goc 50
rad/s.
Tai
thoi
diem ban dau
'^J^tcStoa
dp goc la 5 rad. Sau 2s vat co toa dp goe la: |, ;
•
A. 100 rad. B. 105 rad. C. 110 rad. . D. 115 rad.
Huang
dan gidi: . ^ ,
Ta
eo

~
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 tu luc ham
den
liic
banh xe dung han la
A.
64 rad. B. 128 rad. C. 350 rad. D. 563 rad.
Huang
dan gidi:
2 2
Taco:
Acp
= cp-cpo = ^^^^ = = 128rad ChpnB
2y 2.(-4)
Cau 14.Mot banh da
dupe

= ^ = 5rad/=^ Chpn C
t-to
5
Cau_16,Mpt vat ran dang quay quanh mpt true co dinh xuyen qua vat voi toe
«lo
goe
25rad/s
thi bat dau quay cham dan deu va dung lai sau 5s. Goc ma vat
quay
dupe
trong Is cuoi cung truoc khi dirng lai la
A.l,25rad
B. 2,5rad C. 5,0rad D. 8,5 rad
Huang
dan
gidi:
Gia
toe goc: y = — = -5rad /
At
. ;, , •
Phuong
trinh
chuyen dpng:
(p
= -yt^
+
cogt. '
Goc ma vat quay dugc trong 1 s cuoi cimg truoc khi dung lai la:
^(t=5)
~

Cau 18. Mpt vat ran quay bien doi deu c6 phuong
trinh
chuyen dpng cp = 5tl
Ket
luan nao sau day la
sai?
A.
Toe dp goc ban dau
ciia
vat bang 0.
B.
Gia toe goc eiia vat c6 gia tri bang 10 rad/5^ .
\. Toe dp goc ban dau eiia vat c6 gia tri bang 5
rad/s.
D.
Tpa dp goc ban dau eiia vat
dupe
ehpn bang 0.
Huang
dan
gidi:
Phuong
trinh
eiia chuyen dpng quay bien doi deu eiia vat ran quang tryc co
djnhcodang:
(p
=
(pQ+a)Qt
+ iyt^
\o dau bai (p

coQt
+
iyt^
Trong
do: (pg = 0; COQ = 207i(rad / s) ^
Thay so ta
dupe
cp
= 0 + 20n.20
-^7t.20^
= 2007t(rad) '' ' ''' ''
^
^'
So'vong banh xe quay
dupe
la: n = — = = JOO vong => Chpn D
Cau
20.Mpt banh da
ciia
dpng ea quay nhanh dan deu, sau khi
khoi
dpng
dupe
2s thi goc quay
ciia
banh da la 14 rad. Toe dp goc tai
thoi
diem do la:
A.
13

7rad/s
2 t 4
Mae
khae
y = ^ =^=> oi = yy = 7.2 = 14rad / s => Chpn B
Cau 21.Mot vat ran bat dau quay quanh true
ciia
no voi gia toe goc khong doi.
Sau 5s no quay
dupe
mpt goc 50 rad. Chpn moc
thoi
gian t = 0 tai
thoi
diem vat
ran bat dau quay, tpa dp goc ban dau
(pQ
= 0. Chpn ehieu duong la chieu quay
ciia
vat rSn. Toe dp goe tai
thoi
diem t = 5s bang:
A.
30
rad/s.
B. 20
rad/s.
C. 50
rad/s.
D. 80

=
4rad/s
2 t^ 5^
Vi
vat quay voi gia toe goe khong doi nen tai thai diem t = 5s gia toe goc
ciia
vat ran bang 4rad / s^
Ap
dyng
cong
thiic:
<B
=
COQ
+ yt =
0
+ yt =
4.5
=
20rad
/
s
Chpn
B
Cau
22.
Mpt
vat ran
dang quay
deu

dung. Chon chieu duong
la
chieu quay
cua
vat ran. Thai gian
tir
khi vat ran
chiu
luc ham tac
dung
den
liic
dirng
lai va goc
quay trong
khoang thai gian do
la
A.
t
=
4s;
(p =
48
rad.
B.
t = 2,5
s;
(p =
12,5
rad.

nen
y
=
-4rad
/
s.
Khi
vat ran dtmg lai thi (o =
0
=>
0
=
10 - 4t
=>
t
=
—
=
2,5s.
.
4
Vay
sau 2,5s
thi vat ran dung lai.
Chon
moc
thai gian
t = 0 tai
thai diem
vat hit

Cau 23.
Banh
da cua
mpt dpng
ca, tir luc
khoi dpng
den khi dat toe dp goc
120
rad/s,
da quay
duac
goc
bang
240
rad.
Bie't
banh da quay nhanh dan deu. Thai
gian tu liic bat dau khoi dpng den khi banh da dat toe dp
4800
vong/phiit la:
A.
9,76 s B. 12,48 s C. 16,75 s
D.
28,12 s
Huang
dan
gidi:
2 2
Taco:
co^

Gia toe goc cua
banh
xe la
A.
1,571
rad/s^
B.
27trad/s^
C.
3,57trad/D.
5,5jtrad/s^
Huang
dan
gidi:
Taco:
COQ
= 180
vong/phiit =
671
(rad/s); co =
480
vong/phiit =
16Tt
(rad/s)
a)-cO(.
1671-671
^ / . 7\. i
Gia toe goc: y =
^
= =

va goc
quay
ke tu
Iiic
chat
diem
bat
dau
chuyen dpng
cham
dan deu den liie dung lai Ian
lupt
la
A.
t
=
30s;
(p
=
1800
rad.
B. t
=
40s;
(p
=
3600
rad.
*
C.t =

=> Chpn
A
Cau 26. Tai thoi diem
t = 0,
mpt
vat ran bat
dau quay quanh mpt trye eo'
dinh
xuyen
qua
vat voi
gia toe goc
khong doi.
Sau 8s no
quay dupe mpt
goc 80
rad.
Goc ma vat r^n quay dupe tu thai diem Os den thai diem
10s la
A.
45
rad
B. 38
rad
C. 75
rad D.
125
rad.
'
Huang

=1.2,5.10^
=125rad=>
Chpn
D
Cau_27.Mpt dia tron
bit
dau quay quanh true vai gia
toe goe
khong doi.
Sau 6s
dla quay dupe
36
vong.
So'vong
quay dupe trong
6s
tiep
theo
la
A.
54
vong
B. 108
vong
C. 216
vong D.
321
vong.
Huang
dan

(vong)
=>ChQn B
Cau
28.
Mot banh da dang quay quanh true voi toe do goe 240 vong/phiit thi
quay eham lai vi c6 ma sat voi o trye. Sau 1 giay, toe dp ehi con 0,6 Ian toe do
ban
dau, eoi ma sat la khong doi. Toe do goc sau giay thu hai la
A.
CO
= 0,27t rad/s B. (o = 0,97trad/s
C. w = l,27r rad/s D. co = l,6rad/s
C Huang dan gidi:
Ta eo:
COQ
= = 87r(RAD /S), suy ra: = 0,6tOo = 4,87t(rad
/
s).
60
Gia toe goc eua banh da la: y = — = -3,2(rad
/
s^)
At
\
Toe dp goc sau giay thu hai la: =
O)Q
+ yt =
87i3,27t.2
=
l,67t(rad

= 2 +
2.1
= 4(rad
/
s)
Toe dp: v = coR = 32em/s => Chpn D
Cau 30. Mot vat ran quay quanh mot trye theo phuang
trinh
cp = 12 - 5t - 0,5t^
trong
do
cp
tinh
theo rad, t
tinh
bSng s. Phat bieu nao sau day khong diing?
A. Vat quay eham dan deu
B.
Toe dp goc eua v^t la ham
so'bae
nhat theo
thai
gian
C. Gia toe goc eua vat khong thay doi theo
thoi
gian
D.
Momen lue tac dyng len vat khong doi theo
thoi
gian

gian => D dung
- V^t ehi ehuyen dpng eham dan khi coy < 0 => A sai => Chpn A
Cau 31.Mpt cai dla dang quay voi toe dp goc 5 rad/s thi bat dau quay eham
dan
deu, sau 5s thi no dung lai. So vong ma dia da quay dupe trong
thai
gian
do xap xi bang:
A. 0,85 vong B. 1,99 vong C. 2,15 vong D. 3,39 vong
Huang
dan gidi:
^ ,^
(0 - C0(, -5 / T \
Gia toe goe eua dTa: y = —p^ = —= -l|rad/s j
Goc ma dia quay dupe cho den khi dung lai la:
<p
=
co„t
+
-^yt^
= 5.5 + ^.(-l).5^ = -12,5(rad)
Suy ra so vong dTa quay dupe trong
thoi
gian do la: n
n
==* 1,99 vong =>Chon B
2K
2.3,14 ^
£ju_32.Mpt
banh da quay nhanh dan deu tu trang

Ta c6:
COQ
= 0 (rad/s); coj = 120 (rad/s); coj =
3600
vong/
phiit
= 120Tt (rad)
_ (Of -
en
=
cOg
+ yt => t =
-(0
2cp
'0 _ 120^ -0
2.180
1207C-0
= 70(rad/s2)
=
9,42(s)
Y
40
Chon D
Cau 34. Mot banh xe quay nhanh dan deu tu trang thai dung yen, sau 3s banh
xe dat van toe goe 12 rad/s. Goe ma banh xe quay duge trong
thoi
gian do la
A.
9,5 rad. B. 18 rad. C. 36,5 rad. D. 54 rad.
Huang

=(5.0,4)^2,4
=
9,6(m/s^)
Chc)n B
Cau 36. Mot vat ran quay quanh mot true c6'
djnh
theo phuong
trinh
cp = 27 +
48t - 2t^ trong do (p
tinh
theo rad, t
tinh
bang s. Goc vat quay duge ke tir
thoi
diem
ban dau cho den khi no dung lai la
A.
288 rad B. 435 rad C. 567 rad D. 982 rad
Huang
dan
gidi:
Taco:
(o =
48-4t
= 0 t = 12 (s)
(p
= 24 +
48.12-2.122
= 315 (rad);

liic
banh xe hk dau quay. Van toe dai eiia
mpt
diem N tren vanh banh xe 6
thoi
diem t = 4 s bang
A.
21 m/s. B. 27 m/s. C. 35 m/s. D. 49 m/s
Huong
dan
gidi:
^
•
i.i
V?in
toe goe tai thai diem t = 4s la (o = coo + yt = 0 + 3,5.4 = 14 rad/s
=> Van toe dai v = (oR =
14.2,5
=
35m/s
=> Chon C
Cau 39^ Mot banh xe dang quay voi toe dg goe 28 rad/s thi bj ham lai voi mpt
gia toe goe eo dp Ion khong doi 2,5 rad/s^. Thai gian tu luc ham den
liic
dirng
lai
la
A.
5,6s B. 11,2s C. 13,4s D. 18,9s
Huong dan

gidi:
1
Taco:
a, - r.y - 3.4,5 =
13,5(m/s'J
^ Chpn C
Cau 42. Do bj mat dien mpt
chie'c
may mai quay cham dan deu, biet van toe goc
ban dau la 360 vong/phut va gia toe goc la -3n^ rad/sl So vong ma may eon c6
the quay dupe truoe khi dung lai la
A. 12 vong B. 18 vong C. 24 vong D. 36
vong
J
Huang
dan
gidi:
Ap dung cong thue:
(o2-(o2=2y.Acp=^A9 = —^ = ^-^^^ = 247r(rad)
•'•v:'^
— 29
bo vong quay: n = —^ = = 12 vong =?> Chpn A
2n 2n
Cau
43. Mot banh xe c6 duang
ki'nh
60 cm quay nhanh dan deu trong 2s thi toe
dp
goe tang tu 180 vong/phiit den 240
vong/phiit.

liic
bat dau quay, mpt diem
each
true quay 20 cm c6 gia toe
huong
tam la 80 m/s^. Gia toe goe ciia banh xe la
A.2,5rad/s2 B. 5 rad/s^ C. 7,5 rad/s^ D. 12,5 rad/s^
Huang
dan
gidi:
Ta c6: a„ = =^ = ^f" = = 20(rad / s)
y
= ^ = ^ =
5(rad/s^)
^ChonB
Cau
45. Mot banh xe dang quay vai toe dp goe 20 rad/s thi hit dau quay cham
dan
deu. Sau 8s banh xe dung lai. So vong da quay dupe eiia banh xe la
A.
4,6 vong B. 6,4 vong C. 8,3 vong D. 12,7 vong
Huang
dan
gidi:
Gia toe goe cua banh xe: y = — = -2,5(rad / s^).
At
^ /
Ap
dung cong thue: (o^ - co^ =
2y.A(p

tron
de chuyen huong. Ban
kinh
ciia
^^^^J^lupn la 50m, toe dp 6 to giam deu tu 18 m/s xuong 10 m/s trong 3,2s.
Gia toe goe ciia 6 to tren duong
lupn
c6 dp Ion la
A.
Y = 0'05 rad/s2. B. y = 0,1 rad/s^. C. y = 0,125 rad/s^ D. y = 2,5 rad/s^
Huang
dan
gidi:
Av
10-18 o r/ , 2\
Gia toe hep tuyen: a, = — = ^ ^ = -2,5^m / s J ,
At
3,2
Suy ra gia toe goe:
2,5
(rad/s^j
Chpn
A
r
50
Cau
48. Mpt dia
tron
quay nhanh dan deu tir trang thai
nghi,

thoi
gian do Ian
lupt
la
A.
y = 2 rad/s2; 4) = 4 rad. B. y = 4 rad/s^; (}) = 8 rad.
C. y = 3 rad/s^; (j) = 6 rad. D. y = 5 rad/s^; cj) = 10 rad
Huang
dan
gidi:
Gia toe goe
trung
binh
ciia vat: Y = =
S^rad
/ s^ (voi (oo = 0).
Goe quay dupe la:
Aip
= —-—- = 10(rad) => Chpn D
£a]i50.Mpt
nguoi di xe dap
khoi
hanh dat dupe toe dp 18 km/h trong 25s, biet
duong
kinh
ciia banh xe bang
80cm.
Gia toe goe
trung
binh

dyng,
banh xe quay cham dan deu va
dung
lai sau 10
vong
quay. Gia toe goc va
thai
gian banh xe
dung
lai ke tir
liic
ngoai lyc
dimg
tac
dpng
la / '
A.
y =
-—rad/s2,t
=
llJ4§,,
^ 1
7t
C. y = -—rad/s2,t = 12,ls
71
40 •>
B. y = rad/s2,t = 3,14s
7t
D.
y = -—rad/s^t =

djnh
voi gia toe goc
bang 1 rad/s^. Tai
thoi
diem Os thi banh xe co toe dp goc 3 rad/s. Hoi den
thoi
diem
5s thi banh xe co toe dp goc b^ng bao nhieu? ''^
A.
2 rad/s B. 4 rad/s C. 6 rad/s D. 8 rad/s
Huattg
dan
gidi:
Ap
dung
cong thuc: co = (oo + yt = 3 + 1.5 = 8 (rad/s) => Chpn D
Cau
53. Mot canh quat dang quay voi toe dp 16
v6ng/s
thi bat dau quay cham
dan
deu va
dung
lai sau
thoi
gian 8 giay. Gia toe goe eua canh quat do co dp
Ion
bang bao nhieu?
A.2rad/s2 B. 47i rad/s^ C. 6 rad/s^ D. 8n rad/s^
Huang

liic
bat dau quay cham dan) la
A.
1,25 rad B. 2,5 rad C. 5 rad D. 7,5 rad
Huang
dan
gidi:
Gia toe goc eua banh xe: y = — =-sfrad
/
s^)
At
V /
Goc ma vat quay dupe den khi
dung
lai:
A(p'
=
—
^ =
40(rad)
2y ^ .
Sau 3S ke tir khi bat dau quay cham dan, toe dp goc cua v$t la:
Wj
=(00+yt =
20-5.3
=
5(rad/s)
Goc vat quay dupe sau 3s la:
Acp
=

Cau_56.
Trong mpt may A-
tiit,
hai vat nang nol voi nhau bang spi day khong
CO dan vat qua mpt rong rpc. Mpt
trong
hai vat co
khoi
lupng
200 g, vat kia co
khoi
lupng
205 g. Rong rpc eo true quay nam ngang, khong ma sat, co ban
kinh
=
10 cm. Khi dupe tha tu
nghi,
nguoi ta thay qua nang hon roi dupe doan
duong
s = 1,8 m
trong
khoang
thoi
gian t = 6 s. Gia toe goe y eua rong rpc bang:
A.
0,5 rad/sl B. 1 rad/s^. C. 2 rad/sl D. 3 rad/s^
Huang
dan
gidi:
(.; / r:

diem t = Is?
-»^0.4m/s. ,
B.50m/s.
C. 0,5 m/s.
D.40m/s
Huong
dan
giai:
Theo
bai ra, ta c6: y = 2 rad/s^, coo = 2rad/s.
Van toe goc: co = cp'(t) = 2 + 2t
Khi
t = Is thi van toe goe co dp Icjn: w = coo + yt = 4 (rad/s).
Khi
do toe do dai eiia diem do la: v = co.r =
0,4m/s
=> Chon A
Cau 58. Mot banh xe eo dirang
kinh
50 em quay nhanh dan deu, trong 4 giay
van
toe goe tang tu 120 vong/phiit len 360 vong/ phut. Gia toe huong tam cua
diem
M 6 vanh banh xe sau khi tang toe duoe 2 s la
A.
137,8m/s2.
B. 147,8 mM C. 157,8 m/s^ D. 167,8 m/s^
Huang
dan
giai:

giay (s). Mot diem tren vat ran va
each
true
quay khoang r = 10cm thi gia toe toan phan co dp Ion bang bao nhieu vao
thoi
diem t =
1
s?
A.0,92m/s2. B. l,84m/sl C. 2,68 m/s^. D.4,16m/s2
Huong
dan
giai:
Theo
bai ra, ta co: y = 2 rad/s^ cpo = 1 (rad/s).
Van toe goe: co = (p'(t) = 1 + 2t
Khi
t = Is thi (0 = coo + yt = 3 (rad/s). Khi do:
Gia toe huong tam: a,,,
=co^.r
=
0,9|m/s^j
Gia toe tiep tuyen: a, = r.y = 0,2|m / s^ .
Gia toe toan phan cua diem do la: a = ^a^, + a\ 0,92 m / s^ => Chon A
Cau 60. Mot banh xe co duong
kinh
4 m quay v6i gia toe goe khong doi
3 rad/s^. Gia toe tiep tuyen eiia diem N tren vanh banh xe b3ng
A.
Im/s2. B. 3m/s2. C.6m/s2. D.9m/s2.
Huong

gian de banh da dung lai: t = — = «15(s) Chon C '
Cau 62. Mot banh xe co duong
kinh
4 m quay voi gia toe goc khong doi 4
rad/s^
thoi
gian ban dau to = 0 la
liic
banh xe bat dau quay. Gia toe huong tam
ciia mpt diem N tren vanh banh xe 6
thoi
diem t = 2 s bang
A.84m/s2. B. 128m/s2. C. 264 m/s^. D. 386 m/s^
Huang
dan
giai:
Ta co:
CO
= coo + yt = 0 + 4.2 =
8rad/s
Gia toe hu(?ng tam a
|,,
= — = co — = 8 - = 128m / s => Chon B
R 2 2
Cau 63. Banh da ciia mpt dong co tu
liic
khoi dong den
liic
dat toe dp goc 140
rad/s phai mat 2,5s. Biet banh da quay nhanh dan deu. Goc quay ciia banh da

deu va giay dau tien nguoi ta thay may quay dupe mpt vong. Hoi giay thu
hai
may quay dupe bao nhieu
vong?
A.
1 vong. B. 2 vong. C. 3 vong. D. 4 vong
Huang
dan
giai:
Do
COQ
=0 nen
goequay
cp-cpy =^yt^ . '
i
So'vongquay n = —^ = —
yt^
=> so vong quay ti If voi t^.
271 471
Theo
de ra, trong Is quay dupe 1 vong nen trong 2s quay dupe 4 vong.
i~>
So vong quay trong giay
thii
2 la: 4 - 1= 3 vong => Chpn C
M
muat
gJAt nhanh
tiTTRViU
11

nhanh dan deu, trong 3s van
toe goc tang tu 120 vong/ phut len 300 vong/phiit. Gia toe tiep tuyen ciia diem
M
tai vanh banh xe la
A.
0,157im/s2 B.0,3nm/s2 C. 0,67tm/s2 D. 0,97tm/s2
Huang
dan gidi:
Gia toe goc: y = = = 27trad / s
t
3
Gia toe tiep tuyen: a„ = Ry =
0,3.27t
= 0,67tm / s^ => Chpn C
Cau 67. Mot eon lac vat ly c6
khoi
lupng m =
1,6kg,
momen quan
tinh
I
= 0,4(kg.m^), dao dpng nho tai nai eo gia to'c trong truang g = m/s^ xung
quanh mpt true
quay
nam
ngang
v6i khoang
each
tu true
quay

giam41an
C. tang 16 Ian D. giaml61an
Huong
dan gidi:
Ta eo: I = mr^. Khi n = 4r thi = mr^ - m.(4r)^ = 16mr^ = 161 => Chpn C
Cau 69. Mpt con lac vat li c6 momen quan
tinh
do'i voi true
quay
la 3 kgm^, eo
khoang
each
tu trpng tam den true
quay
la 0,2 m, dao dpng tai noi eo gia toe
roi
tu do g =
71^
(m/s^)
voi ehu ki rieng la 2,0 s. Khoi lupng cua eon lac la:
A.
10 kg B. 15 kg
C.20kg
D. 12,5 kg
=> m =
f2n^
_L^-i5(kg)
=>Ch9nB
gd
^mgd V W 6"

^2
R
A-
ro
runff
ehieu cao,
duoc
lam
bang
cung mpt
,Z
quay
erung
vai tt„c dac cua mSi hinh .r^) cua hai h,.h m nay la
=
3^=243=>1A=243IB
=^ChpnD
B ^ = 9
I1
C. ^-27
^1
1
^ ,
Huong
dan
giat:
Momen quan
tinh
cua cac
hinh

dan gidi: , ,
Theo
djnh ly true
song
song,
ta c6:
=
3^ = 81 => Chpn D
37
I
= Ic
+md2 =^mR2 +mR2
=
|mR2
=
2,25(kg.m^)
=>ChQnD
Cau 73.Tai
each
dinh
A,
B, C, D cua
mpt
hinh
vuong canh
a =
80cm
c6
g3n Ian
luot

kg.m^.
D.
3,6
kg.m^
Huong
dan
giai:
Ta
c6:
MC^
=
MD^
=
raf
-
\
AM2=BM2=a2-h
I2j
5a^
Momen
quan
tinh
ciia
hf:
^mj.AM^
+m2.BM^ +m3.CM^ +m,.DM^ =3,6(kgm^)
=>
Chpn
D
Cau

giai:
D.
I =
—MR2
19
Taco:
l = l^ +
md^ =-MR2+M
5
f-
.3
•
Chon
C
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

I =
I,
+=
(„,^R2
^
^^R2 J
^ ^
2)
= Imp
=>
Chgn
D
Cau 76. Mot thanh manh
c6
khoi
lugng
m = 2
kg, chieu
dai 3 m.
Doi
voi
true
quay
di qua
khoi
tam va
vuong
goc vai
thanh, momen quan
tinh

khoi
lugng ciia
vanh
la 600 g.
Momen quan
tinh
ciia
chie'c
vanh banh
xe
d^p doi vol true ciia
banh
xe la t
A.0,016kgm2.
B. 0,037
kgm2. C.
0,053
kgm^.
D.
0,096
kgm^
Huong
dan
gidi:
TaehgnBvi
I =
mR^
= 0,6.0,4^
=0,096kgm2
Chon

I
=
|mR2
=0,08kg.m2
Chon
D -
Cau 79. Mot dia
tron
dong chat
c6
khoi
lugng 2kg. Momen quan
tinh
ciia dTa
doi
voi true quay di qua tam dia
I =
Ikg.m^.
Ban
kinh
ciia dia
la
A.R
=
lm.
B.
R
=
l,5m.
C.R =

r
theo phuong tiep tuyen voi quy
dao
chuyen dong ciia diem
N.
Momen luc
tac
dung vao vat
c6
gia trj 200N.m. Khoang
each
r
bang
A.
4
m.
B. 3
m. C.
2
m. D. 1
m
Huang
dan
gidi:
M
Ap
dung cong thiie
M =
F.d
=

banh
da
chuyen dong quay quanh true quay
eo
^linh
di qua
tam.
Sau 15s ke tu
khi ehiu momen
lye tac
dyng,
toe dg goe
eiia
•^anh
da la? I
A.
75rad/s.
B. 50
rad/s.
C. 25
rad/s. D.
150rad/s
Huang
dan
gidi:
^ .
Ap
dung phuong
trinh
dong luc hoc vat ran:

Ian
thi momen luc se la: M' = F'.d' - 8F = 2F.d = 2M => Chon B
4
Cau 83. Mgt
khoi
try dac, dong
chat,
nam ngang, ban
kinh
R,
khoi
lugng M, e6
the quay ty do xung quanh true cua no. Mpt sgi day qua'n quanh
kho'i
try vn
M
dau
ty do ciia day c6 gan mgt vat nho
khoi
lugng m = —. Gia toe ciia vat nho
la (ggi g la gia toe trgng truong)
A.
^ B. ^ C. ^ D. g
Huang
dan
gidi:
Voi
I = -MR^ m = -M, ta duoe:
2 4
a =

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^
Huang
dan
gidi:
Ta c6:
V
3 '
I
= lmR2
2
•
m =
21 640

chuyen dgng quay voi gia toe goc 4 rad/s^. Momen quan
tinh
ciia dTa la
A.
120kg.m2. B. 140kg.m2. C. 180 kg.m^. D. 360 kg.m^
Huang
dan
gidi:
•
Chgn C
Cau 88. Mot dTa
tron
dac quay quanh true doi xung di qua tam va vuong goc
voi
mat dTa
duoi
tac dyng ciia momen lyc khong doi 6 Nm. Sau 3s ke tu
liic
bat
dau
quay, toe do goe ciia dTa la 36 rad/s. Momen quan
tinh
ciia dTa la
A.
0,25 kg.m^.
B. 0,5
kg.m^.
C. 0,75 kg.m^.
Huang
dan

.ml
„ 4mP ^ 5ml r-, o i
A.
— B. C. —— D. 3mlv
3v
V V
Huang
dart
gidi:
Momen
quan
tinh
cua thanh co hai
chat
diem m, va mj la:
I
=
mjl^+m2l^
=3ml^
_^ „ :.^|-
Momen
dong lugng ciia he (thanh va hai
chat
diem) la:
M
= Ira =
31^(0
=
3mP
y =

lugng ciia
vat?
A.
t = 10s;m = 15kg. B. t = 15s; m = 20 kg.
C. t = 25s; m = 30 kg. D. t =
35s;m
= 40kg
S
Huang
dan
gidi:
f
Theo
phuong
trinh
dong luc ciia vat ran quay quanh mpt true:
M
=
I.7=>y
= —= —= 10rad/s2
Matkhac
co
=
W(,
+
7t=>
100 = 0
+10t=>
t = 10s
Ap

dan
gidi:
Goc quay ciia vat ran tu khi chju momen luc can tac dung den khi
dimg
lai
la
n27t.
Suy ra:
(O^
-
to?.
=
2yA(p
- 2Y.n.2n => y = —^
47tn
* J 2
i
Ap dung phuong
trinh
dong luc hgc vat ran: M = ly = —
inn
Thay so ta dugc M =
-IN.m.
Suy ra dg ion ciia momen lyc can bang 1 N.m
Chgn
A
(^2u 92. Mgt vanh
tron
khol
iugng m, ban

cp
=
coot
+ ^yt^
1
2 •
Goc quay dugc sau z (s) dau
ticn:
(p
=
(OQT
+
—yt
=
Atp,
^ ,
1
Goc quay dugc sau
2T(S): tp
=
2a)oT
+ —y4t^
Suy ra goe quay dugc trong t (s) thu ba la:
Aipj
=
93
-
(P2
= +
^yt^

M nua thi no quay cham dan deu voi gia toe goc 1 rad/s^
duoi
tac dung
Ciia
momen lye ma sat eo dg Ion 0,8
Nm.
Mgmen nggai lyc co dg Ign la
A.
1,6 N.m B. 2,4N.m
C. 0,8(1 +
47T)
N.m D.
3,27i
N.m ; :
Huang
dan
gidi:
^ Khi
CO
tac dyng ciia momen M: M - M^ = ly .
mm
CtyTNHHMTVDW H
KhangVift
V§t quay
dvtac
16
vong trong
4
giay:
cp

vat ran c6 the
quay quanh
mot
true
co
djnh
di qua
trpng tam. Vat
ran
bat dau
quay khi chju
tac
dung ciia
mot luc
khong
doi F = 2,4 N tai
moj
diem
M
each
true quay mpt doan
d = 10 cm va
tiep tuyen
vai quy dao
chuyeti
dong
cua
M.
Sau
khi quay dugc

luc F,
Tinh
toa
dp
goc
tai thoi diem t2
= 20s?
A.
(p
= 300
rad.
B.
(p
=
500rad.
C.
(p
=
900rad.
D.
(p
=
800rad.
Huong
dan
gidi:
la
CO
co
=

Soi day
noi
hai vat
khong
dan va
khong
M
=
F.d
=
I.y
=^ I =
F.d
2,4.0,1
=
0,04kg.m'
Tai thoi diem
t, = 10s, vat
ran khong chju
tac
dung
cua
lue
F nen M = 0, suy
ra
I.y
= 0 => y = 0. Vay vat
ran ehuyen dong quay deu v6i
toe do goc
bang:

cua vat
ran trong
qua
trinh
vat
ran ehuyen dpng qua\
deu trong khoang thai gian t2
- tj = 20 -10 = 10s .
Tpa
dp goe cua vat tin tai
thoi diem
tj = 20s
dupe
xac
djnh (p
=
(pj
+
(pj
£
Ta
co:
Suy
ra:
=^ChpnC,
cpi
=
(Po
+
(0(,t

ngoai rong
rpc vao
thai diem
sau
khi
tha
tv
do
he
dupe
2s.
A.
l,5m/s
B.2,5m/s
C. 4m/s D. 6m/s
Huang
dan
gidi:
Chpn chieu duong
la
chieu ehuyen dpng ciia
cae
vat
Ap
dung djnh luat II Newton
cho mj:
Tl
+ Fms
= ^i^i
0),

ehuyen dpng quay
cua
rong rpc:
M
=
ly «(T2
-
T,) R
=
1 mR^y
«
(T2
-
T,)
= i
mRy
(3)
Vi
spi
day
khong dan
nen
ai
=
a2
= a.
Sg^i day khong truat tren rong rpc nen
y = —
Thay
vao (1); (2); (3) ta co:

Sau.96.Mpt
lue tiep tuyen
eo
dp Ion 4N
tac
dyng
vao
vanh ngoai
cua
mpt banh
^6
CO
duong
kinh
80em
dang quay deu. Trong giay cuoi cung truoc khi
toe dp
cua banh
xe
bang khong, mpt diem tren
mep
ngoai
cua
banh
xe di
dupe
|uang duong bang mpt phan
tu
ehu vi banh
xe.

Ap
dung cong thuc
cp
= o)(,t + ^yt^ va w =
(OQ
+ yt ta dugc y =
7t
rad/s^.
Fd
= Iy:
I
=
f^
=
lM.o,51kgV/s
=>
Chgn C
Cau 97. Mot rong roc c6
khol
lugng
m
= 2kg
(Hinh
ve). Bie't mj = 2kg va
1kg,
ban dau cac vat dugc giu
dung yen, sau do tha nhe cho he chuyen
dong thi gia toe
ciia
moi vat la 9,2m/s^.

Djnh
luat
II
Newton cho vat mi:
f2 + m2g = m2a2 f
m2
~T2 = m2a2
Ap
dung djnh luat
II
Newton cho chuyen dong quay cua rong rge:
M
= ly c:> (T2 - T,) R = 1
mR2y
«(T2 - Tj) = 1 mRy (3)
Vi
sgi day khong dan nen a^ = aj = a.
0)
(2)
Sgi
day khong trugt tren rong rge nen y = —
R,
mi
Vi
sgi day khong dan nen
3^=32
= a.
Thay vao (1), (2) va (3) roi
gisi
h? phuong

Huong
dan
giai:
Ban
dau: M = M, +M^^ =24(N.m)
Toic
dg goc
ciia
banh xe
liic
co
Mi:
(o = a)(, + yt ^ y = 2rad / s^ '
Momen
quan
tinh
ciia
banh xe: I = — ~~2~
^^^kg.m^
j
Khi
Ml
thoi
tac dung: w'= w + y't = 0-> y'=-0,2rad / s^ ^
Suy ra: M^^ = y'l =-0,2.12 =-2,4(N.m)
Vay
M, = M -
M,^^
= 26,4(N.m) Chgn B
»

= iyt^ = 250(rad) , j
Quang duong ma mgt diem tren vanh dTa di dugc sau 4s la:
s = R(p = 0,2.250 =
50{m)
Chgn B