Mô tả:
T , f k h o n g doi.
• Y > 0 k h i v a t quay n h a n h d a n
deu (co t a n g dan deu theo At)
• Y < 0 k h i v a t quay cham d a n
deu (co g i a m dan deu theo At)
• T o n g quat:
• co.Y > 0 -> vat quay nhanh dan deu.
• oj.Y < 0 ^ vat quay cham dan deu.
i
X
Van de 2: PHL/ONG TRINH DQNG Ll/C HQC CUA VA T RAN QUA Y
QUANH MQT TRUC CO DINH
1. Momen lUc ddi v6i true quay
Momen lue M cua life F d o i v d i v a t r a n co true quay co d i n h l a d a i lucfng
dac t r u n g cho tdc dung c o d i n h l a d a i lifcfng dae trUng cho tae dung l a m
quay v a t r ^ n quanh true co d i n h do va dUOe do bang t i c h so ciia lUc va
each tay don.
M = F.d = F.r.sina
c) V a t l a h h i h t r u r o n g hoac v ^ n h t r o n quay quanh true d i qua tarn.
Trong do:
• M : M o m e n cua life ( N . m ) .
,
• F: Luc tAc dung (N).
(A)
I
• d: C a n h tay don (m).
(Khoang each tCr true quay den gid cua life)
I = m.R=
2. Momen quSn tinh (I)
-
Momen quan t i n h I d o i v6i m o t true la d a i lu'Ong dac t r u t i g eho miJe
quan t i n h cua v a t rMn t r o n g chuyen dong quay quanh true ay.
1=
1
m, .r
d) V a t Ik h i n h t r u dSc hay dia t r o n mong quay quanh true d i qua tarn.
(A)
- Momen qudn t i n h c6 dp I d n phu thupe vao k h o i iMng v a t r ^ n , phu thupc
vao sir p h a n bo' k h o i li^png eiia v a t r ^ n d o i vcJi true quay (gan h a y xa
true quay).
3. PhUdng trinh dong luc hoc cua vSt r3n quay quanh m6t true cd dinh
(A)
c
I = -mR'^
2
M = I.y
Trong do:
e) V a t l a h i n h cau d i e quay quanh m p t true d i qua t a m .
• M : M o m e n lire (N.m)
• I : M o m e n qudn t i n h (kgm^)
• y: Gia toe goe (rad/s^)
I = -mR^
5
Nhqn xet: Ydi cung m o t M o m e n t h i
• Neu I i d n
y nho - > k h o t h a y doi toe dp goe.
• Neu I nho -> y i d n -> de t h a y doi to'e dp goe.
4. Momen quSn tinh cilia m$t s6 v$t dfing ch^t
a) V a t l a t h a n h m a n h dong chat, k h o i lupng m , chieu d a i I eo true quay l a
dudng t r u n g true cua t h a n h .
(A)
I = —ml'
12
1. Momen dOng ladng.
Momen dong liTpng eiia v a t r ^ n d o i v d i m p t true quay b^ng t i c h so eua
momen quan t i n h cua v a t doi v d i true quay do va toe dp goe cua v a t quay
J
b) V a t l a t h a n h m a n h dong chat, k h o i liTpng m , chieu dai / c6 true quay d i
qua m p t dau t h a n h v a vuong gde v d i t h a n h .
Van de 3: MOMEN DQNG LI/0NG DINH LUAT BAO TO AN MOMEN
DQNG LU0NG
quanh true do.
L = I.a)
(u)>0-»L>0;a)<0-^L<0)
Trong do:
• L : Momen dong lirpng (kgm^/s)
• I : M o m e n quan t i n h cua v a t r ^ n (kgm^)
(A)
I = -m.l'
3
• (o: Toe dp goe eiia vat (rad/s)
2. Djnh lu$t b^o to^n momen d6ng lUdng
L = h k n g so
hay
L, +
+ ... = L \
L'j
+
...
Dieu kien dp dung dinh ludt:
TRAC NGHrEM LI THUYET
K h i t o n g d a i so cua cac momen ngoai lye dat l e n mot v a t r ^ n (hay h$ v a t )
doi v d i mpt true quay b^ng k h o n g (hay cac momen ngoai lire t r i $ t tieu)
Luu y: K h i I doi v d i true quay k h o n g doi -> to = 0 hoac w - h k n g so.
(Vat k h o n g quay hoae v a t quay deu)
Van de 4: DQNG NANG CUA VAT RAN QUA Y QUANH
MQTTRUC CODfNH
1. D6ng nSng cCia m6t vat rjn quay quanh m6t true c6 dinh
C a u 1. M p t d i e m t r e n v a n h dia t r o n each true quay d i qua t a m m p t k h o a n g R
k h i dia quay t r 6 n deu quanh true t h i toe dp d ^ i va toe dp goc eiia d i e m do c6
quan he v d i nhau theo bieu thiJe nao t r o n g cac bieu thiifc sau?
A v - - .
B. v = - .
R
CO
C. 0 3 = - .
D . R = vlco.
R
C a u 2. H a i hpc s i n h A va B diing t r e n mpt ehiec du quay t r o n deu quanh true
C O d i n h d i qua t a m . Hoe s i n h A d ngoai r i a , hoc s i n h B d each t a m m p t doan
b^ng mpt p h a n t u b a n k i n h chiee du quay. Gpi T A , TR la ehu k y quay cua hoc
sinh A va hoe s i n h B . Lue nay t a cd:
• W,i: D o n g n ^ n g eua v a t r a n quay quanh m p t true (J)
• I : M o m e n quan t i n h cua vat (kgm^)
• co: Toe dp gdc cua v a t (rad/s)
2. Dinh li dong nSng
Trong do:
A = W,
Trong do:
Luu y:
+
Vp; fe =
2iv.
B.
VE
=
D-
VE
= 2VF; h = fp-
Vp;
=
dia. Gpi (DA, COB, YA, YB I a n lupt l a toe dp gdc va gia toe gdc cua ede d i e m A va
B . Chpn cau k e t l u a n diing.
A. COA = 2(0B; YA = YB-
B.
C.
D - " A = COR; YA = YB-
tOA
= COB; YA =
YB-
(OA
= cou; YA = 2YB.
C a u 5. M p t dia CD quay t r d n deu quanh true d i qua t a m dia. M p t d i e m bat k y
3. Djnh li v l true song song
1(0)
=
ngoai r i a , B l a d i e m each true quay m p t doan b a n g mpt p h a n ba ban k i n h
• Neu v a t thuc h i e n dong thcfi h a i ehuyen dpng la quay quanh
true va t:
tinh tien thi: W j =
VE
C a u 4. M p t dia quay t r o n deu quanh true doi xii'ng d i qua t a m . Gpi A la d i e m d
: Dong nftng lue sau (J)
=
eiia dia. Gpi E va F I a n lupt la d i e m d ngoai r i a va d i e m d each t a m dia m p t
C. vp = 2VE; ffi = fp-
Neu v a t chi c6 chuyen dpng quay quanh true t h i : W j =
1(A)
D . T A = 4T„.
C. T A > T R .
doan b^ng nuTa ban k i n h cua dia. Gpi VR, V F , fs, fp I a n lupt la toe dp d a i va
A.
,^ : Dong nftng lue dau (J)
• Wj
B . TA < TB-
t ^ n so ciia cac d i e m E va F. K e t l u a n nao sau day la diing?
- Wd,,,-,„
• A: Cong eiia ngoai lue (J)
•
A. T A = T B - ' ^
C a u 3. Klpt dia CD coi n h u chuyen dpng t r d n deu xung quanh true d i qua t a m
n k m d mep dia se:
+ inx^
A. k h o n g cd gia toe t i e p t u y e n I a n gia toe phap tuyen.
Trong do:
B . cd gia tdc phap t u y e n n h u l i g k h o n g cd gia toe t i e p tuyen.
• 1(A): M o m e n quan t i n h eiia m p t vat doi v d i true quay ( A ) (kgm^)
C. C O gia tdc t i e p tuyen va ed ea gia toe phap tuyen.
• IQ: Momen quan t i n h eiia true di qua trong tarn G song song vdi (A) (kgm^)
• m: K h o i lupng v a t rSn (kg)
D. ed ea gia tdc t i e p t u y e n va gia to'e phap tuyen n h u i i g gia toe phap t u y e n
• x: K h o a n g each vuong gdc giSa true ( A ) va true song song qua (G) (m)
Hinh minh hga dinh li:
(A)
(G)
'
Idn hon gia toe t i e p t u y e n .
C a u 6. M p t v a t rSn quay t r o n deu quanh true eo' d i n h d i qua v a t t h i m p t d i e m
t r e n v a t d each true quay m p t doan r
A. toe dp gdc thay doi.
0 se cd
B . ehu k y quay t h a y doi.
C. tdc dp dai t h a y doi.
0)
G
D. vecto van tdc dai t h a y doi n h u n g to'e dp Aki eiia d i e m dd, k h o n g ddi.
C a u 7. M p t vat r ^ n quay t r o n deu quanh mpt true cd d i n h . Gpi N la so dao dpng
ma vat thue h i e n t r o n g t h d i gian At, cpo va cp la tpa dp gdc lue dau va lue sau, co
la tdc dp gdc cua vat r a n . Chpn bieu thiire sai t r o n g cac bieu thde sau:
A. T : . — .
CO
B T = — .
N
C. N = ^ ^ ^ .
27;
D. (p = (po -
«At.
C a u 8. Bieu thiJc nao sau day l a dung k h i n 6 i ve dp I d n cua gia toc ph^P t u y e n
(gia toc hudng tarn)?
V
v^
A. an = - .
B. an = w.R.
C. an = — .
D. a^ = (w.R)^.
C a u 9. Bieu thiJc nao sau day l a dung k h i n o i ve do I d n ciia gia toc t i e p t u y e n
cua v a t rSn quay b i e n d o i deu quanh mot true co dinh?
A. at = r.y.
B. a t = - .
C.at=-.
D. at = — .
r
r
C a u 10. M o t v a t r ^ n quay b i e n d o i deu quanh m o t true d i qua v a t r ^ n . Chon
Y
goc t h d i gian to = 0 la luc v a t bat dau quay. Goi t i , t 2 l a cac t h d i d i e m liic sau
(t2 = 2 t , ) . N e u xet m o t d i e m t r e n v a t r ^ n each true quay T ^0 t h i :
A. a,, = 2a,^.
B. a,^ = 2 a , .
C. a,_ = ^
D. a, = a,^.
.
C a u 11. Bieu thiJc nao t r o n g eac bieu thiic sau k h o n g the ap dung cho v a t r ^ n
quay bien d o i deu quanh m p t true co d i n h d i qua vat?
A.
9
C.
cp = (po +
-
cpo
= o)o-t +
•
cD.t.
B.
(0^
-
D. © =
(OQ =
0)0 +
2Y((P - cpo)-
y.t.
C a u 12. Bieu thiJe nao t r o n g eae bieu thiJe dudi day l a sai k h i t i n h gia toe t o a n
p h a n ciia v a t r ^ n quay b i e n d6'i deu quanh m o t true eo d i n h d i qua vat?
A.a=
J ^ ^ .
B.
al=a'-al
C a u 16. M p t v a t rMn quay bien d o i deu quanh m p t true co d i n h d i qua v a t rin.
Chon phat bieu sai t r o n g cac p h d t bieu sau:
A. Gia toc goc l a h k n g so.
B. Toe dp goc l a m p t h a m bac n h a t d o i v d i t h d i gian.
C. Toe dp gdc 1^ m p t h k n g so.
D. T r o n g chuyen dpng quay b i e n d o i deu ciia v a t r k n quanh m p t true co' d i n h
di qua no t h i toe dp goc tSng hay g i a m nhiJng luang eo dp I d n b k n g nhau
t r o n g nhiJng k h o a n g t h d i gian b k n g nhau.
C a u 17. M p t v a t r k n quay v d i toc dp goc k h o n g d o i quanh m p t true ed d i n h d i
qua vat. So' vong quay m a v a t quay dUde t r o n g t h d i gian t ke til luc v a t b a t
dau quay se:
A. t i le v d i t l
B. t i le v d i t .
A. t i le v d i t^.
B. t i le v d i t .
C. t i le v d i
D. t i le v d i - .
t
C a u 18. M p t v a t r k n quay v d i gia toe goc k h o n g d o i quanh m p t true ed' d i n h d i
qua vat. Goc ma v a t quay dupe sau t h d i gian t , ke tCr luc b k t dSu quay se
.
C. t i le v d i \
D. t i le v d i - .
t
t
C a u 19. M p t v a t r ^ n quay n h a n h d a n deu quanh m p t true eo' d i n h xuyen qua
vat. M p t d i e m t r e n v a t r S n k h o n g n k m t r e n true quay va each true quay m p t
doan r ^ 0. Chpn p h a t bieu dung t r o n g eac p h a t bieu sau:
A. Td'c dp gdc k h o n g phu thupc r.
B. Gia to'c gdc phu thupc r.
C. Gia toe t i e p tuyen k h o n g phu thupc r.
D. Gia toe phap t u y e n k h o n g phu thupc r.
C.rV = a^-f—1.
I r j
D. a'= ^co^r + ry .
C a u 13. P h d t bieu nao sau day 1^ d u n g d o i v d i v a t r ^ n eo chuyen dpng quay
deu quanh m o t true?
A. Toc do goc l a m o t hSng so.
B. Toe dp goc l a m o t h a m bae n h a t doi v d i t h d i gian.
C. PhUdng t r i n h chuyen dpng l a m o t h a m bac h a i doi v d i t h d i gian.
D. Gia toe goc 1^ m o t hkng so.
C a u 20. M p t v a t r k n quay quanh m p t true co' d i n h xuyen qua v a t . Cac d i e m
t r e n v a t r k n k h o n g thupc true quay se
A. vaeh n e n cac dudng t r o n n k m t r o n g m a t p h k n g vuong gdc v d i true quay.
B. ed eung v a n toe d a i d eung m p t t h d i diem.
C. quay dUde nhi^ng gdc k h o n g b k n g nhau t r o n g eung m p t k h o a n g t h d i gian.
D. ed gia to'c gdc va to'c dp gde la h k n g so.
C a u 21. H a i dia t r o n dang quay
A. Gia toc goc ciia chiec du quay l a m o t h^ng s6'.
dong true va eiing chieu v d i
toe dp gde coi, 0)2. M o m e n quan
t i n h cua h a i dIa 1^ I i , I 2 . M a
sdt d true quay k h o n g dang
ke. Sau do cho h a i d i a d i n h
vao nhau va quay v d i to'c dp
gdc 0). Bieu thde t h e h i e n m d i
quan he giOfa ede d a i li/dng coi,
^ 2 , I i , I 2 , 0) l a :
B. K h d i lUdng cua chiec du quay l a m o t h k n g so.
A. I i ( O i = l2(02 + d i + 12)0).
B. IiCO] + l2(02 = d l + l2)W-
C. Toe dp cua chiec du quay 1^ m o t h^ng so.
C. Iicoa +
D. Iicoi - I2CO2 = d l + h)o^-
C a u 14. Chpn phat bieu sai k h i n o i ve momen quan t i n h eiia v a t r ^ n
A. Momen quan t i n h phu thupc vao h i n h dang va k i c h thude ciia v a t .
B. Momen quan t i n h phu thupe vao k h o i liTpng ciia v a t r ^ n .
C. Momen quan t i n h k h o n g phu thupc vao v i t r i true quay ciia v a t r ^ n .
D. Momen quan t i n h k h o n g phu thupc v^o toc dp goc ciia v a t .
C a u 15. M o t chiee du quay ehiu tac dung eiia m o t momen lue k h o n g doi. Chon
phat bieu sai t r o n g eac p h a t bieu sau:
D. M o m e n qudn t i n h l a m o t h k n g so.
l2(0i
- d i + l2)(i).
v./a)2
C a u 22. H a i dia t r 6 n m 6 n g n ^ m
n g a n g c6 c u n g t r u e q u a y t h S n g
diJng d i q u a t a r n cua h a i d i a .
M o m e n q u a n t i n h ciia 2 d i a l a I j ,
I2. L u c d a u d i a 1 d i J n g y e n , d i a 2
q u a y v d i to'c do CO2. B o q u a m a
s a t do'i v d i t r u e q u a y . T h a n h e
d i a 1 xuo'ng d i a 2 sau m o t t h d i
g i a n n g S n t h i ca h a i d i a q u a y v d i
Cling mot
toe
dp
goe
A . 0) =
C a u 28. H a i d i a t r 6 n c6 c u n g m o m e n q u d n t i n h
d o i c u n g m o t t r u e q u a y d i q u a cac t a m d i a . L u c
d l u d i a m o t d i J n g y e n , d i a 2 q u a y v d i toe dp goe
u)2. B 6 qua m a s a t d t r u e quay. Sau do h a i d i a
d i n h v a o n h a u v a q u a y c u n g toe d p goe (o. C h p n
k e t l u a n d u n g k h i n d i ve d p n g n a n g cua h e h a i
d i a lue sau so v d i lue d a u .
V_/co
A. G i a m d i 2 I a n
B. T a n g len 2 Ian.
C. T a n g l e n 4 I a n
D. G i a m di 4 Ian.
C a u 29. H a i r o n g rpe 1 v a 2 cd k h d i l i i p n g l a m , v a m 2 = 2 m i , b a n k i n h
la:
B . (0 =
D . 0) =
C. w =
C a u 23. M o t n g i r & i d i J n g t r e n m o t c h i e e b a n x o a y d a n g q u a y . L u c d a u n g u d i a y
d a n g t a y r a t h i g h e v a n g u d i q u a y v d i t o e d p goe l a coi. B o q u a m a s a t d t r u e
q u a y . S a u do ngurdi a y t h u t a y l a i s a t n g i r d i t h i g h e v a n g i r d i q u a y v d i t o e d p
goe C02. B i e u thiirc n a o d i i n g t r o n g eac b i e u thuTc sau?
A . Iicui -
B . I1CO2 = l2Wi-
I2CO2.
C. IiCOi + 12(1)2 = 0 .
D . coi >
(02-
C a u 24. M o t v a n d o n g v i e n t r U p t b a n g q u a y q u a n h m o t t r u e t h ^ n g d i J n g v d i h a i
t a y d a n g r a v a c6 toe dp goe coi, m o m e n q u a n t i n h I i . S a u do v a n d o n g v i e n
t h u t a y l a i d o t n g p t t r o n g k h o a n g t h d i g i a n n h o de ed t h e bo q u a a n h h u d n g
eiia m a s a t do'i v d i m a t b a n g . L u c n a y v a n d p n g v i e n q u a y v d i t o e dp goe l a
C02, m o m e n q u a n t i n h l a I2. C h p n k e t l u a n d u n g .
A . M l = (02; I i = I2.
B . coi = (02; I i < hC. COi > M2; I I >
D . (Oi < (02; I i > 12-
r d n g r p e 1 ga'p 4 I a n b a n k i n h c i i a r d n g r p e 2. T i so giCa j - Ik:
h
A . 2.
B . 4.
C. 6.
D . 8.
C a u 30. H a i d i a t r b n m o n g c6 cung d p n g n a n g quay, t i so giOfa m o m e n q u a n t i n h eiia
dia 1 v a d i a 2 d i qua t a r n cua d i a 1 v a d i a 2 l a i - = 4. H m t i so' toe dp goe
A . 1.
B . 2.
C. 3.
—.
D . 4.
C a u 31. M o t t h a n h m a n h d o n g c h a t d i e n d i e n d e u , c h i e u d a i t h a n h l a I, k h o i
l i i p n g t h a n h l a m . T h a n h ed t h e q u a y x u n g q u a n h m o t t r u e n ^ m n g a n g d i q u a
m o t d a u eiia t h a n h v a v u o n g goe v d i t h a n h . B d q u a m p i m a s a t v a sdc c a n .
B i e t m o m e n q u a n t i n h cua t h a n h l a I =
v a g i a toe r o i ta. do l a g. H o i
o
n e u t h a n h diTpe t h a k h o n g v a n to'c d a u t i f v i t r i nhm n g a n g t h i to'c dp gdc cua
C a u 25. M o t v a n d p n g v i e n triTpt b a n g q u a y q u a n h m o t t r u e t h ^ n g d i J n g v d i t o e
dp goe (iJi, m o m e n q u a n t i n h I i k h i h a i t a y t h u l a i s a t n g u d i . S a u do v a n d p n g
v i e n d a n g t a y r a t h i t h a y t o e d p goe lue n a y l a 0)2 = — .
cua
B o q u a m a s a t giiJa
t h a n h k h i q u a v i t r i t h i n g d d n g l a bao n h i e u ?
3g
2g
3g
C. (0 =
B . (0 =
A . (0 =
21
^31
'
^ I
D . CO =
121 •
C a u 32. M o t t h a n h A B d o n g chat ed chieu d a i I cd t h e quay t r o n g m a t p h a n g t h a n g
n g u d i v d i m a t b a n g . G p i I i , I 2 , vf^^ , W j _ I a n l u p t l a m o m e n q u a n t i n h v a d p n g
d i i n g qua m o t true n k m n g a n g d i qua m o t dau cua t h a n h v a v u o n g gdc vdi t h a n h .
n a n g cua v a n d p n g v i e n k h i h a i t a y t h u l a i sat n g u d i va k h i h a i t a y d a n g r a .
Chpn ket luan diing.
T h a n h ed t i e t d i e n deu, k h d i liTpiig m , gia toe rcri t i l do l a g, I = ^
o
A . I2 = 2I1;
w,
1
C. I2 = 2 1 , ; w d,
. -= - 2" wd ., •
B . I , = 2I2;
w.
= 2w,
D . I2 = 2I1;
vv,^ = w<,_ .
C a u 26. C h p n c a u d u n g k h i n d i ve b i e u thufc t i n h d p n g n a n g c i i a v a t r ^ n q u a y
q u a n h t r u e eo d i n h
A . W d = 1(0
B . Wd = .
21
C. W d =
—
. B o qua m p i m a
sat va sure can. T h a n h d a n g d d n g y e n d v i t r i can b k n g . H o i can p h a i t r u y e n cho
t h a n h m o t toe dp gdc l a bao n h i e u de t h a n h quay d e n v i t r i n k m n g a n g .
2g
6g
3g
3g
D . (0 =
C. (0 =
B . 0) =
A . (0 =
/
^ /
^ /
A/ 3/
C a u 33. M o t t h a n h A B d o n g cha't cd c h i e u dai / cd t h e q u a y t r o n g m a t phSng
t h i n g d d n g q u a m o t t r u e nkm n g a n g d i q u a m o t d a u c i i a t h a n h v a v u o n g goe
.
D . Wd =
2
"
21' '
C a u 27. M o t d i a t r d n c6 m o m e n q u a n t i n h I d a n g q u a y q u a n h m o t t r u e eo' d i n h
CO toe dp goe (o. M a s d t d t r u e q u a y k h o n g d d n g k e . M o m e n d p n g l u p n g v a
d p n g n a n g q u a y se b i e n d o i n h u t h e n a o n e u toe dp goe cua d i a t a n g l e n 3 I a n ?
A . M o m e n d p n g liTpng v a d p n g n a n g q u a y d e u t a n g 3 I a n .
B . M o m e n d p n g liTpng t a n g 3 I a n , d p n g n a n g q u a y t a n g 9 I a n .
C. M o m e n d p n g l u p n g t a n g 3 I a n , d p n g n a n g q u a y g i a m 9 I a n .
D. M o m e n d p n g lifpng g i a m 3 I a n , d p n g n a n g quay t a n g 9 I a n .
eua t h a n h . T h a n h ed t i e t d i | n deu, khd'i l i f p n g m , g i a to'c r p i t u do la g, I = ^
B d q u a m p i m a s a t va sdc c a n . T h a n h d d n g y e n d v i t r i c a n hkng.
.
H o i can
p h a i t r u y e n c h o t h a n h m p t t d c dp gdc l a bao n h i e u de t h a n h q u a y d e n v i t r i
t h i n g d d n g d p h i a t r e n t r u e quay?
A . (0 =
3g .
B . CO =
3g
I
C. CO =
6g
D . CO =
12g
P H A N II: B A I T A P T R A C
NGHIEM
C2.Tac6thld6itCr4^
phut
Cu t h e n h u sau:
+ BAI TAP LUYEN TAP
sang ^
.
s
1 2 0 0 vong/phut = 1 2 0 0 . ^ ^ ^ ^ = 4 0 rad/s
60s
Van de 1: VAT RAN QUA Y TRON DEU
(0 = 4071 (rad/s)
Trong
PHlJolNG P H A P
• t : T h 6 i gian quay N v o n g (s).
(0
• N : So' vong.
• V: Toe do d a i ( v a n toe d a i ) (m/s).
• V = (o.r
= oj .r =
• co: Toe do goe (van toe goc) (rad/s).
—
diTcfc
t r o n g t h d i gian
4
s 1^:
(PQ = co.t
cpo = 4071.4 <=>
cp - cp,| = 1 6 0 7 c ( r a d )
B a i 2. Roto eiia mot dong ecf quay t r o n deu quanh m o t true co d i n h . B i e t r k n g
eiJ m 6 i p h u t t h i Roto quay d M c 1 2 0 0 vong. T i m :
a) Chu k y quay ciia Roto.
b) Gc3c ma ROto quay d M c t r o n g 2 s.
c) So vong ma Roto quay diiac t r o n g 2 s.
;
• r : B a n k i n h quy dao cua v a t (m).
r
• Sin. Gia toe phap t u y e n (gia toe
• a t = 0 (chuyen dong deu)
• (p = (po
—
cp -
• f: T a n so (Hz) (v6ng/s).
T
• an
tp
• T: Chu k i quay ciia v a t (s).
I. C h u y e n dpng tron deu.
N
b) G6c ma v a t quay
do
hirdng tarn) (m/s^).
+ co.t
• a t : Gia toe t i e p t u y e n (m/s^).
• a = a„
• a: Gia toe t o a n p h a n (m/s^).
• 0) = 271.f
Tom
• 9: Toa do goe luc sau (rad).
=> 1 2 0 0 vong/phut
<=> M =
= 4071 r a d / s
T = ?
b)
cp -
• oj > 0: Neu vat quay theo chieu
e) N = ?
b) Goe m ^ Roto quay ducfc t r o n g 2 s.
cpo = ?
=>
cp -
cpo = co.t
cp -
cpo = 4 O 7 1 . 2
cp - cpg = 807i(rad)
<=>
diJOng.
c) So vong ma Roto quay diJgrc trong 2 s.
• 0) < 0: Neu v a t quay ngi/crc chieu
^ 9-9o
ducfng.
B a i 1. Mot banh xe quay deu quanh mot true eo d i n h vdi t a n so 1 2 0 0 v5ng/phut.
a) T i m toe dp goe cua b a n h xe.
b) Goc ma b d n h xe quay duoc t r o n g t h d i gian 4 s.
Hudng
ddn
gidi
xet: Do b a n h xe quay deu quanh m o t true co d i n h n e n t a can silr d u n g
eac k i e n thiJe cua chuyen dpng t r o n deu.
a) De cho t a n so 1 2 0 0 v6ng/phut
Tom tat
B&nh xe quay deu 1 2 0 0 vbng/phut
a)
CO =
b)
cp -
Cl:=>
f = 1200 ^
=
60s
?
(po = ?
2
0
(0 = 2nf ^ CO = 271.20
CO = 407t
^ SOn
22
N = 4 0 (vong)
BAI T A P M A U
Nhdn
271
4071
T = 0,05(s)
60s
a)
K h i v a t r ^ n quay t r o n deu t h i :
gidi
271
T =
1200.27Trad
• co: K h o n g doi (la h ^ n g so).
ddn
a) Chu k y quay cua Roto
Moi phut t h i Roto quay duoe 1 2 0 0 vong
• cpo: Toa do goe liic dau (rad).
I I . luvtu y
HUdng
tat
(rad/s)
^
s
B a i 3. M o t b a n h xe quay t r o n deu quanh m o t true co d i n h . B i e t toa do gc5c
iue dau la - r a d va toa do g6c sau t h d i gian la i
3
b a n h xe la 50 em. T i m
a) Toe do goe cua b a n h xe.
b) Toe do d a i eua m o t d i e m t r e n v a n h b d n h xe.
s la ^
0
0
e) Gia toe huc?ng t a m cua m o t d i e m t r e n v a n h b a n h xe.
= 2 0 Hz
Tom
• cpo =
—
3
Hiidng
tat
rad
ai)
dan
Toe do g6c ciia b a n h xe
Ap dung
cong
thiic:
(p - cpo = co.t
gidi
rad, ban k i n h
• (p =
—
_
rad
?
b)
V
?
=
C a u 2. K i m p h i i t c i i a 1 chie'e d o n g h 6 g a p 4/3 I a n c h i e u d a i k i m g i d . C o i
m
k i m n h u q u a y d e u . T i so g i a t o e h i f d n g t a m giura d a u k i m p h u t v a d a u k i m
V = M . R = 71.0,5 =
c) G i a t o e h u d n g t a m c i i a m o t d i e m t r e n
vanh
b a n h xe
gicf. Cac k i m coi n h u ' q u a y d e u q u a n h m o t t r u e co d i n h . T i m t i so giuTa to'c
do d a i cua d a u k i m p h u t v a d a u k i m g i d .
•
Rphui
pillit
dan
gidi
N e u x e m k i m gid va k i m p h u t quay t r d n
mot
t r u e co
dinh
v d i t a n so
2400
d e u , cii: m o i p h i i t q u a y d u o c 3 6 0 0
vdng.
B. 160;: (rad/s).
C. 8071 ( r a d / s ) .
D . 2407i ( r a d / s ) .
Cau
4. R o t o cua
mot dong
co q u a y
120071 rad.
B.
24007t
rad.
D . 4 8 007r r a d .
27T
goc
luc sau l a
r a d t r o n g t h d i g i a n 2 s. B i e t b a n k i n h q u y d a o t r d n c i i a
o
A . 7t/120 m / s .
B . 7t/60 m / s .
C. 7i/240 m / s .
D . 7i/360 m/s
C a u 6. M o t v a t c h u y e n d o n g t r d n d e u q u a n h m o t t r u e v a t q u a y 10 v d n g h e t 20
s. B a n k i n h q u y d a o c u a v a t l a 20 c m . G i a t o e h u d n g t a m cua v a t l a
* T h d i g i a n de k i m g i d q u a y m o t v o n g l a 12 g i d
A . 1,25 m / s ^
T„i,
^
12 g i d
phut = 1 gid ^
B . 0,65 m / s l
C. 0,85 xnJ&\. 1,97 m / s l
C a u 7. M o t v a t q u a y t r d n d e u d e u co p h u o n g t r i n h : cp = 7[/2 + 27tt ( r a d ; s).
• T h d i g i a n de k i m p h u t q u a y m o t v d n g l a 6 0
^gid
quanh
d e u q u a n h m o t t r u e co' d i n h t h i :
^
_
deu
v a t l a 10 c m . T o e do d a i c i i a v a t l a
Hiidng
tdt
2 Rgij,.
=
quay
C a u 5. M o t v a t - c h u y e n d o n g t r d n d e u v d i t o a do goc l u e d a u l a — r a d v a t o a do
2
B a i 4 . K i n i p h u t c u a m o t e h i e c d 6 n g h o c6 c h i e u d a i b a n g 2 I a n c h i e u d a i k i m
. T g i , = 12 gior.
xe
C . 360071 r a d .
a„ « 4 , 9 3 ( m / s ^ )
xet:
banh
D . 200.
A . 12071 (rad/s).
A.
_0A_
R
Nhan
Mot
C. 1 9 2 .
T r o n g 20 s t h i r o t o q u a y diroc m o t goc l a
1,57'^
60 p h u t = 1 g i d .
3.
B . 108.
v d n g / p h i i t . T o e do goc c i i a b a n h x e n a y l a
c) an = ?
•Tphat=
A. 92.
Cau
0,571
V = l,57(m/s)
Tom
cac
gid la
b ) T o e do d a i c u a m o t d i e m t r e n v a n h b a n h xe.
• R = 50 c m = 0,5
(0 =
3 ~
(0 = 7 t ( r a d / s )
. t = - s
a)
1
3
IL _
3
Tphut
1 gid.
=
* K h i x e t d i e m d d a u m i i t c i i a k i m g i d v a k i m p h u t t h i k h o a n g e a c h tCf t r u e
q u a y d e n cac d i e m n a y b K n g d u n g c h i e u d a i cua k i m g i d v a k i m p h u t n e n
Toa
dp goc l i i c d a u v a c h u k i q u a y c i i a v a t l a
A . 7i/2 r a d ; 2 s.
B . 71/6 r a d ; 1 s.
C. 71/6 r a d ; 1/2$.
D . 7t/2rad; I s .
C a u 8. M o t v a t q u a y t r d n d e u c6 p h u o n g t r i n h t o a d o : cp -
n/4 + 6nt
( r a d ; s).
Goc q u a y c i i a v a t s a u 2 s k e t i f l i i c t = 0 l a
A.
871 r a d .
B.
IOTI
rad.
C.
127c
rad.
D.
147T
rad.
• T i m t i so t o e do d a i cua d a u k i m p h u t v a d a u k i m g i d
Van de 2: VAT RAN QUA Y BIEN DO I DEU
fv = C3.R
T a co:
^
271
=5"
v = — .R (*)
A p d u n g (*) cho d i e m d d a u k i m p h u t v a d a u k i m g i d
271
2n
.R gid
<=>
271
' pllllt
1. Quay
=
nhanh
dan
t
2. Quay
k i m gid la
C.
3/4.
deu
24
1 . K i m p h i i t c i i a m o t c h i e c d o n g h o co c h i e u d a i b f t n g 4/3 c h i e u d a i eiia
B . 16.
do
* CO,): V a n to'c goc liic b a n d a u (rad/s)
0
10
20
60
80
0
2
4
6
8
chdm
dan
D . 4/3.
...
...
* (o: to'c do goc l i i c sau ( r a d / s ) .
* y: to'c do goc
(rad/s^).
* cpo: T o a do goc l i i c d a u ( r a d ) .
deu
w
... 8 0
60
40
20
0
t
... 0
1
2
3
4
k i m g i d . Cac k i m c o i n h u q u a y d e u . T i so toe do d a i c i i a d a u k i m p h u t v a d a u
A . 1/16.
Trong
I. P h a n loai
R phiit
BAI TAPTRAC NGHIEM
Cau
PHl/CfNG P H A P
* (p: T o a do goc l i i c sau ( r a d ) .
* a„: G i a tdc h u d n g t a m (gia
p h a p t u y e n ) (m/s^).
to'c
CO
-
xet
(p = cpo + coo-t +
cp -
12071 r a d / s t h i b i h a m l a i v a q u a y c h a m din
d e u s a u t h d i g i a n 10 s t h i
toe dp g(5c c o n 407t r a d / s .
* r : B u n k i n h q u y c!ao e i i a d i e m
= 2y(cp - cpo)
ml
la
* a: G i n toe t o a n p h a n (m/s^).
= coo + Y-t
CO
B a i 2. R o t o eua m p t d p n g ccf d a n g q u a y q u a n h m O t t r u e c6' d i n h v6i t6c d p g6c
* a t : G i a t o e t i e p t u y e n (m/s^).
I I . C a c c o n g thtfc.
a) T i m g i a toe goc c u a R o t o .
( h a y v a t dutfc x e t ) ( m ) .
b ) T i m gdc q u a y v a so v d n g mk R o t o q u a y dMc
2
t r o n g t h d i g i a n 10 s k e tiT
liic h a m .
c) So v 6 n g m a R o t o q u a y dugrc k e tiir l u c b i h a m c h o d e n k h i dCfng h i n 1^
ipo = (Oo-t +
bao n h i e u ?
+ a.
Tom
HUdng
tat
ddn
gidi
a„ = CO . r
• coo = 1207T ( r a d / s )
C h o n e h i e u q u a y cua R o t o
at = r . y
• CO = 407r ( r a d / s )
t h d i g i a n (t = 0) l a luc Roto b ^ t d a u b i h a m l a i
. t = 10 s
a) G i a t o e goe eua R o t o
* Li/u y: C a c h n h a n b i e t v a t q u a y n h a n h d a n d e u h a ^ c h a m d a n d e u :
a) y = ?
• N h a n h d a n deu
-
Y =
b ) cp - (po = ?
N = ? t r o n g 10 s
* (Oo = 0
• C h a m d a n deu
ham
* (o.y < 0
4071 -- 12071
-
10
quay eiia R o t o quay diTOc s a u 10 s k e tCr l u c
b) Goc
c) N = ? k e t d l i i c
goc
y = -87i(rad/s^)
—»•
ke tir luc h a m .
* (o.y > 0
CO - cOo
l a m c h i e u duc(ng,
b ^ t d a u bi h a m l a i .
cho d e n l u c
ddng h^n.
cp - cpo = COo.t +
• Chuyen dong quay b i e n doi deu t h i y k h o n g doi
yt^
(-87t).10'
cp - cpo = 1207r.lO +
BAI T A P M A U
(p-cpo = 80071 ( r a d )
Bai
1. M o t b a n h xe q u a y n h a n h d a n d e u q u a n h m p t t r u e tiT t r a n g t h a i durng
yen
< So' v o n g rak Roto quay dircfe i l n g v d i g6c quay t r e n .
v a sau 5 s t h i d a t d u g c t o e do goc l a 10 r a d / s . T i m :
N=
a) G i a toe goc c i i a b a n h x e .
b ) Goc q u a y cua b a n h x e t r o n g t h d i g i a n 5 s k e t i r t r a n g t h d i d i l n g y e n .
tat
Hiidng
dan
C h p n c h i e u q u a y c u a b d n h x e l ^ m c h i e u ducfng, goe
• t = 5 s
t h d i g i a n (t = 0) l a liic v a t b ^ t d a u quay,
• CO = 10 raci/s
a) G i a toe goc e i i a b a n h xe.
a) y = ?
b) cp -
Y =
(po = ?
(o-coo
10-0
N
gidi
• tOo = 0
= 0.5 +
co^ -
cof,
= 2y (cp CO
2
cpo)
2
-COn
0 ' - (12071)='
2y
The ( 2 ) v a o ( l ) ^
25
2.3,14
N =
_ -1440071^
2.(-87r)
90071
271
-16;:
(2)
o
|N ^ 4 5 0 ( v d n g )
2.5'
B a i 3. M p t d I a m a i c6 b a n k i n h 4 0 c m hAi d a u q u a y k h o n g to'c dp goc l u c d a u
v d i g i a t o e goc k h o n g d o i c6 d p I d n l a 27i (rad/s^). T i m :
a) T o e d p goe m a d i a m a i d a t dugtc sau 4 s k e iii l u c t = 0.
c) So v o n g m a b a n h x e q u a y dugc t r o n g t h d i g i a n 5 s d t r e n .
271
« | N = 400vong
(1)
2K
y = 2(rad/s')
cp - (p„ = 2 5 ( r a d )
=
271
D o l u c sau R o t o dCtog l a i - > co = 0
b) G6c m a b d n h x e quay difcfc t r o n g t h d i g i a n 5 s k e tiT t r a n g t h d i diJng y e n .
y.t^
^
• T i m cp - cpo = ?
c) N =
N
=
cp - cpo = 90071 ( r a d )
cp - CPo = (Ofl.t +
« N =
e) So v d n g m a R o t o q u a y diToc k e tijf l u c h a m p h a n h cho d e n l u e di^ng h ^ n .
c) So v o n g m a b a n h x e q u a y dugfe t r o n g t h d i g i a n 5 s d t r e n .
Tom
271
N = 3,98 ( v o n g )
b ) G i a to'c t i e p t u y e n , g i a toe p h d p t u y e n c u a m p t d i e m t r e n v d n h d i a t a i
_
t h d i d i e m t = 4 s k e t d l i i c t = 0.
c) Gia toe toan ph^n ciia mot diem tren vanh dia tai thdi diem 5 s ke tCf
luc t = 0.
C a u 10. T a i th6i diem t = 0, mpt bdnh xe dap bdt dau quay quanli
IUUL
true vdi
gia toe goc khong doi. Sau 4s no quay dupe mpt goc 20 rad. Toe dp goc va gia
toe goc ciia banh xe tai thcfi diem t = 5 s la
Tom
Hu6ng ddn gidi
Chon ehieu quay ciia dia mai lam chieu dUcfng va
goe thdi gian (t = 0) la luc dia mai bdt dau quay,
a) To'c do goe cua dia mai dat duoe sau 4 s.
tat
• R = 40 em
• (Oo
- 0
• y = 271 rad/s^
a) (0 = ? sau
(I) =
o
t = 4s
b) at = ? an = ? tai
(0
0^0
+ Y-t
A. 12,5 rad/s; 2.5 rad/s'.
B. 20 rad/s; 2,5 rad/s^
C.IO rad/s; 22 rad/s^
A. 10 rad/s; 12 rad/s"".
C a u 11. Mpt banh xe eo ban kinh I m quay nhanh dan deu trong 4 s to'c dp goc
tang tCf 20 rad/s len 30 rad/s. Gia to'c goe eiia banh xe v^ gia to'c hir(Jng tarn
ciia 1 diem tren vanh banh xe sau 2s la
= 0 + 271.4
A. 2 rad/ s'^; 400 mJs\. 2,5 rad/ s^; 625 m / s l
C. 4 rad/s^ 300 m / s l
w = 87t (rad/s)
t = 4s
D. 5 rad/ s^; 196 m/s^
C a u 12. Mpt banh xe C