chapter 4 sbvl
DESCRIPTION
tlTRANSCRIPT
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https://sites.google.com/site/trangtantrien/
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Chng 4: c Trng Hnh Hc Mt Ct Ngang
1 Gii Thiu
2 Din tch-Mmen Tnh-Trng Tm Ca Hnh Phng
3 Cc Mmen Qun Tnh
4 Cng Thc Chuyn Trc Song Song
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Gii Thiu1
* Kh nng chu lc ca chi tit khng nhng ph thuc vo hnhdng, kch thc mt ct ngang m cn ph thuc vo cch b tr camt ct ngang.
x
y
P
xy
P
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2.1 Din tch ca hnh phng
2 Din tch-Mmen Tnh-Trng Tm Ca Hnh Phng
F
F dF
2.2 Mmen tnh ca hnh phng
- i vi trc Ox: F
x ydFS
- i vi trc Oy: F
y xdFS
x
y
x
y dF
O
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2 Din tch-Mmen Tnh-Trng Tm Ca Hnh Phng
2.2 Mmen tnh ca hnh phng
* Mmen tnh c th m, dng hoc bng khng
0 yx SS
* Mmen tnh ca hnh phng i vi mt trc no bng khng,trc c gi l trc trung tm. Giao im ca hai trc trung tml trng tm hnh phng.
x
y
dF
dF
y
y
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2 Din tch-Mmen Tnh-Trng Tm Ca Hnh Phng
2.2 Mmen tnh ca hnh phng
* Gi C l trng tm hnh phng, cc trc Cx0 v Cy0 l hai trc trungtm
0
0
0
0
0
0
Fy
Fx
dFxS
dFyS
Ta c
0
0
yyyxxx
C
C
x
y
x
y dF
O
0y
0x0x
0y
C
Cx
Cy
FF
CF
CF
x dFydFydFyyydFS 00
FySFyS CxCx .. 0
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2 Din tch-Mmen Tnh-Trng Tm Ca Hnh Phng
2.2 Mmen tnh ca hnh phng
x
y
x
y dF
O
0y
0x0x
0y
C
Cx
Cy
FxSFyS
Cy
Cx
.
.
Nu hnh phng l hnh phc tp
n
iiCy
n
iiCx
FxS
FyS
i
i
1
1
.
.
Trong : ,i iC C
x y Ta trng tm ca hnh th i
iF Din tch ca hnh th i
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2 Din tch-Mmen Tnh-Trng Tm Ca Hnh Phng
2.3 Trng tm ca hnh phng
n
ii
n
iiC
xC
n
ii
n
iiC
yC
F
Fy
FSy
F
Fx
FS
x
i
i
1
1
1
1
x
y
x
y dF
O
0y
0x0x
0y
C
Cx
Cy
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3.1 Mmen qun tnhca hnh phng
3.2 Mmen qun tnh cc ca hnh phng i vi tm O
- i vi trc Ox: F
x dFyJ2
- i vi trc Oy: F
y dFxJ2
3 Cc Mmen Qun Tnh
x
y
x
y dF
O
F
dFJ 2
Ta thy: 222 yx yx JJJ
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3.3 Mmen qun tnh ly tm ca hnhphng i vi h trc xOy
F
xy xydFJ
3 Cc Mmen Qun Tnh
x
y
x
y dF
O
* Mmen qun tnh ly tm c th m, dnghoc bng khng.
* Nu mmen qun tnh ly tm ca hnh phng ivi mt h trc no bng khng, h trc cgi l h trc qun tnh chnh.
* Nu h trc qun tnh chnh i qua trng tm mtct c gi l h trc qun tnh chnh trung tm.
x
y
dF dF
xx
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3.4 Mmen qun tnh ca mt s hnh thng gp
3 Cc Mmen Qun Tnh
* Hnh ch nhtx
y
y
dy
b
h
dF
12
32/
2/
22 bhbdyydFyJh
hFx
3 3
;12 12x ybh hbJ J
x
y
dR
C
* Hnh trn4 4
2 2 4
0
2 0,12 32
R
F
R DJ dF d D
44
44
0,05 ;64
2 0,132
x y
x
DJ J D
DJ J D
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3 Cc Mmen Qun Tnh
* Hnh tam gic
3 3
;12 36Cx xbh bhJ J
b
h
Cx
cxy
dydF
rb r
r
b h yb
hdF b dy
2 /3 32 2
/3
32 2
0
36
12
C
h
xF h
h
xF
b h y bhJ y dF y dyh
b h y bhJ y dF y dyh
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* Bit:
4 Cng Thc Chuyn Trc Song Song
x
y
x
y dF
O
0y
0x0x
0y
A
Ax
Ay
00, yx JJ
* Tm: yx JJ ,
Vi 00 //,// yyxx
Ta c
0
0
yyyxxx
A
A
F
AFF
AF
AF
x dFyydFydFydFyydFyJ 020
220
2 2
00
00
.2.
.2.2
2
yAyAy
xAxAx
SxJFxJ
SyJFyJ
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4 Cng Thc Chuyn Trc Song Song
x
y
x
y dF
O
0y
0x0x
0y
A
Ax
Ay
* Nu A l trng tm mt ct, Ax0 vAy0 l hai trc trung tm ca mt ctngang
000 yx SS
FxJJ
FyJJ
Ayy
Axx
.
.2
2
0
0
Ta c
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* V d 1: Tnh mmen qun tnh ca hnh ch nht i vi cc trc x,y
6122
32
122
43
43
bbbJ
bbbJ
c
c
y
x
Ta c
x
y
b2
bx
y
b2
b
cx
cy
C
42
2
422
322.
2
382.
bbbJJ
bbbJJ
c
c
yy
xx
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* V d 2: Tnh mmen qun tnh ca hnh tam gic i vi cc trc x
36
3bhJcxTa c
1221.
3
32 bhbhhJJcxx
xb
h
b
h Cx
cx
3
3
36
12
cx
x
bhJ
bhJ
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* V d 3: Tnh mmen qun tnh ca hnh tam gic i vi cc trc x, y
12
481222
3
3
3
hbJ
bhhb
J
y
x
x
b
h
y
x
b
2h
y
2h
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* V d 4: Tnh m men qun tnh chnh trung tm ca hnh phng
b b b b
x
y
(1)
(2)
3
4
22 .2
212 12x y
bbbJ J
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* V d 5: Tnh cc mmen qun tnh chnh trung tm ca hnh phng
900
30
30450
450 30
y
x 1 2 3
x x x xJ J J J
1
2 3
3
423
30.90012
76626450.30 900 30 .450.30
12 2 2
x
x
x x
JJ cm
J J
1 2 3
3 34900.30 30.4502 45765
12 12y y y yJ J J J cm
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* V d 6: Xc nh trng tm v tnh cc mmen qun tnh chnh trungtm ca hnh phng
To trng tm ca hnh phng
b
b
8b
7b
b
b
8b
7b
1x
x
(1)
(2)
cy
y
2
2 21
2 2 2
1
0
4 .8 8,5 .7 6,18 7
i
C
C ii
C
ii
x
y Fb b b by b
b bF
3 32 21 2 2 2 4
3 31 2 4
. 8 7 .4 6,1 .8 8,5 6,1 .7 118,85b
12 12
8 . . 729,25
12 12
x x x
y y y
b b b bJ J J b b b b b b
b b b bJ J J b
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* V d 7: Xc nh trng tm v tnh cc mmen qun tnh chnh trungtm ca hnh phng
b
b 7b
15b
b
b7b
15b1x
y
xC
cy
2
12
1
0
3,5 .15 .7 3 .13 .6 8915 .7 13 .6 18
i
C
C ii
C
ii
x
y Fb b b b b by b
b b b bF
To trng tm ca hnh phng
3 32 21 2 4
3 31 2 4
15 . 7 13 . 689 893,5 .15 .7 3 .13 .6 118,917b12 18 12 18
7 . 15 6 . 13870,25
12 12
x x x
y y y
b b b bJ J J b b b b b b b b
b b b bJ J J b
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* V d 8: Xc nh trng tm v tnh cc mmen qun tnh chnh trung tmca hnh phng
50cm
75cm
40cm70cm
50cm
75cm
40cm70cm x
y
3 34
23 34
75.70 12,5.204 2110416,66712 12
70.75 40.12,5 100 12 40.12,5 1901041,66712 36 3 2
x
y
J cm
J cm
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* V d 9: Tnh cc mmen qun tnh chnh trung tm ca hnh phng
53014 14
3609 5 5b b2b
6
6
30
22
6
50cm75cm
40cm
70cm
25cm
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* V d 10: Xc nh trng tm v tnh cc mmen qun tnh chnh trungtm ca hnh phng. Khi tnh b qua cc gc ln. So snh kt qu tnh cvi tra bng thp hnh L70x70x6
70
70
6
6
* V d 11: Tnh cc mmen qun tnh chnh trung tm ca mt ct ngangnh hnh v. Mt ct ngang gm hai thp hnh L70x70x6 ghp li.
70
6
6
70
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* V d 12: Tnh cc mmen qun tnh chnh trung tm ca hnh phng
70 7
40 40 5L
40 40 5L 40 40 5L
40 40 5L
174
6
40 40 5L
184
40 40 5L
40 40 5L
40 40 5L
18I
22I xx
y
y
18I
18I
12
400
xx
y
y
18I