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BY : SEPTIKO AJI
FINDING CENTER OF MASS AND CALCULATE OF THE MOMEN INERTIA
SOLID HEMISPHERE
a
a
cm
cm
cm
dzza
dzzazZ
dzr
dzrzZ
dm
zdmZ
dzrdm
dVdm
0
22
0
22
2
2
2
)(
)(
adzza
dzzzaZ a
a
cm 83
)(0
22
0
32
HEMISPHERICAL SHELL
rdzdmdAdm
2
adz
zdzZ
rd
rdzz
dm
zdmZ
a
a
cm
cm
21
2
2
0
0
SEMICIRCLE
sinazaddmdldm
aZ
ad
adaZ
dm
zdmZ
cm
cm
cm
2
sin
0
0
SEMICIRCULAR LAMINA
rz
drrddAdmdrrddA
sin
drrd
drrdz
dm
zdmZcm
0 0
0 0a
a
rdrd
rdrdz
0 0
0 0
sin
a
a
rdrd
rdrdr
0
2
0
3
2131sin
da
da
a
34
THIN RODMoment Inertia thin rod for an axis perpendicular to the rod at one end
dxaMdm
dxdm
2
3
0
2
2
3131
MaI
aaMI
dxaMxI
dmxIa
THIN RODMoment Inertia thin rod for an axis is taken at the center of the rod
dxaMdm
dxdm
2
3
21
0
2
2
121
)21(
312
2
MaI
aaMI
dxaMxI
dmxI
a
CYLINDRICAL SHELL
222 MadmadmaI
CIRCULAR DISC/CYLINDER
zdzdmdAdmzdzdA
2
2
2
42
0
3
0
2
2
21
412
2
2
MaI
aaMI
dzzI
zdzzI
dmzI
a
a
SPHERE
dzra
Mdm
dzrdm
dVdm
2
3
2
34
2
5553
0
42243
0
43
0
2
3
2
2
52
)51
32(
43
)2(43
43
34
MaI
aaaaMI
dzzzaaaMI
dzraMI
dzra
MrI
dmrI
a
a
a
SPHERICAL SHELL
adraMdm
adrdmjadi
adrdAdAdm
sin24
sin2
sin2
2
dmrI 2
adMa sin2
sin)( 2
dadl
daM 32 )(sin
2
0
32 sin2
daM
34
22aM
2
32Ma
PLEASE, FIND CENTRE OF MASS AND MOMEN INERTIA
Please find center of mass and moment inertia this body with density of field is σ= 2-x
GOOD LUCK
BANYAK HAL YANG HARUS DIKERJAKAN DAN PERLU RENUNGAN YANG SANGAT MENDALAM