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BY : SEPTIKO AJI FINDING CENTER OF MASS AND CALCULATE OF THE MOMEN INERTIA

Center of mass and momen inertia

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Page 1: Center of mass and momen inertia

BY : SEPTIKO AJI

FINDING CENTER OF MASS AND CALCULATE OF THE MOMEN INERTIA

Page 2: Center of mass and 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

Page 3: Center of mass and momen inertia

HEMISPHERICAL SHELL

rdzdmdAdm

2

adz

zdzZ

rd

rdzz

dm

zdmZ

a

a

cm

cm

21

2

2

0

0

Page 4: Center of mass and momen inertia

SEMICIRCLE

sinazaddmdldm

aZ

ad

adaZ

dm

zdmZ

cm

cm

cm

2

sin

0

0

Page 5: Center of mass and momen inertia

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

Page 6: Center of mass and momen inertia

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

Page 7: Center of mass and momen inertia

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

Page 8: Center of mass and momen inertia

CYLINDRICAL SHELL

222 MadmadmaI

Page 9: Center of mass and momen inertia

CIRCULAR DISC/CYLINDER

zdzdmdAdmzdzdA

2

2

2

42

0

3

0

2

2

21

412

2

2

MaI

aaMI

dzzI

zdzzI

dmzI

a

a

Page 10: Center of mass and momen inertia

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

Page 11: Center of mass and momen inertia

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

Page 12: Center of mass and momen inertia

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

Page 13: Center of mass and momen inertia

BANYAK HAL YANG HARUS DIKERJAKAN DAN PERLU RENUNGAN YANG SANGAT MENDALAM