Calculating inertia moment
Appendix
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13-2
Calculating inertia moment
Formula of mass and inertia moment
(1) Both centerlines of rotation and gravity are the same:
The following table includes formulas to calculate mass and inertia moment.
m: mass (kg);
Ix
,
Iy
,
Iz
: inertia moments which rotate around
x-
,
y-
,
z-
axes respectively (kg·m
2
)
G: distance from end face of gravity center
ρ
: specific gravity
Unit Length: m; Mass: kg; Inertia moment: kg·m
2
Object form
Mass, inertia,
gravity center
Object form
Mass, inertia,
gravity center
Cylinder
Circular pipe
Slanted cylinder
Ball
Ellipsoidal cylinder
Cone
Rectangular pillar
Square pipe
R
L
z
x
y
ρ
L
R
m
2
π
=
2
R
m
2
1
Ix
=
+
=
3
L
R
m
4
1
Iy
2
2
+
=
3
L
R
m
4
1
Iz
2
2
R
1
L
R
2
z
x
y
R
1
: outer diameter,
R
2
: inner diameter
(
)
ρ
π
L
R
R
m
2
2
2
1
−
=
(
)
+
+
=
3
L
R
R
m
4
1
Iy
2
2
2
2
1
(
)
2
2
2
1
R
R
m
2
1
Ix
+
=
(
)
+
+
=
3
L
R
R
m
4
1
Iz
2
2
2
2
1
B
L
z
x
y
C
ρ
L
BC
m
4
1
=
(
)
2
2
C
B
m
16
1
Ix
+
=
+
=
3
L
4
C
m
4
1
Iy
2
2
+
=
3
L
4
B
m
4
1
Iz
2
2
R
L
z
x
y
G
ρ
π
1
L
R
3
m
2
=
2
R
m
10
3
Ix
=
(
)
2
2
L
4R
m
80
3
Iy
+
=
(
)
2
2
L
4R
m
80
3
Iz
+
=
4
L
G
=
z
x
y
C
B
A
ρ
A
BC
m
=
(
)
2
2
C
B
m
12
1
Ix
+
=
(
)
2
2
A
C
m
12
1
Iy
+
=
(
)
2
2
B
A
m
12
1
Iz
+
=
D
B
A
z
x
y
(
)
ρ
D
-
B
4AD
=
m
(
)
{
}
2
2
D
D
-
B
m
3
1
Ix
+
=
(
)
+
+
=
2
2
2
D
D
-
B
A
m
6
1
Iy
2
(
)
+
+
=
2
2
2
D
D
-
B
A
m
6
1
Iz
2
ρ
L
R
m
2
π
=
(
)
{
}
θ
θ
2
2
2
2
sin
L
cos
1
3R
m
12
1
I
+
+
×
=
θ
R
L
θ
R
ρ
π
3
R
3
4
m
=
2
R
m
5
2
I
=
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Summary of Contents for FHA-Cmini Series
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