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3-26
CHAPTER 3 Installation
5) When the object's center line is offset from the rotation center.
The equation for the moment of inertia, when the center of the cylinder is
offset by the distance "x" from the rotation center as shown in Fig. 3-16, is
given as follows.
D
h
J=
ρπD h
32g
WD
8g
=
4
2
... (Eq. 3.5)
x
+
ρπD hx
4g
2
+
Wx
g
2
Center line
Rotation center
2
I=
ρπD h
32
4
+
ρπD hx
4
22
mD
8
=
2
mx
2
+
ρ : Density (kg/m
3
, kg/cm
3
)
g : Gravitational acceleration (cm/sec
2
)
m : Mass of cylinder (kg)
W : Weight of cylinder (kgf)
(kgfcmsec
2
)
(kgm
2
)
Fig. 3-16
In the same manner, the moment of inertia of a cylinder as shown in Fig. 3-17
is given by
W
4g
=
... (Eq. 3.6)
D
4
h
3
(
22
+
)
h
D
x
Cneter line
J=
ρπ D h
16g
+
2
D
4
h
3
(
22
+
)
ρπ D h x
4g
22
+
Wx
g
2
I=
ρπ D h
16
+
2
D
4
h
3
(
22
+
)
ρπ D h x
4
22
m
4
=
D
4
h
3
(
22
+
)
+
mx
2
(kgfcmsec
2
)
(kgm
2
)
Fig. 3-17
In the same manner, the moment of inertia of a prism as shown in Fig. 3-18 is
given by
J=
ρabc(a + b )
12g
W(a + b )
12g
=
2
2
... (Eq. 3.7)
2
2
+
ρabcx
g
Wx
g
+
2
2
a
c
b
x
Center line
I=
ρabc(a + b )
12
22
+ ρabcx
2
=
m(a +b )
12
22
+ mx
2
m : Mass of prism (kg)
W : Weight of prism (kgf)
(kgfcmsec
2
)
(kgm
2
)
Fig. 3-18