Fuji Electric FRENIC-AQUA series, User Manual

Page: 103 / 751

3-8
Table 3.1 Moment of Inertia of Various Rotating Bodies
Mass: W (kg) Mass: W (kg)
Shape
Moment of inertia:
J (kg·m
2
)
Shape
Moment of inertia:
J (kg·m
2
)
ρ −
π
=
• • •
L ) D D (
4
W
2
2
2
1
ρ =
• • •
L B A W
Hollow cylinder
) D D ( W
8
1
J
2
2
2
1
+ =
• •
ρ
π
=
• •
3
D
6
W
Sphere
2
D W
10
1
J
• •
=
) A L ( W
12
1
J
2 2
a
+ =
• •
) A
4
1
L ( W
12
1
J
2 2
b
• • •
+ =
) L
3
1
L L L ( W J
2
0
2
0 c
• • •
+ + ≈
ρ
π
=
• • •
L D
12
W
2
ρ
π
=
• • •
L D
4
W
2
Cone
2
D W
40
3
J
• •
=
ρ =
• • •
L B A W
Rectangular prism
) B A ( W
12
1
J
2 2
+ =
• •
) D
4
3
L ( W
12
1
J
2 2
a
• • •
+ =
) D
16
3
L ( W
3
1
J
2 2
b
• • •
+ =
) L
3
1
L L L ( W J
2
0
2
0 c
• • •
+ + ≈
ρ =
• • • •
L B A
3
1
W
ρ =
• • • •
L B A
3
1
W
Square cone (Pyramid,
rectangular base)
) B A ( W
20
1
J
2 2
+ =
• •
ρ =
• • •
L A
4
3
W
2
) A
4
1
L ( W
10
1
J
2 2
b
• • •
+ =
) L
5
3
L L
2
3
L ( W J
2
0
2
0 c
• • • •
+ + ≈
Triangular prism
2
A W
3
1
J
• •
= ρ
π
=
• • •
L D
12
W
2
ρ =
• • •
L A
12
3
W
2
Tetrahedron with an
equilateral triangular
base
2
A W
5
1
J
• •
=
) D
8
3
L ( W
10
1
J
2 2
b
• • •
+ =
) L
5
3
L L
2
3
L ( W J
2
0
2
0 c
• • • •
+ + ≈
Main metal density (at 20
°
C)
ρ
(kg/m
3
) Iron: 7860, Copper: 8940, Aluminum: 2700