Tabela momentos de inércia Meriam (2)

Prévia do material em texto

Useful Tables   677
TABLE D /4 PROPERTIES OF HOMOGENEOUS SOLIDS
(m = mass of body shown)
MASS MASS MOMENTS
BODY CENTER OF INERTIA
Circular
Cylindrical —
Shell
Half
Cylindrical 
Shell
Circular
Cylinder
—
Semicylinder
Rectangular
Parallelepiped
—
 Iy2 y2 � 
1
3 m(b
2 � l2)
 Iy1 y1 � 
1
12 mb
2 � 13 ml
2
 Izz � 
1
12 m(a
2 � b2)
 Iyy � 
1
12 m(b
2 � l2)
 Ixx � 
1
12 m(a
2 � l2)
 Izz � �12 � 169�2� mr2
 Izz � 
1
2 mr
2
 � 14 mr
2 � 13 ml
2x � 4r
3�
 Ix1x1 � Iy1y1
 � 14 mr
2 � 112 ml
2
 Ixx � Iyy
 Izz � 
1
2 mr
2
 Ix1x1 � 
1
4 mr
2 � 13 ml
2
 Ixx � 
1
4 mr
2 � 112 ml
2
 Izz � �1 � 4�2� mr2
 Izz � mr2
 � 12 mr
2 � 13 ml
2x � 2r�
 Ix1x1 � Iy1 y1
 � 12 mr
2 � 112 ml
2
 Ixx � Iyy
 Izz � mr2
 Ix1x1 � 
1
2 mr
2 � 13 ml
2
 Ixx � 
1
2 mr
2 � 112 ml
2
–
 
–
 
x1
z
x
y
G
l–
2
l–
2
r
x1
z
x
y
G
l–
2
l–
2
r
y1
x1
z
x
G
l–
2
l–
2
r
x1
z
x
y
G
l–
2
l–
2
r
y1
z
x
y
y2
y1
G
l–
2
l–
2
b
a
678  Appendix D  Useful Tables
MASS MASS MOMENTS
BODY CENTER OF INERTIA
Spherical —
Shell
Hemispherical
Shell
Sphere —
Hemisphere
Uniform
Slender Rod
—
 Iy1 y1 � 
1
3 ml
2
 Iyy � 
1
12 ml
2
Iyy � Izz � 
83
320mr
2
x � 3r
8
Ixx � Iyy � Izz � 
2
5mr
2
Izz � 
2
5mr
2
Iyy � Izz � 
5
12mr
2
x � r
2
 Ixx � Iyy � Izz � 
2
3mr
2
Izz � 
2
3mr
2
–
 
–
 
–
 
–
 
r
G
z
z
x
G
r
y
r
G
z
z
x
G
r
y
y
G
l–
2
l–
2
y1
TABLE D /4 PROPERTIES OF HOMOGENEOUS SOLIDS Continued
(m = mass of body shown)
 Useful Tables   679
MASS MASS MOMENTS
BODY CENTER OF INERTIA
Quarter-
Circular Rod
Elliptical
Cylinder
—
Conical
Shell
Half
Conical
Shell
Right-
Circular
Cone
 Iyy � 
3
20 mr
2 � 380 mh
2
 Izz � 
3
10 mr
2
 Iy1y1 � 
3
20 mr
2 � 110 mh
2
z � 3h
4
 Iyy � 
3
20 mr
2 � 35 mh
2
 Izz � �12 � 169�2� mr2
 Izz � 
1
2 mr
2z � 2h
3
 � 14 mr
2 � 16 mh
2
 Ix1x1 � Iy1y1x � 
4r
3�
 � 14 mr
2 � 12 mh
2
 Ixx � Iyy
 Iyy � 
1
4mr
2 � 118mh
2
Izz � 
1
2mr
2
Iy1y1 � 
1
4mr
2 � 16mh
2
z � 2h
3
Iyy � 
1
4mr
2 � 12mh
2
Iy1y1 � 
1
4mb
2 � 13ml
2
Izz � 
1
4m(a
2 � b2)
Iyy � 
1
4mb
2 � 112ml
2
Ixx � 
1
4ma
2 � 112ml
2
Izz � mr2
 � 2r�
Ixx � Iyy � 
1
2mr
2
 x � y
–
 
–
 
–
 
y
_
y
_
x
z
x
r
G
z
x
G
l–
2
l–
2
y1 y
b
a
z
y1
y
G
h
r
y1
yh
z
x
r
x1
G
z
y1
y
G
h
r
TABLE D /4 PROPERTIES OF HOMOGENEOUS SOLIDS Continued
(m = mass of body shown)
680  Appendix D  Useful Tables
MASS MASS MOMENTS
BODY CENTER OF INERTIA
Half Cone
Semiellipsoid
Elliptic
Paraboloid
Rectangular
Tetrahedron
Half Torus
Izz � mR2 � 
3
4ma
2
Ixx � Iyy � 
1
2mR
2 � 58ma
2
x � a
2 � 4R2
2�R
Izz � 
3
80m(a
2 � b2)
Iyy � 
3
80m(a
2 � c2)
z � c
4
Ixx � 
3
80m(b
2 � c2)
y � b
4
Izz � 
1
10m(a
2 � b2)
x � a
4
Iyy � 
1
10m(a
2 � c2)
Ixx � 
1
10m(b
2 � c2)
Iyy � 
1
6m(a
2 � 13c
2)
Ixx � 
1
6m(b
2 � 13c
2)
Izz � 
1
6m(a
2 � b2)z � 2c
3
Iyy � 
1
6ma
2 � 12mc
2
Ixx � 
1
6mb
2 � 12mc
2
Iyy � 
1
5m(a
2 � 1964c
2)
Ixx � 
1
5m(b
2 � 1964c
2)
Izz � 
1
5m(a
2 � b2)z � 3c
8
Iyy � 
1
5m(a
2 � c2)
Ixx � 
1
5m(b
2 � c2)
 Izz � � 310 � 1�2� mr2
 Izz � 
3
10 mr
2
 � 320 mr
2 � 110 mh
2
z � 3h
4
 Ix1x1 � Iy1y1
x � r�
 � 320 mr
2 � 35 mh
2
 Ixx � Iyy
–
 
–
 
–
 
–
 
–
 
–
 
–
 
–
 
y1
yh
z
x
r
x1
G
y
zG
x
a
b
c
x2
—
a2
y2
—
b2
+
z2
—
c2
+ = 1
x
z
G
y
b
a
c
x2
—
a2
y2
—
b2
+
z
–
c
=
x
y
b
a
c
z
G
y
z
x
G
R
Ra
TABLE D /4 PROPERTIES OF HOMOGENEOUS SOLIDS Continued
(m = mass of body shown)
	PART II DYNAMICS OF RIGID BODIES���������������������������������������
	APPENDICES�����������������
	APPENDIX D USEFUL TABLES�������������������������������
	Table D/4 Properties of Homogeneous Solids�������������������������������������������������