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PROBLEM B.56
Determine the mass moment of inertia of the steel fixture of
Problems 9.145 and 9.149 with respect to the axis through
the origin that forms equal angles with the x, y, and z axes.
32
4.0627 10 kg m
xy
yz
I
x
yz
Now 222 2
13 1
xyz x
3
xyzxyyzzx
We have
1[26.4325 31.1726 8.5773
3
OL
I
OL
PROBLEM B.57
The thin bent plate shown is of uniform density and weight W. Determine its
mass moment of inertia with respect to the line joining the origin O and
Point A.
PROBLEM B.57 (Continued)
gg
zx z x
2
()
22222 8
aa
g
gg
Substituting into Equation (9.46)
3
xyzxyyzzx
We have
32 6 4 8 8
36 4
gg g g g g
g
2
g
0
PROBLEM B.58
A piece of sheet steel of thickness t and specific weight
is cut and
bent into the machine component shown. Determine the mass
moment of inertia of the component with respect to the joining the
origin O and Point A.
PROBLEM B.58 (Continued)
12
() ()
yy y
II I
12.00922
g
Now observe that the centroidal products of inertia, ,,
x
yyz
II
and ,
zx
I
of both components are zero
4
23
1.33333
g
ta
g
0.66667
g
0
PROBLEM B.58 (Continued)
Substituting into Eq. (9.46)
222
22
222
OA x x y y z z xy x y yz y z zx z x
II I I I I I
4
(3.15223 5.12635 2.00154 0.88889 4.76106 0.22222)
ta
g
or 4
4.41
OA t
I
a
g
PROBLEM B.59
Determine the mass moment of inertia of the machine
component of Problems 9.136 and 9.155 with respect to
the axis through the origin characterized by the unit vector
(4 8 )/9.
λijk
OL x x y y z z xy x y yz y z zx z x
32
481
175.503 308.629 154.400
999
48 81
14
2(94.0266) 10 kg m
99
or
32
281 10 kg m
OL
I
PROBLEM B.60
For the wire figure of Problem 9.148, determine the mass
moment of inertia of the figure with respect to the axis
through the origin characterized by the unit vector
(3 6 2)/7.
ijk
Then
222 333
()
xy x y
IImxymxymxy
2
(0.0672 kg)(0.6 m)(1.2 m) (0.0672 kg)(1.2 m)(0.6 m)
0.096768 kg m
()0
yz y z
IImyz
444 555
2
()
(0.0672 kg)(0.6 m)(1.2 m) (0.0672 kg)(1.2 m)(0.6 m)
0.096768 kg m
zx z x
IImzxmzxmzx
From the solution to Problem 9.148, we have
2
2
0.32258 kg m
0.41933 kg m
x
yz
I
II
0
0
PROBLEM B.60 (Continued)
Substituting into Eq. (9.46)
222
222
OL x x y y z z xy x y yz y z zx z x
II I I I I I
0
PROBLEM B.61
For the wire figure of Problem 9.147, determine the mass moment of inertia of
the figure with respect to the axis through the origin characterized by the unit
vector
(3 6 2)/7.
ijk
333 444
()
yz y z
IImyzmyzmyz
Now
34 34 4 3
,, 0
yz
mm yy z z I
()or0
zx z x zx
IImzx I
0
