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PROBLEM 9.163
The homogeneous circular cone shown has a mass m.
Determine the mass moment of inertia of the cone with respect
to the line joining the origin O and Point A.
PROBLEM 9.164
The homogeneous circular cylinder shown has a mass m. Determine the mass
moment of inertia of the cylinder with respect to the line joining the origin O and
Point A that is located on the perimeter of the top surface of the cylinder.
222
OA x x y y z z
II I I
22
222
22 22
11
(3 4 )
212
ha
ma m a h
ha ha
or
22
222
1103
12
OA
ha
Ima
ha
Note: For Point A located at an arbitrary point on the perimeter of the top surface, OA
is given by
22
1(cos sin )
OA
aha
ha
ij k
which results in the same expression for
.
OA
I
PROBLEM 9.165
Shown is the machine element of Problem 9.141. Determine its
mass moment of inertia with respect to the line joining the
origin O and Point A.
PROBLEM 9.165 (Continued)
222
222
OA x x y y z z xy x y yz y z zx z x
II I I I I I
22
32
32
23
(13.98800) (20.55783)
13 13
22
2(0.39460) 10 kg m
13 13
(4.30400 14.23234 0.36425) 10 kg m
32
or 18.17 10 kg m
OA
I
PROBLEM 9.166
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.
SOLUTION
PROBLEM 9.167
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 9.167 (Continued)
111 2 2 2
()
zx z x
I
Imzxmzxmzx
2
113
()
22222 8
Wa a Wa W
aa
g
gg
Substituting into Equation (9.46)
222
222
OA x x y y z z xy x y yz y z zx z x
II I I I I I
Noting that
222 1
3
xyzxyyzzx
We have
22 2 2 2 2
2
11 5 1 1 3
2
32 6 4 8 8
114 3
2
36 4
OA WWW WWW
Iaaaaaa
gg g g g g
Wa
g
2
5
or 18
OA W
I
a
g
PROBLEM 9.168
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 9.168 (Continued)
12
22 22
2
222 2
() ()
14(2)4()
12
116 4 ()
yy y
II I
tt
aa aa
gg
tta
PROBLEM 9.168 (Continued)
