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APPENDIX B
PROBLEM B.1
A thin plate of mass m is cut in the shape of an equilateral triangle of side a.
Determine the mass moment of inertia of the plate with respect to (a) the
centroidal axes AA and BB, (b) the centroidal axis CC that is perpendicular
to the plate.
SOLUTION
13 3
12
PROBLEM B.2
A ring with a mass m is cut from a thin uniform plate. Determine the
mass moment of inertia of the ring with respect to (a) the axis AA, (b) the
centroidal axis CC that is perpendicular to the plane of the ring.
CC AA BB AA
12
2
CC
PROBLEM B.3
A thin, semielliptical plate has a mass m. Determine the mass moment of
inertia of the plate with respect to (a) the centroidal axis BB, (b) the
centroidal axis CC that is perpendicular to the plate.
4
PROBLEM B.4
The parabolic spandrel shown was cut from a thin, uniform plate.
Denoting the mass of the spandrel by m, determine its mass
moment of inertia with respect to (a) the axis BB, (b) the axis
DD that is perpendicular to the spandrel. (Hint: See Sample
Problem 9.3.)
,area 11 ,area
4
AA
PROBLEM B.4 (Continued)
2
1
710
70
PROBLEM B.5
A piece of thin, uniform sheet metal is cut to form the machine
component shown. Denoting the mass of the component by m,
determine its mass moment of inertia with respect to (a) the x axis,
(b) the y axis.
,mass 2
2
48
3
31
72
z
a
ma
PROBLEM B.5 (Continued)
Finally, ,mass ,mass ,mass
yxz
III
y
PROBLEM B.6
A piece of thin, uniform sheet metal is cut to form the machine
component shown. Denoting the mass of the component by m,
determine its mass moment of inertia with respect to (a) the axis
AA, (b) the axis BB, where the AA and BB axes are parallel to the
x axis and lie in a plane parallel to and at a distance a above the xz
plane.
SOLUTION
PROBLEM B.7
A thin plate of mass m has the trapezoidal shape shown. Determine
the mass moment of inertia of the plate with respect to (a) the x
axis, (b) the y axis.
SOLUTION
18 ma
,mass
y
PROBLEM B.8
A thin plate of mass m has the trapezoidal shape shown. Determine
the mass moment of inertia of the plate with respect to (a) the
centroidal axis CC that is perpendicular to the plate, (b) the axis
AA that is parallel to the x axis and is located at a distance 1.5a
from the plate.
PROBLEM B.8 (Continued)
From the solution to Problem 9.193:
2
5
,mass
18 9
AA
or
2.33
AA
Ima
PROBLEM B.9
Determine by direct integration the mass moment of inertia
with respect to the z axis of the right circular cylinder shown,
assuming that it has a uniform density and a mass m.
12
z
PROBLEM B.10
The area shown is revolved about the x axis to form a
homogeneous solid of revolution of mass m. Using direct
integration, express the mass moment of inertia of the solid
with respect to the x axis in terms of m and h.
SOLUTION
2
hh
10 7 70
x
or
1.329
x
Imh
PROBLEM B.11
The area shown is revolved about the x axis to form a
homogeneous solid of revolution of mass m. Determine by
direct integration the mass moment of inertia of the solid with
respect to (a) the x axis, (b) the y axis. Express your answers in
terms of m and the dimensions of the solid.
3
33
44 4
22 2
223
111126
63 627
1 2 13 13
63 9 54
xx
aa
xx
ah ah
aa
ah h mh
or
0.241
x
Imh
PROBLEM B.11 (Continued)
y
PROBLEM B.12
Determine by direct integration the mass moment of inertia with
respect to the x axis of the tetrahedron shown, assuming that it has
a uniform density and a mass m.
SOLUTION
ay
PROBLEM B.12 (Continued)
10
x
PROBLEM B.13
Determine by direct integration the mass moment of inertia with
respect to the y axis of the tetrahedron shown, assuming that it has
a uniform density and a mass m.
SOLUTION
ay
,mass ,mass
12 12
BB DD
PROBLEM B.13 (Continued)
10
y
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