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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
,mass
5
18
x
Ima
2
22
54
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.
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.
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.
PROBLEM B.11 (Continued)
(b) For the element: 2
22
1
4
yy
dI dI x dm
rdm xdm
22
21227 108
a
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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.
PROBLEM B.12 (Continued)
Now
2
4
3
434
11
12 2
y
ab dy
hh
h
Now 1
6
m abh
4
234
25 3 2 5
hh
h
or
22
1()
10
x
I
mb h
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.
PROBLEM B.13 (Continued)
Now
,mass ,mass
22
22
1()
12
12
yBB DD
dI dI dI
xz x z dy
hh
4
22
1()1
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