978-0073398242 Appendix B Solution Manual Part 2

subject Type Homework Help
subject Pages 9
subject Words 1346
subject Authors Brian Self, David Mazurek, E. Johnston, Ferdinand Beer, Phillip Cornwell

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page-pf1
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.
page-pf2
PROBLEM B.8 (Continued)
From the solution to Problem 9.193:
2
,mass
5
18
x
Ima
2
22
54


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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.
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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.
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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.
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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.
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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
page-pf9
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.
page-pfa
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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