978-0073398242 Appendix B Solution Manual Part 12

subject Type Homework Help
subject Pages 9
subject Words 1471
subject Authors Brian Self, David Mazurek, E. Johnston, Ferdinand Beer, Phillip Cornwell

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page-pf1
PROBLEM B.61 (Continued)
From the solution to Problem 9.147, we have
32
39.1721 10 lb ft s
x
I

32
77
(7.19488 26.6357 2.48313 6.43210) 10 lb ft s


or
2
0.0427 lb ft s
OL
I

page-pf2
PROBLEM B.62
For the wire figure of Problem 9.146, 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
()0
zx z x
IImzx


page-pf3
PROBLEM B.62 (Continued)
From the solution to Problem 9.146, we have
32
10.3642 10 lb ft s
xz
II

(1.90663 14.03978 0.8
 32
4606 0.55771 0.37181) 10 lb ft s

or
32
16.61 10 lb ft s
OL
I


page-pf4
PROBLEM B.63
For the homogeneous circular cylinder shown, of radius
a
and length
L
,
determine the value of the ratio
a/L
for which the ellipsoid of inertia of
the cylinder is a sphere when computed (
a
) at the centroid of the cylinder,
(
b
) at Point
A
.
page-pf5
PROBLEM B.64
For the rectangular prism shown, determine the values of the
ratios
b
/
a
and
c
/
a
so that the ellipsoid of inertia of the prism is a
sphere when computed (
a
) at Point
A
, (
b
) at Point
B
.
page-pf6
PROBLEM B.64 (Continued)
(b) Using Figure 9.28 and the parallel-axis theorem, we have at Point B
2
22
1()
12
z
Imab


Now observe that symmetry implies
12 12 12
Then 2222
44bcac or 1
b
a
and 2222
4bcab
 or
1
2
c
a

page-pf7
PROBLEM B.65
For the right circular cone of Sample Problem 9.11, determine the
value of the ratio
a/h
for which the ellipsoid of inertia of the cone is a
sphere when computed (
a
) at the apex of the cone, (
b
) at the center of
the base of the cone.
page-pf8
PROBLEM B.66
Given an arbitrary body and three rectangular axes x, y, and z, prove that the mass moment of inertia of
the body with respect to any one of the three axes cannot be larger than the sum of the mass moments of
inertia of the body with respect to the other two axes. That is, prove that the inequality
x
yz
I
II
and
the two similar inequalities are satisfied. Further, prove that 1
2
yx
IIif the body is a homogeneous solid
of revolution, where x is the axis of revolution and y is a transverse axis.
page-pf9
PROBLEM B.67
Consider a cube of mass
m
and side
a
. (
a
) Show that the ellipsoid of inertia at the center of the cube is a
sphere, and use this property to determine the moment of inertia of the cube with respect to one of its
diagonals. (
b
) Show that the ellipsoid of inertia at one of the corners of the cube is an ellipsoid of
revolution, and determine the principal moments of inertia of the cube at that point.
page-pfa
PROBLEM B.67 (Continued)
First note that at corner A
2
2
3
xyz
I
II ma


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