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PROBLEM 9.152
Determine the products of inertia
,
xy
I
,
yz
I
and
zx
I
of the steel machine
element shown. (The specific weight of steel is
3
0.284 lb/in . )
SOLUTION
First compute the mass of each component
mV
g
γ
=
Then
()
3
2
1
2
0.284 lb/in
5 in.
4.5 in.
0.9 in.
0.1786 lb s /ft
32.2 ft/s
m
=×
×
=
⋅
3
2
2
2
0.284 lb/in
3 in.
2.5 in.
0.8 in.
0.05292 lb s /ft
32.2 ft/s
m
×
=
⋅
3
2
2
3
2
0.284 lb/in
0.6 in.
0.5 in.
0.0049875 lb s /ft
32.2 ft/s
m
π
=
⋅
Now observe that the centroidal products of inertia,
,,
x
yy
z
I
I
′
′′
′
and
,
zx
I
′ ′
of each component are zero because of
symmetry. Now
uv
u v
I
Im
u
v
=+
so that
body
.
uv
I
mu v
=Σ
2
,lb s /ft
m
⋅
,ft
x
y
z
2
lb ft s
mx y
⋅
⋅
2
lb ft s
my z
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This note was uploaded on 07/11/2011 for the course EGM 2511 taught by Professor Jenkins during the Spring '08 term at University of Florida.
 Spring '08
 Jenkins
 Statics

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