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PROBLEM 9.130
Shown is the cross section of an idler roller. Determine its moment of
inertia and its radius of gyration with respect to the axis
.
AA
′
(The
density of bronze is 8580 kg/m
3
; of aluminum, 2770 kg/m
3
; and of
neoprene, 1250 kg/m
3
.)
SOLUTION
First note for the cylindrical ring shown that
( )
()
22
21
44
mV
t
dd
t
π
ρρ
ρ
==
×
−=
−
and, using Figure 9.28, that
11
2
2
AA
Im
m
′
=−
1
84
4
td
d
d
ππ
=×
−
×
1
td d
2121
1
td d d d
+
( )
12
1
8
md
d
=+
Now treat the roller as three concentric rings and, working from the
bronze outward, have
Have
( )
(
)
{
3
8580 kg/m
0.0195 m
0.009 m
0.006 m
4
m
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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, Moment Of Inertia

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