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PROBLEM B.14
Determine by direct integration the mass moment of inertia and
the radius of gyration with respect to the x axis of the paraboloid
shown, assuming that it has a uniform density and a mass m.
PROBLEM B.15
A thin rectangular plate of mass m is welded to a vertical shaft AB as
shown. Knowing that the plate forms an angle
with the y axis,
determine by direct integration the mass moment of inertia of the
plate with respect to (a) the y axis, (b) the z axis.
PROBLEM B.15 (Continued)
222
1(4sin)
12
y
Imba
222
1
12
1cos
a
b v btdv
12
222
1(4cos)
12
z
Imba
PROBLEM B.16*
A thin steel wire is bent into the shape shown. Denoting the mass per
unit length of the wire by m, determine by direct integration the mass
moment of inertia of the wire with respect to each of the coordinate
axes.
PROBLEM B.16* (Continued)
Alternative solution:
1/3
aa
2
z
PROBLEM B.17
Shown is the cross section of an idler roller. Determine its
mass moment of inertia and its radius of gyration with respect
to the axis AA. (The specific weight of bronze is 0.310 lb/in
3
;
of aluminum, 0.100 lb/in
3
; and of neoprene, 0.0452 lb/in
3
.)
PROBLEM B.17 (Continued)
22 22
113 31
AA
Now 62
262
1.15960 10 lb ft s 809.09 10 ft
AA
km
AA
PROBLEM B.18
Shown is the cross section of a molded flat-belt
pulley. Determine its mass moment of inertia and its
radius of gyration with respect to the axis AA. (The
density of brass is 8650 kg/m
3
and the density of the
fiber-reinforced polycarbonate used is 1250 kg/m
3
.)
PROBLEM B.18 (Continued)
and 22 22
1[(11.4134)(0.005 0.011 ) (2.8863)(0.011 0.017 )
8
AA
I
92
(208.29 147.92 37.00 443.48) 10 kg m
3
17.4806 10 kg
AA I
or
6.92 mm
AA
k
PROBLEM B.19
The machine part shown is formed by machining a conical
surface into a circular cylinder. For
1
2
,bh
determine the
mass moment of inertia and the radius of gyration of the
machine part with respect to the y axis.
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