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Problem 10.86
An object is constructed of a brass rod and aluminum cylinder having densities
of
8500 kg=m3
and
2700 kg=m3
, respectively. The brass rod fills the hole in the
aluminum cylinder. Determine the mass moment of inertia of the object about
the yaxis.
Problem 10.87
The cam shown consists of a circular cylinder
A
with a circular hole to reduce
its moment of inertia and a circular shaft
BC
about which it rotates. If the cam
is made of cast iron with
7200 kg=m3
density, determine the mass moment of
inertia about the ´axis.
2.0:7238 kg/.40 mm/2C.0:7238 kg/.25 mm/2
C1
Problem 10.88
A bracket is constructed of a thin semicircular plate of uniform thickness having
0:05 lb=in:2
specific weight and a thick rectangular plate of uniform thickness
having
0:25 lb=in:3
specific weight. The bracket is symmetric about the
x´
plane. Determine the mass moment of inertia of the object about the axis
indicated. Report your answer using slugs and inches.xaxis.
4m2.3 in:/2C.4 in:/2m2
C1
4m3.0:6 in:/2C.4 in:/2m3;(5)
Problem 10.89
A bracket is constructed of a thin semicircular plate of uniform thickness having
0:05 lb=in:2
specific weight and a thick rectangular plate of uniform thickness
having
0:25 lb=in:3
specific weight. The bracket is symmetric about the
x´
plane. Determine the mass moment of inertia of the object about the axis
indicated. Report your answer using slugs and inches.yaxis.
Cm2.3 in:/21
416
92C(4
3 .3 in:/ C0:8 in:2
C.4 in:/2)m2
Problem 10.90
A bracket is constructed of a thin semicircular plate of uniform thickness having
0:05 lb=in:2
specific weight and a thick rectangular plate of uniform thickness
having
0:25 lb=in:3
specific weight. The bracket is symmetric about the
x´
plane. Determine the mass moment of inertia of the object about the axis
indicated. Report your answer using slugs and inches.´axis.
Cm2.3 in:/21
216
92C4
3 .3 in:/ C0:8 in:2
m2
Problem 10.91
An object with
6lb
weight consists of a cylinder and hemisphere of the same
material. Determine the mass moment of inertia of the object about the axis
indicated. Report your answer using slugs and inches. xaxis.
2m1.3 in:/2C2
5m2.3 in:/2:(7)
Substituting for m1and m2, we obtain
12 in:
Problem 10.92
An object with
6lb
weight consists of a cylinder and hemisphere of the same
material. Determine the mass moment of inertia of the object about the axis
indicated. Report your answer using slugs and inches. yaxis.
4.3 in:/2C1
12.5 in:/2C.2:5 in:/2m1
C83
m2:(7)
Problem 10.93
The object shown is made of uniform plastic and weighs
2:34 lb
. Determine
the mass moment of inertia of the object about the axis indicated. Report your
answer using slugs and feet. xaxis.
Problem 10.94
The object shown is made of uniform plastic and weighs
2:34 lb
. Determine
the mass moment of inertia of the object about the axis indicated. Report your
answer using slugs and feet. yaxis.
Problem 10.95
The object shown is made of uniform plastic and weighs
2:34 lb
. Determine
the mass moment of inertia of the object about the axis indicated. Report your
answer using slugs and feet. ´axis.
Problem 10.96
A semicircular area has outside radius
ro
and a concentric hole with inside radius
ri. Determine the polar moment of inertia of the area about point O.
Problem 10.97
(a)
Fully set up the integral including limits of integration that will give the area
moment of inertia about the yaxis.
(b) Evaluate the integral in Part (a).
Problem 10.98
(a)
Fully set up the integral including limits of integration that will give the
area moment of inertia about the yaxis.
(b) Evaluate the integral in Part (a).
Problem 10.99
Determine the constants
c1
,
c2
, and
c3
so the curves pass through the points
shown.
(a)
Fully set up the integral including limits of integration that will give the
area moment of inertia about the xaxis.
(b) Evaluate the integral in Part (a).
Problem 10.100
Determine the constants
c1
,
c2
, and
c3
so the curves pass through the points
shown.
(a)
Fully set up the integral including limits of integration that will give the
area moment of inertia about the yaxis.
(b) Evaluate the integral in Part (a).
0
(6)
1554 Solutions Manual
Problem 10.101
(a)
Fully set up the integral including limits of integration that will give the area
moment of inertia about the xaxis.
(b) Evaluate the integral in Part (a).
Solution
Thus, there are two solutions (a common error is to overlook the negative solution), and these provide
ry
Problem 10.102
(a)
Fully set up the integral including limits of integration that will give the area
moment of inertia about the yaxis.
(b) Evaluate the integral in Part (a).
Problem 10.103
Determine the area moments of inertia Ixand Iy.
12.0:5 in:/.6 in:/3C.3 in:/2.0:5 in:/.6 in:/
Problem 10.104
Determine the area moments of inertia Ixand Iy.
12.40 mm/.10 mm/3C.65 mm/2.40 mm/.10 mm/
C1
