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Problem 10.70
A plastic part with
1100 kg=m3
density is produced by revolving the area shown 360
ı
around an axis of revolution. Determine the mass moment of inertia about the axis of
revolution indicated. Express your answer in units of kgcm2.
The axis of revolution is the yaxis.
0
(3)
Noting that the density of the material is
Problem 10.71
The solid hemisphere shown has a cone-shaped cavity and has uniform density.
(a)
Fully set up the integral, including limits of integration, that will yield
the mass moment of inertia about the xaxis.
(b)
Evaluate the integral obtained in Part (a) using computer software such
as Mathematica, Maple, etc. Express your answer in terms of the mass
m
of the object.
Problem 10.72
The solid hemisphere shown has a cone-shaped cavity and has uniform density.
Determine the mass moment of inertia about the
x
axis using composite
shapes. Express your answer in terms of the mass mof the object.
Problem 10.73
The solid hemisphere shown has a cone-shaped cavity and has uniform density.
(a)
Fully set up the integral, including limits of integration, that will yield
the mass moment of inertia about the ´axis.
(b)
Evaluate the integral obtained in Part (a) using computer software such
as Mathematica, Maple, etc. Express your answer in terms of the mass
m
of the object.
0
0
(7)
1524 Solutions Manual
Part (b) The mass mof the object is
mDZdm DZ.dm1dm2/D
R
Z
R2x2R2
41x
R2dx: (8)
Problem 10.74
The solid hemisphere shown has a cone-shaped cavity and has uniform density.
Determine the mass moment of inertia about the
´
axis using composite
shapes. Express your answer in terms of the mass mof the object.
Problem 10.75
A throwing toy is molded of uniform foam. It consists of an oblong-shaped
portion, a cylindrical portion, and four rectangular fins. The density of the
oblong and cylindrical shapes is
100 kg=m3
, and each of the fins have
1:8
103kg mass.
(a)
Fully set up the integral, including limits of integration, that will yield the
mass moment of inertia about the xaxis for the oblong-shaped portion.
(b)
Evaluate the integral obtained in Part (a) using computer software such
as Mathematica, Maple, etc.
(c)
You should find the result of Part (b) to be
79:8 kgmm2
. Using this value,
determine the total mass moment of inertia about the xaxis for the toy.
2mR2D1
2 hx1x
200 mmi2
200 mmi2
(2)
200 mm
Z
1
2.107kg=mm3/.10 mm/4.100 mm/D0:157 kg-mm2:(5)
12.1:8103kg/.30 mm/2C.25 mm/2.1:8103kg/
D4.1:26 kg-mm2/D5:04 kg-mm2:(6)
Problem 10.76
Approximate the connecting rod in Example 10.11 on p. 604 by a uniform slender rod. Take the length
of this rod to be
0:8 ft
and the mass to be the same as that for the connecting rod. Determine the mass
moment of inertia of this rod about its end, and compare to the value for
IO´
found for the connecting rod
in Example 10.11.
Problem 10.77
A uniform rectangular prism with mass
m
is shown. Beginning with the
appropriate mass moment of inertia given in the Table of Properties of Solids
on the inside back cover of this book, use the parallel axis theorem to determine
the mass moment of inertia of the prism about the axis indicated. The xaxis.
Problem 10.78
A uniform rectangular prism with mass
m
is shown. Beginning with the
appropriate mass moment of inertia given in the Table of Properties of Solids
on the inside back cover of this book, use the parallel axis theorem to determine
the mass moment of inertia of the prism about the axis indicated. The yaxis.
Problem 10.79
A uniform rectangular prism with mass
m
is shown. Beginning with the
appropriate mass moment of inertia given in the Table of Properties of Solids
on the inside back cover of this book, use the parallel axis theorem to determine
the mass moment of inertia of the prism about the axis indicated. The ´axis.
Problem 10.80
A handwheel for a machine has
0:8 kg
mass and center of gravity at point
G
.
When the handwheel is supported at point
O
and is allowed to oscillate as a
pendulum,
1:12
s is required for one full cycle of motion. Determine the mass
moment of inertia about the axis perpendicular to the figure and passing through
point B.Hint: See the helpful information margin note on p. 604.
Problem 10.81
A sector gear for a machine has
0:355 lb
weight and center of gravity at point
G
. When the sector gear is supported at point
O
and is allowed to oscillate as
a pendulum,
0:379
s is required for one full cycle of motion. Determine the
mass moment of inertia about the axis perpendicular to the figure and passing
through point A.Hint: See the helpful information margin note on p. 604.
Problem 10.82
The plate shown has uniform thickness and is made of material with specific
weight
0:7 lb=in:2
. Determine the mass moment of inertia about the axis per-
pendicular to the plate and passing through point A.
2.0:1 in:/2:(4)
Problem 10.83
The antenna shown is constructed of identical small-diameter uniform rods,
each having
0:25 kg=m
mass. Determine the mass moment of inertia of the
antenna about the
(a) xaxis.
(b) yaxis.
(c) ´axis.
12.0:5 kg/.2 m/2)IxD0:500 kgm2:(1)
Part (b)
For
Iy
, there are equal contributions from rods 1 and 2, and equal contributions from rods 3 and 4.
Using the parallel axis theorem,
Problem 10.84
An object is constructed by welding together three small-diameter uniform
identical rods, each having quarter-circular shape and
0:5 lb
weight. Determine
the mass moment of inertia of the object about the xaxis.
Solution
We use the three composite shapes shown at the right. The mass of each rod is
1538 Solutions Manual
Problem 10.85
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 xaxis.
2m1.0:020 m/2C1
2m2.0:050 m/2C1
2m3.0:020 m/2:(4)
