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Statics 2e 1499
Problem 10.55
The tapered solid prism shown has density
and rectangular cross section. Use
integration to determine the mass moment of inertia indicated, expressing your
answer in terms of the mass
m
of the prism and parameters such as
a
,
b
, and
h
.
Ix.
Solution
IxDZdIx:(1)
Problem 10.56
The tapered solid prism shown has density
and rectangular cross section. Use
integration to determine the mass moment of inertia indicated, expressing your
answer in terms of the mass
m
of the prism and parameters such as
a
,
b
, and
h
.
Iy.
Problem 10.57
The tapered solid prism shown has density
and rectangular cross section. Use
integration to determine the mass moment of inertia indicated, expressing your
answer in terms of the mass
m
of the prism and parameters such as
a
,
b
, and
h
.
I´.
Problem 10.58
The Table of Properties of Solids appearing on the inside back cover of this book shows the mass moments
of inertia for a uniform sphere and hemisphere are both
I´D2mr2=5
. If a sphere and hemisphere have
the same radius and density, does this mean their mass moments of inertia I´are the same? Explain.
Problem 10.59
In Example 10.8 on p. 600, the mass moment of inertia of a hemisphere about its axis of revolution was
found to be
2mr2=5
. Show that this result is between those for a cylinder and cone, both having radius
r
and length
r
(the mass moments of inertia for these are given in the Table of Properties of Solids on the
inside back cover of this book). Discuss why this result is expected.
Problem 10.60
The solid hemisphere is constructed of materials with densities
0
and
0=2
as
shown.
(a)
Fully set up the integrals, including limits of integration, that will yield
the mass moment of inertia about the xaxis.
(b)
Evaluate the integrals obtained in Part (a) using computer software such
as Mathematica, Maple, etc.
Problem 10.61
The solid hemisphere is constructed of materials with densities
0
and
0=2
as
shown.
(a)
Fully set up the integrals, including limits of integration, that will yield
the mass moment of inertia about the yaxis.
(b)
Evaluate the integrals obtained in Part (a) using computer software such
as Mathematica, Maple, etc.
Problem 10.62
For the solid of revolution shown, determine the mass moment of inertia
about the
x
axis. The material has specific weight
D0:409 lb=in:3
. Report
your answer using slugs and inches.
Problem 10.63
A solid of revolution is produced by revolving the area shown 360
ı
around the
y
axis.
Use integration to determine the mass moment of inertia about the axis of revolution
assuming the solid has uniform density. Express your answer in terms of the mass
m
of the object.
Problem 10.64
A solid of revolution is produced by revolving the area shown 360
ı
around the
y
axis.
Use integration to determine the mass moment of inertia about the axis of revolution
assuming the solid has uniform density. Express your answer in terms of the mass
m
of the object.
Problem 10.65
The solid 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 10.66
The solid 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 yaxis.
(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 10.67
A thin-walled hollow cone has uniform density with thickness
t1
at the left-hand
end and t2at the right-hand end.
(a)
If the cone’s thickness is uniform with
t1Dt2Dt0
, 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 10.68
A thin-walled hollow cone has uniform density with thickness
t1
at the left-hand
end and t2at the right-hand end.
(a)
If the cone’s thickness varies linearly from
t1D2t0
at the left-hand end
to
t2Dt0
at the right-hand end, fully set up the integral, including limits
of integration, that will yield the mass moment of inertia about the
x
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.
Problem 10.69
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 xaxis.
