Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
PROBLEM B.34
Determine the mass moment of inertia of the steel machine
element shown with respect to the yaxis. (The density of
steel is
3
490 lb/ft .)
SOLUTION
PROBLEM B.34 (Continued)
2
IImd
y
PROBLEM B.35
Determine the mass moment of inertia of the steel fixture
shown with respect to (a) the x axis, (b) the y axis, (c) the
z axis. (The density of steel is 7850 kg/m
3
.)
SOLUTION
PROBLEM B.35 (Continued)
z
Copyright © McGraw-Hill Education. Permission required for reproduction or display.
To the instructor:
The following formulas for the mass moment of inertia of wires are derived or summarized at this time
for use in the solutions of Problems 9.146 through 9.148.
Slender Rod
2
1
0 (Figure 9.28)
12
xyz
IIImL
2
1(Sample Problem 9.9)
3
yz
II mL
Circle
We have
22
y
Irdmma
Now
yxz
III
And symmetry implies
xz
II
2
1
2
xz
II ma
Semicircle
Following the above arguments for a circle, We have
22
1
2
xz y
II ma Ima
Using the parallel-axis theorem
2
2
zz
a
IImx x
or
2
2
14
2
z
Im a
PROBLEM B.36
Aluminum wire with a weight per unit length of 0.033 lb/ft is used to
form the circle and the straight members of the figure shown.
Determine the mass moment of inertia of the assembly with respect to
each of the coordinate axes.
SOLUTION
32
2345 2
2
32.2 ft/s
8.5857 10 lb s /ft
11 ft
0.033 lb/ft 8 in. 12 in.
32.2 ft/s
0.6832 lb s /ft
mmmm
Using the equations given above and the parallel-axis theorem, we have
12345
2
() () () () ()
xxxxxx
II I I I I
x
PROBLEM B.36 (Continued)
24 35
() (), () ()
yy yy
II II
x
z
z
PROBLEM B.37
The figure shown is formed of 1
8-in.-diameter steel wire. Knowing that the
specific weight of the steel is 490 lb/ft3, determine the mass moment of inertia of
the wire with respect to each of the coordinate axes.
SOLUTION
First compute the mass of each component. We have
x
PROBLEM B.37 (Continued)
12 34
() (),() ()
yy y y
II II
z
PROBLEM B.38
A homogeneous wire with a mass per unit length of 0.056 kg/m is
used to form the figure shown. Determine the mass moment of
inertia of the wire with respect to each of the coordinate axes.
SOLUTION
First compute the mass m of each component. We have
(/)
mmLL
yz
z
PROBLEM B.39
Determine the mass products of inertia I
xy
, I
yz
, and I
zx
of the
steel fixture shown. (The density of steel is 7850 kg/m
3
.)
SOLUTION
3
40.024
0.05 m 0.039814 m
3
y
and then
m, kg
,mx
,my
,mz
2
, kg mmx y
2
, kg mmy z
2
, kg mmz x
1 5.02400 0.04 0.025 0.08
3
5.0240 10
3
10.0480 10
3
16.0768 10
3
3
3
PROBLEM B.39 (Continued)
zx
PROBLEM B.40
Determine the mass products of inertia I
xy
, I
yz
, and I
zx
of the steel machine element shown. (The density of
steel is 7850 kg/m
3
.)
xy
PROBLEM B.41
Determine the mass products of inertia I
xy
, I
yz
, and I
zx
of the cast
aluminum machine component shown. (The specific weight of
aluminum is 0.100 lb/in
3
)
SOLUTION
3
1.1
1.8 in.
2
1.25 in.
y
PROBLEM B.41 (Continued)
and then
2
,lb s /ftm ,ft
x
,fty ,ftz2
,lb ft smx y
2
,lb ft smy z
2
,lb ft smz x
3
zx
PROBLEM B.42
Determine the mass products of inertia I
xy
, I
yz
, and I
zx
of the
cast aluminum machine component shown. (The specific
weight of aluminum is 0.100 lb/in
3
)
PROBLEM B.42 (Continued)
and then
2
,lb s /ftm ,ft
x
,fty,ftz 2
,lb ft smx y
2
,lb ft smy z
2
,lb ft smz x
0.8
zx z x
zx
PROBLEM B.43
A section of sheet steel 2 mm thick is cut and bent into the
machine component shown. Knowing that the density of steel
is 7850 kg/m
3
, determine the mass products of inertia I
xy
, I
yz
,
and I
zx
of the component.
SOLUTION
PROBLEM B.43 (Continued)
1
zx
PROBLEM B.44
A section of sheet steel 2 mm thick is cut and bent into the machine
component shown. Knowing that the density of steel is 7850 kg/m3,
determine the mass products of inertia Ixy, Iyz, and Izx of the
component.
zx
