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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 .)
Problem 9.142) for a semicylinder, we have
1
123
3
() () ()
1.36250 10
yy y y
y
II I I
I
PROBLEM B.34 (Continued)
22'
2
yy
IImd
212 12
3
4
2.3470 10
y
I
Now combining all components and substituting for ,
344
490 1.36250 10 9.1837 10 2.3470 10
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
.)
PROBLEM B.35 (Continued)
(b) 123
() () ()
yy y y
II I I
22
12 2 2
32
32
[(13.3973 40.1920) (1.5730 14.7420) (0.0788 6.0229)] 10 kg m
(53.5893 16.3150 6.1017) 10 kg m
22
32
8.5773 10 kg m
32
or 8.58 10 kg m
z
I
To the instructor:
The following formulas for the mass moment of inertia of wires are derived or summarized at this time
12
xyz
2
1(Sample Problem 9.9)
3
yz
II mL
Circle
We have
22
y
Irdmma
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
a
2
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.
PROBLEM B.36 (Continued)
24 35
12345
2
() (), () ()
() () () () ()
yy yy
yy y y y y
II II
II I I I I
2
2[0 (0.6832 10 lb s /ft)(16 in.) ] 12 in.
12 12 in.
32
[(15.2635) 2(1.2146) 2(0.0253 0.6832)] 10 lb ft s
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.
PROBLEM B.37 (Continued)
12 34
1234
2
() (),() ()
() () () ()
yy yy
yy y y y
II II
II I I I
1234
2
32 2
2
() () () ()
14
(6.1112 10 lb s /ft) (18 in.)
zz z z z
II I I I
2
32 2
32
11 ft
[6.8751 20.6253 2(1.4590)] 10 lb ft s
32
30.4184 10 lb ft s
2
or 0.0304 lb ft s
z
I
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.
