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PROBLEM B.45
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.
PROBLEM B.45 (Continued)
Finally,
()
xy x y
IImxy
32
8.0365 10 kg m
32
or 8.04 10 kg m
xy
I
()
(0 0) [0 (0.93775 kg)(0.082761m)(0.195 m)]
1 0.15 0.39
(0.45923 kg)(0.39 m)(0.15 m) (0.45923 kg) m m
yz y z
IImyz
32
12.8950 10 kg m
32
or 12.90 10 kg m
yz
I
32
()
[0 (2.14305 kg)(0.175 m)(0.195 m)] (0 0)
3
zx z x
IImzx
PROBLEM B.46
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.
PROBLEM B.46 (Continued)
While
3333
1
() 12
yz
Imbh
EL ELuv u v
Where
22
EL EL
11
22
uuv v au
22 22
ST 0
22 4 4 4
ST ST
0
1
2
11 1 1 1
22 4 8 2
a
a
tau u ta ma
Thus
2
222
1
() 2
zx
Ima
because of a 90° rotation of the coordinate axes. Also
2
444
1
() 2
yz
Ima
2
32
11
(0.23844 kg)(0.225 m)(0.135 m) (0.22473 kg)(0.135 m)
12 2
yz
2
()()() [( ) ][( ) ]
11
(0.23844 kg)(0.225 m)(0.135 m) (0.62424 kg)(0.225 m)
IIII ImzxImzx
or
32
4.43 10 kg m
zx
I
0 0
PROBLEM B.47
The figure shown is formed of 1.5-mm-diameter
aluminum wire. Knowing that the density of aluminum is
2800 kg/m
3
, determine the mass products of inertia Ixy, Iyz,
and Izx of the wire figure.
PROBLEM B.47 (Continued)
1 3
1.23700 10
0.18 0.125 0 6
27.8325 10
0 0
2 3
0.89064 10
0.09 0.25 0 6
20.0394 10
0 0
3 3
1.48440 10
0 0.25 0.15 0 6
55.6650 10
0
4 3
1.23700 10
0 0.125 0.3 0 6
46.3875 10
0
Then
()
xy x y
IImxy
or 62
47.9 10 kg m
xy
I
zx z x
zx
0
0
PROBLEM B.48
Thin aluminum wire of uniform diameter is used to form the figure shown.
Denoting by m the mass per unit length of the wire, determine the mass
products of inertia Ixy, Iyz, and Izxof the wire figure.
PROBLEM B.48 (Continued)
0
22
Thus, 3
11
1
() 2
yz
I
mR
11
22
because of 90 rotations of the coordinate axes. Finally,
zx zx z x zx z x
or 3
2
1
2
zx
I
mR
0 0
PROBLEM B.49
Brass wire with a weight per unit length w is used to form the figure shown.
Determine the mass products of inertia Ixy, Iyz, and Izx of the wire figure.
PROBLEM B.49 (Continued)
3(1 5 )
0
