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PROBLEM 9.158
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 I
xy
, I
yz
, and I
zx
of the wire figure.
PROBLEM 9.158 (Continued)
1111 3 5555
()[( ) ]() [( ) ]
zx zx z x zx z x
I
IImzxI Imzx
or 3
2
1
2
zx
I
mR
PROBLEM 9.159
Brass wire with a weight per unit length w is used to form the figure shown.
Determine the mass products of inertia I
xy
, I
yz
, and I
zx
of the wire figure.
PROBLEM 9.159 (Continued)
()
zx z x
I
Imzx
or
3
4(12)
zx w
Ia
g
PROBLEM 9.160
Brass wire with a weight per unit length w is used to form the figure
shown. Determine the mass products of inertia I
xy
, I
yz
, and I
zx
of the wire
figure.
PROBLEM 9.160 (Continued)
()
zx z x
I
Imzx
or 3
1
4
zx w
I
a
g
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PROBLEM 9.161
Complete the derivation of Eqs. (9.47), which express the parallel-axis theorem for mass products of
inertia.
PROBLEM 9.162
For the homogeneous tetrahedron of mass m shown, (a) determine by
direct integration the mass product of inertia I
zx
, (b) deduce I
yz
and I
xy
from
the result obtained in part a.
PROBLEM 9.162 (Continued)
PROBLEM 9.162 (Continued)
