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0593_C07_fm Page 233 Monday, May 6, 2002 2:42 PM

Inertia, Second Moment Vectors, Moments and Products of Inertia, Inertia Dyadics 233

4 kg, respectively. Find the following moments and products of inertia of S relative to the
origin O of the X-, Y-, Z-axis system of Figure P7.3.3: I SO , I SO , I SO , I SO , I SO , and I SO .
xx xy xz yy yz zz

FIGURE P7.3.3
Particles at the vertices of a triangle.
P7.3.4: See Problems P7.2.5, P7.2.8, P7.2.9, and P7.3.3. For the system S shown in Figure
SG
SG
SG
P7.3.3, find the following moments and products of inertia: I , I SG , I , I , I SG ,
xx xy xz yy yz
and I SG where G is the mass center of S, as determined in Problem P7.2.8. (Compare the
zz
magnitudes of these results with those of Problem P7.3.3.)
P7.3.5: See Problems P7.2.9 and P7.3.3. For the system S shown in Figure P7.3.3, find the
following moments and products of inertia: I GO , I GO , I GO I , GO I , GO , and I GO .
xx xy xz yy yz zz
P7.3.6: See Problems P7.2.10, P7.3.3, P7.3.4, and P7.3.5. Show that:
xyz)
I SO = I SG + I GO ( i j = , ,
,
ij ij ij
P7.3.7: See Problems P7.2.5, P7.2.6, P7.2.7, and P7.3.3. As in Problem P7.2.6 let n and n b
a
be the unit vectors:

.
.
.
n = 0 75 n − 0 5 n + 0 433 n
a x y z
and
.
.
n = 0 655 n + 0 756 n
b y z
Find I SO I , SO , and I SO .
aa ab bb

Section 7.4 Inertia Dyadics

P7.4.1: Let vectors a, b, and c be expressed as:

a = 6 n − 3 n + 4 n 3
1
2
b =−5 n + 4 n − 7 n 3
1
2
c = 3 n − n + 9 n 3
1
2