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0593_C07_fm Page 237 Monday, May 6, 2002 2:42 PM

Inertia, Second Moment Vectors, Moments and Products of Inertia, Inertia Dyadics 237

P7.5.10: A thin uniform circular disk D with mass m and radius r is mounted on a shaft
S with a small misalignment, measured by the angle θ as represented in Figure P7.5.10.
Knowing that the moments of inertia of D for its center for directions parallel to and
2
2
perpendicular to its axis are mr /2 and mr /4, respectively, and that the corresponding
products of inertia of D for its axis and diameter directions are zero (see Appendix II),
find the moment of inertia of D for its center G for the shaft axis direction x: I DG .
xx

D
G S
X

FIGURE P7.5.10
A misaligned circular disk on a shaft S.

Section 7.6 Parallel Axis Theorems

P7.6.1: Consider the homogeneous rectangular parallepiped (block) B shown in Figure
P7.6.1. From Appendix II, we see that the moments of inertia of B for the mass center G
for the X, Y, and Z directions are:

(
(
(
2
2
2
2
2
2
b
c
c
I BG = 1 m b + ), I BG = 1 m a + ), I BG = 1 m a + )
xx yy zz
12 12 12
where m is the mass of B and a, b and c are the dimensions as shown in Figure P7.6.1. Let
B have the following properties:
m = 12kg, a = 2m, b = 4m, c = 3m
Determine the moments of inertia of B relative to G for the directions of X, Y, and Z.
Z
Q
c
G
O
Y
a
b
FIGURE P7.6.1
A homogeneous rectangular block. X
P7.6.2: Repeat Problem P7.6.1 with B having the following properties:

.
m = 15lb, a = 2 5ft, b = 5ft , c = 3ft
P7.6.3: See Problems P7.6.1 and P7.6.2. For the properties of Problems P7.6.1 and P7.6.2,
find the moments of inertia of B for Q for the direction X, Y, and Z where Q is a vertex
of B with coordinates (a, b, c) as shown in Figure P7.6.1.