Page 258 - Dynamics of Mechanical Systems

0593_C07_fm Page 239 Monday, May 6, 2002 2:42 PM

Inertia, Second Moment Vectors, Moments and Products of Inertia, Inertia Dyadics 239

Sections 7.7, 7.8, 7.9 Principal Moments of Inertia
P7.7.1: Review again the example of Section 7.8. Repeat the example for an inertia matrix
given by:

32 2 6 
  2
I = 2 32 9 slugft
ij  
 6 9 16  

P7.7.2: A 2 × 4-ft rectangular plate OABC is bonded to a 2-ft-square plate CDEF, forming
a composite body S as in Figure P7.7.2. Let the rectangular plate weigh 40 lb and the
square plate 20 lb.

a. Determine the x, y, z components of the mass center G of S.
b. Find the inertia dyadic of S for G. Express the results in terms of the unit vectors
n , n , and n shown in Figure P7.7.2.
y
z
x
c. Find the principal moments of inertia of S for G.
d. Find the principal unit vectors of S for G. Express the results in terms of n , n ,
x
y
and n .
z
Z E
2 ft
O
2 ft D
A
F 2 ft
X S
C
4 ft
2 ft
FIGURE P7.7.2
A composite plate body. B Y
P7.7.3: Repeat Problem P7.7.2 if the square plate CDEF weighs 30 lb.
P7.7.4: Repeat Problem P7.7.3 if the square plate CDEF weighs 10 lb.