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0593_C07_fm Page 238 Monday, May 6, 2002 2:42 PM
238 Dynamics of Mechanical Systems
P7.6.4: A body B has mass center G with coordinates (1, 3, 2), in meters, in a Cartesian
reference frame as represented in Figure P7.6.4. Let the mass of B be 0.5 kg. Let the inertia
dyadic of B for the origin O have the matrix I BO given by:
ij
9 − .2 634 − 1
I BO = I BO n n I , BO = − .2 634 4 −3 kgm 2
ij i j ij
−1 −3 − 7
where n , n , and n 3 are parallel to the X-, Y-, and Z-axes. Determine the components of
1
2
the inertia dyadic I BQ of B for point Q, where the coordinates of Q are (2, 6, 3), in meters.
ij
Z
n 3
B
Q(2,6,3)
G(1,3,2)
O
Y
n
2
FIGURE P7.6.4
A body B in a Cartesian reference n
frame. X 1
P7.6.5: A thin, rectangular plate P weighs 15 lb. The dimensions of the plate are 20 in. by
10 in. See Figure P7.6.5, and determine the moments of inertia of P relative to corner A
for the X, Y, and Z directions (see Appendix II).
Y
P
A
G
10 in.
FIGURE P7.6.5
A rectangular plate in a Cartesian X
reference frame. O 20 in.
P7.6.6: Repeat Problem P7.6.5 for a plate with a 5-in.-diameter circular hole centered in
the left half of the plate as represented in Figure P7.6.6.
Y
A
G
10 in.
FIGURE 7.6.6
5 in
A rectangular plate with an offset X
circular hole. O 20 in.