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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.
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