Page 180 - Dynamics of Mechanical Systems
P. 180

0593_C05_fm  Page 161  Monday, May 6, 2002  2:15 PM





                       Planar Motion of Rigid Bodies — Methods of Analysis                         161


                       and

                                                    Q
                                                  V =−50  n + 120  n cen sec
                                                            x      y
                       where n  and n  are horizontal and vertical unit vectors as in Figure P5.7.2. Determine
                              x
                                     y
                       (a) the coordinates of the instant center C of B, (b) the angular velocity ω of B, and (c) the
                       velocity of point A of B (in terms of n  and n ), whose coordinates are (30, 10).
                                                        x
                                                               y
                                                               Y

                                                             n  y             Q(25,13)

                                                                      P(13,8)    A(10,30)

                                                                                       B
                       FIGURE P5.7.2                           O
                       A body  B in planar motion with                                     X
                       known velocities of two points.                                n  x


                       Section 5.8 Instant Center of Zero Acceleration
                       P5.8.1: A 2-ft-radius circular disc rolls to the right, with its center O having a speed of 3.5
                       ft/sec, as in Figure P5.8.1. The disc, however, is decelerating so that O has an acceleration
                       to the left of 1.5 ft/sec . Determine the X–Y coordinates of the center at zero acceleration.
                                          2

                                                                         Y


                                                                     2 ft
                                                                        O
                                                                a  = 1.5 ft/sec v  = 3.5 ft/sec
                                                                        2
                                                                O        O
                       FIGURE P5.8.1
                       A rolling but decelerating circular              C               X
                       disc.
   175   176   177   178   179   180   181   182   183   184   185