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                              ~- (Ro+rb) x 8F, = dd ~-- Ri x 8m Vi                 (4.313)
       Ro x ~: 8F: + ~- rl x 8Fr =  ddt L- (Ro + -o,)  x 8m Vt                  (4.314)
                                d
                                                          = ddt E Ro x 8m V: + ddt ~- }:b X 8m Vi.
            (4.315)
                                                                -
                                         = Ro x z~8m V: + Ro x E8mv:
                                                          +ddt y-)  b X 8m V:                       (4.316)
We -note that
                         Ro x ~_ 8m Vi = Ro x X) 8m (Ro + 77lb)                             (4.317)
                                               = Ro x >] 8mRo + R,
         N      Rox~8mrb  (4.318)
                                                        -. O
                                                                                        N                                                                                                    (4.3 19)
     The first term on the right-hand side ofEq. (4.318) vanishes because Ro x Ro  = 0
and the second term vanishes because the body is assumed to be rigid. Furthermore,
using Eq. (4.294), we obtain Ro x 8F1 - Ro x 8m V/.
    With these simplifications, Eq. (4.316) reduces to
E7bx8F,=/t~rbx8m.V:    (4.320) ..
Thus, according to Eq. (4.320), the statement Gr.=dllt/dt of Eq. (4.311) is
　
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