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First, consider
. That is, we apply an
upward unit-force impulse at time 0 in the middle of the rod. The
total momentum delivered in the neighborhood of
and
is
obtained by integrating the applied force density with respect to time
and position:
This unit momentum is transferred to the two masses
. By symmetry,
we have
. We can also refer to
as the
velocity of the center of mass, again obvious by symmetry.
Continuing to refer to Fig.B.5, we have
Thus, after time zero, each mass is traveling upward at speed
, and there is no rotation about the center of mass at
.
The kinetic energy of the system after time zero is
Note that we can also compute
in terms of the total mass
and the velocity of the center of mass
:
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