#### Striking the Rod in the Middle

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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Striking One of the Masses
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Circular Cross-Section