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

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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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University