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Working with center of percussion - A baseball bat problem

A baseball bat rests on a frictionless, horizontal surface.
The bat a length of 0.900m, a mass of 0.800 kg, and its center of mass is 0.600m from the handle end of the bat.
ThE MOMENT OF INERTIA OF THE BAT ABOUT ITS CENTER OF MASS IS 0.0530kg*m^2
The impact applies an impulse :

J= integral from t2 to t1 of F*dt.

at a point a distance x from the handle end of the bat.
What must x be so that the handle end od the bat remains at rest as the bat begins to move?

ThE MOMENT OF INERTIA OF THE BAT ABOUT ITS CENTER OF MASS IS 0.0530kg*m^2

Solution Preview

If an impulsive force is applied at an arbitrary point on a suspended object, there will, in general, be a reaction force at the suspension point. If the distance L from the suspension point to the point of impact is chosen carefully, no such reaction force will occur. This point of impact is called the center of percussion.

An impulsive force F applied at right angles to a free beam at a distance x from the center of mass will cause the center of ...

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