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The reaction force is the object ball moving away after being struck. The cue ball may or may not come away with any energy, but it usually retains a bit. There is a "science" to where to strike the cue ball with the cue to achieve "position" in the game. You already know the zillion different things that a good player can do (must do!) with the cue ball to win a rack, though. The basic answer is that the kinetic energy of the cue ball will be transferred to the object ball in an largely inelastic collision. The object ball will then carry the energy away after the momentum of the cue ball is passed on to it. This is the case for a "straight shot" on the table with no English on the cue ball.

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Q: If an action force is a cue ball hitting a billiard ball then what is the reaction force?
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