I would be interested in knowing what physics books you get your information from. You can never store more energy than you input. This is laughable, check your laws of motion. Since these laws and logic seem to have been replaced with a need to be "right", I respectfully submit this as my last post.
The physics is in pretty much any high school text book. The particular fact about the cue ball moving faster than than the cue stick is explained by Bob Byrne in his "Advanced Technique" book.
Two objects colliding with unequal masses is a standard situation in physics that is often used to introduce changes of frames of reference to simplify the problem. Here is an example of how that works. Suppose we want to know what would happen to a stationary tennis ball when struck by a freight train. Imagine some kids have dangled a ball from a bridge in the path of a train. How fast will the tennis ball be going after being hit by the 60MPH train (the bottoms of the flanges of which are moving backwards)?
The answer, ignoring any loss of bounce in the ball and wind resistance, is that the ball will be going 120MPH right after the collision.
How to see this easily? First imagine a stationary train parked on a siding. The kids have made a tennis-ball cannon that can shoot the ball at 60 MPH. They shoot it at the front of the train.The train's speed doesn't change perceptibly -- it is unmoved by the tennis ball -- but the ball bounces off at 60MPH in the other direction, more or less. I hope this result is comfortable for everyone. If not, please try throwing a tennis ball at a heavy object like a freight train or a concrete wall. It really does bounce off.
Now, in the case of the moving train, we simply "change frames of reference" and get on the moving train with the engineer. To us, it looks like the dangling tennis ball is coming at us at 60 MPH. After the collision, the ball bounces away from us at 60 MPH relative to us on the train, more or less. That means that the ball is moving 120 MPH relative to the ground.
The point of this discussion is to show that if a heavy object hits a stationary light object, the light object will be moving faster than the heavy object was. The case of the train and the tennis ball was extreme. For objects of closer weights, the change is not so large.
When a cue stick hits a cue ball, it slows to 50% of its initial speed, and the cue ball leaves at 150% of the initial stick speed, similar to the tennis ball being struck by the train. (Actually, because the tip is not perfectly springy, the number will be closer to 130%).
Then, after parting the mass somewhat, the CB proceeds forward with what is left of the rotational momentum.
