Physics of the Flywheel Launcher

That is a good question. Here is an example (from here):

Consider a bicycle wheel, where the bicycle is traveling with the speed V.

The bottom point of the wheel touches the ground and therefore has zero velocity. If you try to figure out what would be the speed of the top point of the wheel you will see that it has to be 2*V.

With launcher we have the same situation. One side of the ball touches the static ramp and is stationary. In order to speed up the ball to V you will need to make the other side of the ball to have velocity 2*V.

However the bigger problem with single flywheel is rolling resistance. You will end up loosing some energy to deform the ball and momentum transfer will be less efficient.