Can someone explain the physics of how more axis rotation creates more skid and length before the ball makes a move toward the pocket?
Not really explaining the physics of it, but think of it like this. The more axis rotation you have, the further the ball has to go to get into a roll.
Skid, hook, roll.
In the skid phase, the ball is turning in a different direction than it is moving down the lane (speed is the directing force at this point)
In the hook phase, the balls downlane speed starts to decrease due to friction, and the ball begins to lose axis rotation. It gets closer and closer to losing its axis rotation.
In the roll phase, the forces of speed, rotation, and friction have come together to create the roll phase, in which the ball has lost some of its downlane speed, allowing the rotational friction to overtake it as the main factor in ball direction (reaction).
Now, two demonstrations. Take two bowlers who, due to all other factors, end up with a rolling vector of 40 degrees in relation to the lane surface. Both bowlers balls will reach the roll phase at that point.
HOWEVER, the first bowler has 75 degrees of axis rotation at the start, and the second bowler has 85 degrees of axis rotation.
With 85 degrees of rotation, the second bowlers ball has further to go to reach the 40 degrees. If all other factors are the same, the second bowlers ball will naturally take longer to transition to the 40 degrees, thus causing it to skid slightly further than bowler ones ball will.
Bowler ones ball only has to go from 75 degrees to 40 degrees (75-35=40), while the second bowlers ball has to burn off 10 more degrees of axis rotation before it rolls (85-45=40).
Lots of other factors come into play, but this is the simple explanation (sort of).