Physics of a Spinning Bowling Ball

[kiranimo]

I'm going to simplify this situation so I can hopefully better understand what is going on. A bowling ball is given a certain initial rotational velocity and a certain initial linear velocity when thrown down a bowling lane. If everything needed to solve this problem is given, such as radius of the ball, coefficient of friction, etc. How far down the lane will the bowling ball begin to break?

What I don't understand is how at one point the ball can be spinning but not rolling side to side, then I'm assuming due to friction, the rotational velocity decreases and then when it reaches a certain speed the ball starts to roll from one side to another (when the ball breaks). Why doesn't it roll at one point and it does later on? How can I model this mathematically?

Hopefully my questions make sense...

 

[LostConjugate]

The faster the ball is spinning the more momentum any particular particle has when it meets a particle of wax on the floor tangent to the direction of spin. The momentum of each particle is so high that almost all of that particle's velocity is transferred to the wax particle. Conservation of energy means that the wax particle will gain nearly 2x the velocity of the ball's particle. This can be seen when a billiard ball meets a ping pong ball. As the momentum is reduced (the spinning slows) the velocity transfer becomes more even between the two particles.

In other words the friction co-efficient is lower if it is kinetic.

Same thing happens with the old hoolahoop trick.

Good lecture on the subject
http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/lecture-8/

 

[kiranimo]

The faster the ball is spinning the more momentum any particular particle has when it meets a particle of wax on the floor tangent to the direction of spin. The momentum of each particle is so high that almost all of that particle's velocity is transferred to the wax particle.
I'm not entirely certain I understand what you're saying, but I believe you're making the point that as the ball is spinning and in contact with the floor, it is losing energy due to the friction. Which makes sense, and explains why the ball's rotational velocity decreases. I have only learned about static and kinetic friction, so maybe there is a part of one of these two that I don't understand yet, but how I see it is the ball is spinning so fast that none of the tiny imperfections in both the ball and floor can catch each other to make the ball start rolling in the direction of the spin. This seems similar to a block sliding on a floor, since the imperfections that contribute to kinetic friction are not catching against each other enough to make the block stop yet. So while the ball is spinning to the right, but not yet moving to the right, is that kinetic friction? But then once the ball is both spinning and moving to the right, is that a different type of friction? It doesn't make sense to be either kinetic or static to me.

 

[rcgldr]

It's possible that the bowling ball never achieves static friction before striking the pins. What may appear to be bowling ball "breaking" is that the sliding (kinetic) friction from the ball spinning causes the path to change because the lateral acceleration remains about the same, but the forward speed decreases causing the path to curve a bit more as the ball slows. The waxing of the lanes also cause the coefficient of kinetic friction to change, perhaps with lower coefficient of kinetic friction on the sides and front part of the lane. In the case of some tournaments, the way the lanes are waxed are changed from event to event to vary what type of throws are "favored" at each event.

The ball may also transition from sliding to rolling, which would result in a path change.

 

[LostConjugate]

It's possible that the bowling ball never achieves static friction before striking the pins. What may appear to be bowling ball "breaking" is that the sliding (kinetic) friction from the ball spinning causes the path to change because the lateral acceleration remains about the same, but the forward speed decreases causing the path to curve a bit more as the ball slows. The waxing of the lanes also cause the coefficient of kinetic friction to change, perhaps with lower coefficient of kinetic friction on the sides and front part of the lane. In the case of some tournaments, the way the lanes are waxed are changed from event to event to vary what type of throws are "favored" at each event.

The ball may also transition from sliding to rolling, which would result in a path change.

Some good points here as well.

@kiran
The ball must be not moving in order for the friction co efficient to be static. I was saying that the amount of kinetic energy makes a difference as well.