# How does the distance between two rails effect the speed of a steel ball bearing?

As part of a school science project, I constructed a Rollercoaster using Polyurethane tubing as rails for a steel ball bearing to rest on. In the process of building the coaster I observed that sections of track where the rails were closer together would cause the ball bearing to roll faster, as the cost of stability as the ball bearing was more likely to fall off the track. Increasing the distance between the rails would cause the ball bearing to roll slower, but increased the odds that the bearing stayed on the track.

What caused this phenomena?

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This is a rather nice conceptual puzzler, and I intend to add it to my bag of teaching tricks. – dmckee Oct 3 '11 at 17:15

A good way to get intuition as to why this is happening is to look at how fast the balls are spinning. With the tracks very close together the ball spins slowly. With the tracks almost as far apart as the diameter of the ball, the ball has to spin madly to move even a small distance. The energy has to come from somewhere, as Kris pointed out.

But you can also just intuitively see that the farther apart tracks will cause balls to roll slowly because of the cross-sectional circumference of the part of the ball that is touching the track. It's like a gear assembly where some really tiny gear is spinning crazily trying to turn a giant gear and the big one spins slowly.

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I think the cross-sectional circumference comment is the key to understanding what is going on. An interesting follow up is to ask how the toys work that have two inclined rods mounted on a board and hinged at the low end; the goal is to move the ball up hill by judiciously seperating the rails. – AdamRedwine Oct 3 '11 at 17:07

To move along the ramp at a certain speed, the ball needs to spin faster if the rails are more apart.

Basically you are trading potential energy (from gravity) for kinetic energy. But the kinetic energy has to split between linear velocity and angular velocity. With the rails more apart, the angular kinetic energy takes a larger piece of the pie.

So, the ball would accelerate slower. When you gradually narrow the rails halfway, your ball would get a speed up as a part of the spinning energy is traded for extra linear velocity.

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Reading carfully reveals that Dylan asked about ball bearings, not plain balls! – Georg Oct 3 '11 at 10:17
@Georg, A strange feature of English is that the rollers from inside ball bearing assemblies are usually (and confusingly) referred to as "ball bearings" instead of the more logical "bearing balls". You add "assembly" or just drop saying "ball" if you have to be certain of differentiating and the context does not make it clean. In this case I think the OP means the steal spheres. – dmckee Oct 3 '11 at 13:49
I'd prefer Dylan would confess this. BTW "steal speres" are stolen? :=) – Georg Oct 3 '11 at 17:37
The assignment was to build a "Marble Rollercoaster". I just happened to use a steel ball bearing, call it what you will :) – Dylan Baker Oct 4 '11 at 5:43