Bankor

Meet Bankor, a rolling ball who lets the tilted track do the turning.

To go around a curve, anything moving needs a net force pointing toward the centre of the circle. On a flat track a rolling ball has nothing pushing it inward, so it carries straight on. On a banked track the surface is tilted, so the normal force from the track leans toward the centre and supplies that inward push.

When the normal force alone does the turning, there is one ideal speed for each banking angle. Balancing the forces gives tan θ = v²/(rg). For a curve of radius 100 m taken at 20 m/s, tan θ = 400 / (100 × 9.81) ≈ 0.41, so the ideal bank angle is about 22°.

Go slower than the ideal speed and Bankor drifts down the slope. Go faster and he rides up and out over the edge.

That is why racetracks, bobsled runs and motorway ramps are tilted, and why the steepest banks are built where things go fastest.