The Rolling Wheel

The cycloid and the tautochrone

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• A cycloid is traced by a point on a rolling wheel.
• One arch is 8 times the radius long.
• It’s also the tautochrone: equal descent times from any start.

Steps

1. A point on a rolling circle
2. Length of an arch
3. Area under the arch
4. The coin rotation paradox
5. The top of the wheel
6. The tautochrone
7. Four beads, one finish