Coin Roll Simulation
Roll one coin all the way around an identical coin and it turns twice, not once. This simulation demonstrates the classic coin rotation paradox and lets you vary the radius ratio to find the general rule.
How to use this simulation
- Change the radius of the rolling and fixed coins
- Roll around the outside or the inside
- Mark a point on the rim to trace its path
What to look for
- Equal coins give two full rotations, not one
- Rolling inside the fixed circle gives R/r − 1 rotations instead
- The marked point traces a cardioid when the coins are equal
The physics behind it
A coin of radius r rolling without slipping around a fixed coin of radius R makes R/r + 1 rotations relative to the ground. The extra turn comes from the fact that the centre of the rolling coin itself travels a full circle. Relative to the line joining the centres it does rotate only R/r times — the paradox is a question of frame of reference.