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Rolling Coin Spins During One Outside Circuit

The moving center travels a circle with radius equal to the sum of the two coin radii. Dividing that path length by the moving coin circumference gives two self-axis spins for equal coins. This assumes outside rolling without slipping.

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

Example in initial displayed units: Diameter of the fixed coin 20, Diameter of the rotating coin 20 gives Self-axis spins per outside circuit 2.

self-axis spins = 1 + fixed diameter / moving diameter

Worked example

Enter these known values and leave the other values blank.

Diameter of the fixed coin
20 mm
Diameter of the rotating coin
20 mm
Self-axis spins per outside circuit
2

Assumptions and limitations

  • The moving circular coin rolls without slipping around the outside of a fixed circular coin and completes one circuit. The result counts rotations about its own axis relative to a stationary frame, not orbital circuits. Positive fixed diameter requires more than one self-axis spin. Inside rolling is a different model.
  • Use compatible units and enough independent values. Clear unknowns before solving backward. Original reference drawings are schematic and do not scale to entered values.

Common questions

Why do equal coins spin twice during one outside circuit?

The moving center travels a circle with radius equal to the sum of the two coin radii. Dividing that path length by the moving coin circumference gives two self-axis spins for equal coins. This assumes outside rolling without slipping.

References

Require more than one self-axis spin for outside no-slip rolling with two positive coin diameters.

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