Coin Rotation Paradox Calculator
Find the spins of a disk rolling without slipping once around the outside of a fixed disk.
Formula
Spins relative to the room = (R + r)/r = 1 + R/r.
Fixed radius R: 2 cm · Rolling radius r: 1 cm · Spins per orbit ≈ 1+(2 cm × 0.01 m/cm)÷(1 cm × 0.01 m/cm)
How to use
- Enter the fixed disk radius R.
- Enter the rolling disk radius r.
- Read the spins after one complete orbit.
Examples
- With R = 2 cm and r = 1 cm, one orbit gives 3 spins.
Frequently asked questions
Why is there an extra turn?
The direction of the line joining the centers turns once during the orbit, in addition to the relative rolling rotation.
What if the disks are equal?
The moving disk spins twice after one orbit, measured against a fixed external direction.
Does this cover rolling inside a ring?
No. This formula applies to external rolling with no slip. The spin count need not be an integer.
Sources
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