A wheel is placed inside another that has exactly twice its radius. If the inner wheel rolls around once without slipping, how many revolutions has it completed?

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## Solution

The inner wheel rotates around its axis one time.

If one looks at the proportion of the circumferences of the circles, one would expect an answer of 2 counterclockwise. However, you have to subtract 1 because the inner wheel goes round the circle once clockwise.

This problem is well known for a wheel (or coin) rolling on the outside of another. The inside configuration is known as the Tusi couple. What’s interesting is that a point on the circumference of the inner wheel moves in a straight line along a diameter of the outer wheel.