Drag the outside circle to roll it around the inside one,
and count how many times it completely rotates. The answer may surprise you!
Use the ratio buttons to change the relative sizes of the circles.
Selecting Drag only prevents the outside circle from rolling, and
may help you discover exactly what is going on.
Choose a ratio:
About the activity
This is an interesting and somewhat counter-intuitive problem that
illustrates important concepts about rotations and gears.
Students will enjoy trying it out with coins.
One possible starting point is the question: if you roll a coin half way around
another coin of the same type, what position will it end in — upside down
or the right way up? Clearly it rolls a distance of half the circumference,
and if this was a straight line distance it is easy to see it would have rotated
one half revolution. Then
imagine dragging the straight line into a circle so that the point the rolling
coin is touching is at the bottom (thus making a circle of the same size as the coin).
This action takes the upside down coin and
makes it the right way up!
Considering the curve described by a point on the outer circle
leads to the Epicycloid and Cardioid curves, which
themselves can open up interesting explorations of locus, polar coordinates,
cyclic curves and even Ptolemaic astronomy and epicycles.