Permalink Submitted by Anonymous on March 17, 2016

The additional rotation occurs because the smaller circle traverses the circumference of the larger circle, in the same way that the moon rotates once every time it orbits the Earth, even though it maintains the same face towards the Earth. Of course, this assumes that the smaller circle moves as well as rotates, and that the larger circle neither moves nor rotates. If the centres of the two circles are fixed and both are free to rotate, as gears, then the answer will be 4, not 5. Furthermore, if your frame of reference is the larger circle and that circle is allowed to both move and rotate, then it is possible to envisage the smaller circle appearing to rotate 4 times without it moving or rotating at all! - Paul Baron

## The additional rotation

The additional rotation occurs because the smaller circle traverses the circumference of the larger circle, in the same way that the moon rotates once every time it orbits the Earth, even though it maintains the same face towards the Earth. Of course, this assumes that the smaller circle moves as well as rotates, and that the larger circle neither moves nor rotates. If the centres of the two circles are fixed and both are free to rotate, as gears, then the answer will be 4, not 5. Furthermore, if your frame of reference is the larger circle and that circle is allowed to both move and rotate, then it is possible to envisage the smaller circle appearing to rotate 4 times without it moving or rotating at all! - Paul Baron