I prefer to think of this problem as a coin rotating around a spot; i.e. the 'big' circle has a radius of zero.

It's easy to see that the 'small' circle will rotate once, even though it's travelled a circumference on 0cm.

Then, if the 'big' circle has any additional circumference (in this case 4cm), the 'small' circle will rotate that once, then travel the additional circumference.

I hope this makes sense!