A previously discussed problem, but what the heck.
Imagine two circles one of radius "r" and the other "2r" . Let the bigger circle be stationary and the smaller circle moves on the bigger circle with out " SLIP". In one complete revolution of the smaller circle on the larger one :
How many rotations does the smaller circle go through around its center in completing the revolution?
To complete a rotation, the small circle will have to go around the length that equals it's circumference = 2 * pi * r
Number of rotations made by small circle = Length travelled / circumference of smaller circle = 2 * pi * (2r) / 2 * pi * r = 2