Question

A pin is connected perpendicular to the center of a circular disk as shown. A little push will make it roll over a grey circle. How many turns does it take to come back to its original position? 

Hint:

When dealing with rotational systems, consider both the rotational path and the orientation of the object to determine the total number of rotations.

Answer 1

1. The pin attached to the disk creates a tilted plane, and as the disk rolls along the grey circle, the center of the disk traces a circular path.
2. Since the disk is tilted, it completes one full rotation for every turn around the grey circle.
3. To return to its original position, the disk must complete 2 rotations, as the pin's orientation must align with its starting position.
Conclusion: It takes 2 turns for the disk to come back to its original position.