Airplane on a treadmill - Variant Thought Experiment
This thought experiment is in a way related to the (in)famous airplane on a treadmill problem.
If you take a ball and place it on a treadmill, will the ball:
- Move backwards relative to the ground at the same speed as the treadmill (as if placing any other non-circular object on the treadmill)?
- Roll in place without moving relative to the ground (the speed of the treadmill is converted directly into rolling motion of the ball)?
- Exhibit some other behavior such as rolling while also moving backwards?
For this problem assume that there is no slippage between the treadmill and the ball (sufficient friction to make full contact at all times), and assume that the ball has mass.
I know the answer is not #1. I am not sure if the answer is #2 or #3. If the answer is #3, what factors affect the movement of the ball? Is it the mass of the ball, the speed or acceleration of the treadmill, and/or other factors?