The pencils will never point in the same direction though. The length of the pencils will get longer or shorter; however, the direction of the pencils will always be opposite (excluding the point where the system is momentarily stopped at which point the pencils do not exist).
So, the answer...
You need to be more methodical in you description. Here, I'll give you a hand:
this means clockwise(<) for the purpose of this analysis and this means anticlockwise(>).
You are on terra firma feet planted. You strike or push a significant
mass (say the moon) that is tethered to the north...
First off you are making no mention of relative sense (which way the Earth and ball are spinning) and this is a glaring omission in your analysis. The Earth and ball will spin in opposite directs. This is a first year physics concept call simple harmonic motion(do a search on this site and...