Gravity, Gravity center/Changing it?

,

So,
Im making a little game (I just started some weeks ago, although I have worked a bit with c# before) and my character has to avoid obstacles and is much like a flappy bird game but I have a little problem.

I want to make it fall like a Badmington plume. It has to fall on one side, lets say that the left side is heavier so it has to fall on the left side. the hard thing of the plume does Always has to “look” where it is falling. does someone (more experienced) know how to script this?

thank you in forward.

try this