Statement: I understand similar questions have been asked; however, none of them really helps me.
The detailed version of my question is as follows:
Why do unconstrained and unfixed objects always rotate about the lines passing through their CMs when a constant tangential forces are applied to them? I understand that if an object does not rotate about its CM, then its rotation will decay to the rotation about the axis passing through its CM.
I would like to have a mathematical proof since a proof using Reductio ad absurdum has been made by a person from another forum -- he argued that if the axis of rotation is not the centre of mass, then the torque created by the force will cause the centre of mass to accelerate, which is a violation of Newton's laws of motion. Thank you.
Edit: The proof (Appendix 20A) has been found. A big thank you to Farcher.
