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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.

Leo Liu
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  • Lots of answers here:https://physics.stackexchange.com/questions/311606/why-a-body-always-rotate-about-its-center-of-mass/311616#311616 – mike stone Jun 24 '20 at 20:14
  • @mikestone 1. No tangential forces are applied, so the situation is slightly different. 2. No math. – Leo Liu Jun 24 '20 at 20:22

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