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Suppose a ring is given to us with no hinge as such. Now a bullet comes and strikes the ring and gets embedded in the ring.

The ring will now have linear momentum and some rotation going on. Okay, the question is about the axis of rotation. Intuitively it seems that the rotation will be about the COM of the system. But is there any formal justification to this as to why does it rotate about the COM and not any other point. Everything of course is frictionless.

Here is a picture for reference...everything of course is frictionless

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If the rotation happened around another point, then the COM would be moving around that point in a circle.

This would mean that the COM was accelerating - without any external force and that's not possible.

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    $\begingroup$ ohhhhhhh popped my mind open. Thanks ! $\endgroup$ Sep 4, 2021 at 22:31
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    $\begingroup$ @ chittaranjan rout Glad it helped $\endgroup$ Sep 4, 2021 at 22:33
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    $\begingroup$ This is super intuitive! I never thought of it that way. Awesome answer! $\endgroup$ Sep 5, 2021 at 13:32

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