Why does a free body rotate about centre of mass when torque is applied?

Asked Sep 20 '23 at 11:05

Active Sep 20 '23 at 11:29

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Suppose a body is kept in space and is not fixed about any point (i.e, not hinged). If an external force is applied, the body rotates about the centre of mass.

I saw one answer pointing out that moment of inertia is minimum about the centre of mass, and thus motion around any other axis is unstable. Is this view correct? And if true, how do we go about proving that it indeed is the most stable?

edited Sep 20 '23 at 11:29

Qmechanic

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asked Sep 20 '23 at 11:05

Eisenstein

Does this answer your question? Why does a body always rotate about its center of mass? – John Rennie Sep 20 '23 at 11:10
I am afraid the formulation of the problem is mistaken. When arbitrary force is applied on a body, it is not merely rotating about its CM. Actually, CM is moving according to Newtons $\vec{F}=m\vec{a}$. – John Sep 20 '23 at 11:10

Why does a free body rotate about centre of mass when torque is applied?

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