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Consider a free body, not hinged about any point. If a force is applied to one end of the body, the body has a net nonzero torque about many points in space. About which will it rotate? Am I wrong in thinking that it will rotate at all?

Note that I am not asking about a couple, but a single force.

I asked a similar question a few days before, but it got closed, with links not at all answering my question.

Eisenstein
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2 Answers2

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The body will rotate about the centre of mass. The body will also undergo translation. If the force is applied at the centre of mass, the body will undergo pure translation.

Mechanic
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  • Why would it rotate about the C.O.M? Can you please provide some more detail? – Eisenstein Sep 23 '23 at 05:18
  • @Eisenstein because the moment of inertia about the centre of mass is minimum – Mechanic Sep 23 '23 at 05:20
  • Yes, I too read about that in a similar question. But why does minimum moment of inertia ensure maximum stability? – Eisenstein Sep 23 '23 at 05:23
  • Im not sure what you mean by stability here. But all processes tend to happen through the path of least resistance. Minimum moment of inertia implies a minimum resistance to rotation. – Mechanic Sep 23 '23 at 05:26
  • "But all processes tend to happen through the path of least resistance" Can you provide some sources to further read up on this? – Eisenstein Sep 23 '23 at 05:30
  • this is more of a explanation used to satisfy a layperson. There are other ways to look at the problem you posted. Here are some related questions http://physics.stackexchange.com/q/53465/2451, http://physics.stackexchange.com/q/81029/2451 – Mechanic Sep 23 '23 at 05:51
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enter image description here

the torque $~\vec\tau~$ is

$$\vec\tau=\vec{r}_{Ao}\times \vec F=r\,F\,\underbrace{(\hat e_{Ao}\times \hat e_F)}_{\hat e_\tau}$$

where A is arbitrary rigid body point

thus the rotation of the rigid is at point A about the axis $~\hat e_\tau$

Eli
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