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.
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.
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 $~\hat e_\tau$
