newtonian mechanics - Force acting on an object?

You have a bar of metal in an environment with no gravity. A force is applied on one end of it. How does it rotate?

There is a non-zero torque on any random point selected on the bar. For example, on point A the torque is $T_A = F*y$, but on point B the torque is $T_B = F*x$. So the torque on any point on the bar except the point where the force is applied, is non-zero. If there is a non-zero torque on one point, the object must rotate around that point. But since there is a non-zero torque on every point, and the object can't rotate around every point, how does it rotate and around what point?

Answer

See here for something about rotation and torque.
As is explained there, the IAOR is defined as the point about which every point is in pure rotational motion i.e. every point has a velocity perpendicular to the position vector to that point from IAOR. This point's position can vary in space and with time and is usually difficult to treat in most problems.
Theoretically, you can find the torque about any point from where you define the rotational variables ($\theta, \omega$) but a particularly useful point is the centre of mass.

Treating the rotation to be about the COM, you eliminate pseudo forces in the COM frame and that allows you to treat that frame as an inertial frame. Therefore, for any arbitrary unconstrained body, motion can be divided into two parts:-

1)The translational motion of the COM ($dv_{com}/dt=a$,$a=F_{net}/m$)
2)Rotation of the body about the COM ($d\omega/dt=\alpha$,$\alpha=\tau_{com}/I_{com}$)

Tell me if you want any more details.