The accepted answer said that objects in general do not rotate around their center of mass.
I'm confused about this. I've seen derivations that conclude that the sum of forces acting on a system of masses (like a rigid body) divided by the mass of the system equals the acceleration of the center of mass of the object.
Now let's apply a set of forces on an object. The object is free, that is, it is not bound by any kind of hinge. We have concluded that the center of mass of the object will start accelerating. Since the forces are constant, the acceleration of the center of mass is constant. But if the acceleration is constant, the acceleration should be linear and the COM should be moving in a straight line, and therefore not be rotating. But the accepted answer on the question disagrees. So what am I getting wrong?
And if this unbound object does not rotate around its COM, around what point does it rotate? If the have an object floating in space (like a straight rod), and we apply a force to one of its ends, how do we determine the point around which it starts rotating?
I also found this website.
It states that a thrown knife rotates around its center of mass. This seems to agree with my reasoning: When flying in the air, all parts of the knife experience gravitational force. These forces summed divided by the mass of the knife gives the acceleration of the COM of the knife. From projectile motion we know thrown object fly in parabolic paths. Therefore, the COM of the knife flies in a parabolic path, and so it cannot be in rotation.
So could somebody shed some light on this matter? When do objects tend to rotate around their centers of mass?