Long rod rotating on frictionless surface

[Horvath Bela]

If I take a rod of length L and lay it down on a surface with no friction and act upon it with a force F off its center of mass by let's say L/4, there will be a torque on the object and it will start to rotate around its center off mass. My question is why does the object necessarily rotate around its center of mass and not simply around some arbitrary point on its self, since I could write the torque equation for every point on the rod.

 

[berkeman]

If I take a rod of length L and lay it down on a surface with no friction and act upon it with a force F off its center of mass by let's say L/4, there will be a torque on the object and it will start to rotate around its center off mass. My question is why does the object necessarily rotate around its center of mass and not simply around some arbitrary point on its self, since I could write the torque equation for every point on the rod.

While you are applying the force, it won't necessarily rotate about its CM. After you have let go of it, it will do so. What's the difference?