Hello,
it has been some time already since I had physics on school or university and so I'd welcome a help with solving this situation:

Have an object with a center of mass T
A gravitational force Fg is constant in whole the object, so its point of action is in T
Point P on the surface of the object is a point of action of outer force F

I am thinking now about the translation and rotation effects these forces will have on the object? What direction will have the final translation force and where would be the center of rotation?
I tried to combine the forces somehow, but everything I tried looks like an absolute nonsense.

Well, the force will be vertical in that case, you just have to sum the two vectors. The other thing that comes into play is the torque. Look into that and "rigid body physics", "rigid body dynamics" too.

Thanks. The simple sum of the forces for translation came on my mind but I thought the position of F origin would couse some horizontal translation too. That made me puzzled.
Thanks again for quick response