Calculating the rotational force from a linear force

Question

I don't know what the problem is called formally (that's why I didn't find it by searching) and I am happy to be informed of another thread which is answered.

When a force is exerted on an object not tangential to its centre of mass, the force will result in linear motion and rotational motion (assuming we speak of an object not moving before..)

Now I wonder how to calculate the amount of torque and linear force.

Example: An impulse of 5N is excerted at 310° (Clockwise) to a circle of radius 1m.

Answer 1

When you apply a force that is not in line with the center of mass of the object:

1. the center of mass will accelerate as though the force is applied there
2. the object will experience a torque $\vec{\Gamma} = \vec{r}\times \vec{F}$, where $\vec{r}$ is the vector from the center of mass to the point where the force acts.

This second point can be put another way - the torque is the product of the force and the "distance of closest approach" of the line of action of the force and the center of mass: