Let's define the angular momentum for a point object similar to the way we did it for the torque
If this is really analogous, the first thing we should check is if the analogy to holds:
Here we used the fact that the cross product of a vector with itself is zero.
So it does seem like this definition of makes sense from a mathematical point of view. If we have many forces acting on the system, it is straightforward to extend this so that in general
For a continuous object let's look at the two dimensional case considered above where we showed that , where points perpendicular to the rotating object. Since I is constant in time this says that
(note that if all velocities are zero so ).