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
So
(note that if 
all velocities are zero so 
).