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 ).

Sun Feb 23 15:54:50 PST 1997