How does the angular momentum of the rod (not the rod-clay system) change as the clay rod is at rest. A piece of clay collides with the edge of it and sticks, so they rotate together counterclockwise around the frictionless axle at the other edge. How does the angular momentum of the rod (not the rod-clay system) change as the clay collides?

The angular momentum increases.

Explanation:

Thinking process:

Lets take an example of an angular momentum given by the system with  the following equation:

This then equates to:

As we can see, there is an increase in the momentum

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