I'm having a hard time trying to understand the conservation of angular momentum. Let's assume the following 2D experiment:
At the start of the experiment both rectangles have no angular momentum, but if the upper moves downwards and their corners hit, they will both start to rotate clockwise (red arrows). In my apparently flawed understanding of angular momentum this would mean that the total angular momentum has increased because two clockwise rotations would be added together and a clockwise rotation would have to be countered by a counterclockwise rotation. The math would work out if we would subtract the second rectangles angular momentum from the first's but I don't understand why and if we had more than two bodies which rotations would we have to add and which to subtract?