Seeming violation of angular momentum conservation

Question

Consider a rod being having a small length hanging over the edge of a table. Suppose an impulsive force is acted on at the tiny portion of length extended over the table then it should produce zero torque at the point where force is applied(*). However, it is still seen that the rod rotates about the point. Why?
How can the angular momentum change without any external torque?

*: Force is efficetevly acting at zero distance from the point we are taking moments about

BowlOfRed · Accepted Answer

Besides the force you push, there are other forces on the rod.  There is gravity, and there is the normal force from the table.
As you push down, gravity does not change, but the normal force from the table changes.  It increases and it shifts toward the edge of the table.  Eventually the force increases to the point that the COM will lift up, and the torque from the normal force is no longer countered by gravity and the rod begins to rotate.

Seeming violation of angular momentum conservation

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