# TIL: The momentum of a particle can be non zero with zero velocity.It depends upon the Vector field it is present it.

I've decided to start this trend of writing something that I learn everyday which really is due to misunderstood fundamentals.

It is often misconception in high school physics that momentum $$p = mv$$. But it actually isnt, a generalised definition of momentum comes from the concept of **conjugate momentum** where we see that it is obtained from the action of the system (**Lagrangian Mechanics**). In simpler terms, you see that $$p = mv + qA$$ where $$A$$ is the vector field.

Why is the high school definition wrong? A simple thought experiment which goes by the name Feynmann angular momentum paradox shows you why.

The angular momentum is still conserved, but just that there is some influence of magnetic field of the system on the momentum at the beginning itself. It is **NOT** a mere change of **0 momentum** to some a **non zero** **momentum**.

Where did I learn this? While analysing the action principle in **General R****elativity**! Kudos