# 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 Relativity! Kudos

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

1. Since you are doing physics too at CMI, I wanted to ask that have you completed these pre-college books--> HC verma, Irodov and Resnick Halliday? Or are you doing them now? How helpful have they been if they were done earlier?
- Also..only if you desire..could you post the list of books you have or will be using for the course at CMI..?
Thanks for the great blog.

• Actually, I've a drive with all the course notes, books and exam papers for each course at CMI. I'll make it public soon. Maybe in a week's time! I'm sure many will find it useful.Yes, I did those in school which were really fun for high school physics! 🙂

• That would be brilliant and exceedingly helpful/insightful.
Some other questions I desire to ask which are totally not relevant here:-
1) Is there a Gym at CMI ? Could you ever please post some pictures of it ?(I know thats a crazy ask)
2) What do you do if you want specific food to be cooked for you? Do the chefs there make any expections? What is the content of daily foods ?
3) How long away is IMSc from there? And are there shuttles that take you back and forth?