Hi Question 1 i was wondering if there is any method to find the point from which the angular momentum is a conserved quantity. let me e.g. choose the case of a planet moving in an orbit around the sun. In this case, the angular momentum measured from the center of mass as the point of reference is conserved. But if i choose a different point, that is not exactly on the line connecting the planet and the sun, then the angular momentum is varying with time. so how do i found out how to choose this point, if the system is more complex? Question 2 if F is a conservative force field, then the energy is conserved. is the converse, the energy is conserved, therefore we have a conservative force field also true?
To be more precise: the sun and the planet each orbit their common center of mass. But it is still conserved. You mean you want to find a reference frame in which a particular bodies angular momentum is a constant? Is it not always the center of mass for gravitating systems? Kinetic energy is conserved in an elastic collision: is the collision an example of a conservative force field?
That's up to you :) Both - I hope. It can be hard to tell if a statement followed by a question mark is an actual question or a rhetorical question. All the questions in post #2 can be safely treated as actual questions. I am posing them as a way to help you clarify your thinking and so find the answers you seek.