Consider a situation like this: a massless ring is kept fixed at rest on a horizontal plane. A massless thin string attached at its one end to a point on the circumference of the ring while its other point is attached to a certain point mass.then my a certain mechanism we impart a certain initial velocity to the point mass (the velocity direction is at all instants perpendicular to the string).The string wraps around the ring until the mass hits the ring.
I am not looking for a solution to this problem as i just made it up to clarify the situation physically.
My question is:-
would it be right to apply conservation of angular momentum in this case(there being no external forces)? Seeing as the Instantaneous centre of rotation changes with time?
More generally, does angular momentum conservation laws hold even if the centre of rotation changes?