Imagine i have a particle in the xy plane rotating in a circle around the z-axis at a constant angular velocity. The angular momentum is r cross p which would give me a constant value at all times, there is no change and it's conserved. However if I was to move the rotating particle higher up and then draw my r vector out from the origin the direction of angular momentum would constantly change as the particle rotated. So at one chosen origin the angular momentum is constant, but at another chosen origin it changes? If this is true, wouldn't that imply there is a torque and also that there's no torque?