okay, i realize that the angular momentum of a moving point mass could be looked at about any point, and that angular momentum is conserved as long as no torque is acted on that point mass. but, something i don't understand is how, then, the angular velocity could increase if the moment of inertia decreases. Here me out: We have a string moving a point mass on a horizontal table at a constant speed in a radius of R1. The angular momentum of the point mass about the center of the circle is L1. Now, we pull the spring in, decreasing the distance between the point mass and the center to R2. Technically, since the force always acted parallel/antiparallel to the radial vector from the center to the point mass, no torque was done on the point mass about the center, and angular momentum is conserved... But we decreased the distance between them, and therefore the moment of inertia of the point mass about the center. Hence, the angular momentum of the point mass about the center increased... But how is this possible if there was no torque done on the point mass about the center and therefore no angular acceleration?