I'm a bit confused about angular vs linear momentum conservation, plus the relationship to centripetal force. Below is my attempt to convey the confusion.
1. Consider a uniform disc (e.g., a CD disc) rotating at a constant angular speed on an axis through its center. With no external TORQUE, the angular momentum is conserved -- and hence it will continue to rotate forever (ignoring any friction etc).
Above, I think the total linear momentum is zero (as each point on the disk is offset by a diametrically opposite point of mass). And, thus linear momentum is conserved.
Now -- where is the centripetal force? I.e., what is keeping the each point in a circular motion. I presume this is subsumed in the rigidity of the disk, or is coming from an external point of contact (likely from the axle around which it is rotating).
2. Now, let's say the disk is comprised of just one little point of mass while the rest of the disk is massless. Then, there is certainly linear momentum as well as angular momentum. Is my understanding correct that (i) Linear momentum is not conserved, due to centripetal force from somewhere, (ii) Angular momentum is still conserved, since the centripetal force (being radial) contributes to zero torque?