What colordrops wrote at least suggest that he thinks that circular motion and angular momentum are not fundamental but can be expressed or understood in terms of linear motion and linear momentum. As far as I can tell today this is not true, they are independent concepts and one can not be fully understood in terms of the other, neither by looking at circular motion as piecewise linear motion nor by looking at linear motion as circular motion about a point infinitely far away. I only brought up spin because it makes the point pretty clear - or maybe not - that angular momentum is a fundamental concept that can not be recast in other terms, especially it is not just the sum of many linear momenta.