I understand the mathematical proof of conservation of momentum. The forces of particles on each other in an isolated group if summed together cancel in pairs. So the vector sum of their momentum stays constant unless an external forces acts on the particles. But, I also have an intuition. A single particle keeps drifting in a direction unless forced to change. And a isolated group of particles too keep drifting as a whole in an average direction unless forced to change. The law for an isolated group of particles is exactly of the same form as that for a single particle.
In the proof for angular momentum, it's the same thing. The torques cancel in pairs and angular momentum is conserved. The proof is quite clear, but the intuition is a lot harder for me. A particle cannot keep moving in a circle on it's own, whereas a group of particles keep rotating as a whole unless forced to change the direction about which they are rotating or the magnitude through an external torque. The law for a single particle leads to a law that is of a different form for the group.
Can somebody give me an intuition as to why this is the case without the proof(though the mathematical proof of itself is quite clear and simple)?
Short version: For a single particle, conservation of angular momentum reducing to conservation of linear momentum. But, for a group, it is a new law. A group rotates as long as there is no external torque. How can I develop an intuition for this?
