Conservation of angular momentum is closely related to the fact that there is no privileged spatial direction. As a consequence, once a direction is defined by an isolated system, it has no reason to change during the system evolution, because there is no distinguished absolute direction "calling it back" so to say. The system has a rotational inertia.
Let'sI will get back to this at the end of this discussion. But let's start with your intuition for linear momentum:
A single particle keeps drifting in a direction unless forced to
change.
This is because there is no privileged position in space. So, again, an isolated system that defines a position (by being there) has no reason to change it. Observed from another inertial frame, its center of mass moves uniformly in a straight line: this is how "to be not moving" appears in the most general sense. Else we would need to have a reference for absolute rest, which is precisely what we do not have because there is no absolute position.
So the system, having no reason to change the way it "not moves", has inertia: it takes a force to change the class of inertial frames it defines into another one. The force needed is the product of the eventual frame relative speed with respect to the initial one, with the system mass. The mass measures the inertia.
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.
Another way to say this is: if I drift along a free particle, with the same constant velocity it hasYes, it appears motionless to me. This is because therebut what law are you talking about? Because conservation of momentum is no privileged position innot the universe, so as long as I am at rest,conservation of speed: it does not make a difference if my "absolute position" changes or not. There is no "absolute" position to start with.
This does not depends on whether there is one or several particles, so similarly if I drift along a free system of particles, the centerconservation of massthe overall motion with inertia of the system will appear motionless(else it would require the same force to mestop a fly than to stop a car with the same speed).
WhenAnd this is why things seem different to you when it comes to angular momentum, the fact that there is no privilege position takes another twist, precisely because angular momentum is defined with respect to a specific point in space.:
A group of particles does not keep rotating. See the case described in this question: we have two particles (astronauts there) linked by a taut rope and spinning around their centre of mass. When they let go of the rope, they each follow a straight trajectory: observed from an inertial (non-rotating) frame at rest with respect to their center of mass, they do not have any angular speed anymore. Angular momentum is conserved because they move away from thetheir center of mass, not because they keep moving in circle.
That's because theThe single particle is a solid object: its whole mass distribution is maintained by cohesive forces. If you abstractly divide it into different parts, each one of these parts would follow a straight line and move away from the center of rotation, if it was not bound to the other parts. Exactly as the astronauts diddo: they keptkeep rotating as long as they formed aare bound systemby the rope.
This has all been well explained in @stafusa's answer.
So the law of angular momentum conservation that(that indeed is the same for a single particle and a group) is notnot the law you are thinking of: it is not a law about keeping moving in circle.
that you could imagine It is not at all case is a degenerate one: the particle being identified with its center of mass, which is also its centerabout conservation of rotation,
It is the very same thing for angular momentumspeed.
Consider a spinning particle. If I spin along withWhat is it (I put myself in its axisthen? It is a law about conservation of rotation and observe it while rotating at the same constant angular speed as itoverall direction with rotational inertia. Very much like a uniform linear motion is) the most general way of "not moving", it will appear to me to be not rotating at all. This is because there is no privileged direction in such a manner that the universe, so as long as I am regularly spinning ittotal angular momentum does not make a difference (in some sense, see just below) whether I rotate or not: therechange is no absolute reference directionthe most general way of "not rotating".
There is actually something new though: because a rotating reference frameWhat is not inertial (precisely because it posits a privileged spatial axis by rotating round it, see how this is relatedanalogous to the first part of our discussion), I can now observe centrifugal forces around me.
Now let's see how it works for a systemconservation of particles: itlinear momentum is the same idea. This time I will take a specific example, the one from this question: we have two particles (astronauts therefalse) linkedidea that we can characterize what is being conserved by a taut rope and spinning around their centreclass of massreference frames, because rotating frames are not inertial. How doSo if we intuitively seekept rotating along a many-body system, (in the conservationsame way as we previously followed a group of angular momentum after the link is broken?
Well let's spin along themparticles in inertial motion), while they are still connected: we observe that they arewould not spinning at all, butso easily observe that they are subject to centrifugal forcesthe system keeps "not rotating" (which keep the rop taut). When they let go of the rope,as opposed to the centrifugal forces push them apart, away from theirprevious system center of mass, but, more importantly: in a straight line. There is still no spinning, no global change of direction for the overall system "not moving").
We say the angular momentum is being conserved, but it amountswould have to saytake into account inertial forces (such as the Coriolis force) that if there is no privileged directionseem to start with, there is no reason for such a directioncorrespond to show up at any later time in the evolutiona change of the systemangular speed, while they actually help preserve both rotation axis and rotational inertia.
