# Angular momentum conserved

1. May 14, 2013

### joshmccraney

Hey all!

I am trying to figure out physical situations when angular momentum is and is not conserved. If anyone could share some theory here and illustrate with a few "real life" examples this would be very helpful!

josh

2. May 14, 2013

### Staff: Mentor

Consider cases where friction comes into play like a spinning gyroscope with friction acting on the axis slowing it down slowly.

3. May 15, 2013

### Staff: Mentor

Angular momentum is always conserved.

4. May 15, 2013

### rcgldr

In a closed system, angular momentum is always conserved. In an open system where the angular momentum of one of the objects, such as the earth, is ignored, then angular momentum can appear to be not conserved.

5. May 16, 2013

### Khashishi

keep in mind that light also carries angular momentum, so you could lose some angular momentum from the system if you let light escape.

6. May 16, 2013

### Rap

rgcldr is right - in a closed system (no forces acting on the system from outside the system), then angular momentum is conserved for that system. If there is some mechanism from the outside adding angular momentum to the system, then it wont be conserved for that system, but the angular momentum that the system gains will be exactly the same lost by the outside, so the net angular momentum will be conserved. Even in cases involving friction it will be conserved.

7. May 16, 2013

### WannabeNewton

Here is a cool example of a case where it ostensibly seems like angular momentum is not conserved but the resolution is quite cool, and quite alien if you are new to thinking of classical fields as "physical" entities.

Imagine we have an infinitely long solenoid of radius $R$, current $I$, and turns per length $n$. Furthermore, imagine we have two coaxial cylindrical shells of length $l$ with one at a radius $a < R$ from the common axis and one at a radius $b > R$ from the common axis (so one is inside the solenoid and one is outside). Let the inner shell have a charge $Q$ and the out shell have a charge $-Q$, both uniformly distributed over the surfaces. Now if you start reducing the current in the solenoid to zero, you will start to see the cylinders rotate (you can show this mathematically as well but I won't go into that)! So it seems like they starting rotating out of nowhere. But we know for a closed system that the angular momentum must be conserved so where is the angular momentum coming from that is resulting in the rotation of the cylinders?

Well it turns out that the angular momentum that the cylinders acquire when the current reaches zero actually comes from the angular momentum of the initial electromagnetic field itself! If you are familiar with the theory, this would be a fun little example for you to work out by yourself and verify that the angular momentum of the initial EM field is exactly equal to the angular momentum of the cylinders once the current goes to zero. This is more or less the same as Feynman's so called disk paradox.

On a related, but even cooler note, look up what is called Thomson's dipole.

8. May 18, 2013

### Khashishi

Also, intrinsic angular momentum (spin) is just as real as orbital angular momentum, so if you change the intrinsic angular momentum (by magnetizing a needle, for instance), the orbital angular momentum must change to conserve angular momentum.