# Can it happen that angular momentum is conserved about some points but not others?

So angular momentum is conserved about a point if no external net torques act about that point. But is there any occasion when this is only true about certain points? In other words: can it happen that angular momentum is conserved about some points in a system but not others?

• If the contribution of those points where the torque is not zero cancels when summed up, isn't it possible? – FF10 Aug 9 '17 at 11:22
• -1. Unclear. Please add further information to explain the source of your difficulty. What is the context of your question? – sammy gerbil Aug 9 '17 at 11:44

## 1 Answer

As you already said, angular momentum about a point is conserved if and only if the net external torque about that same point is zero. This is always true.

It might happen though that the net external torque is zero about one point and non zero about some other. In this case angular momentum is conserved about the first point whereas it is not about the second. As an example, consider a particle in free fall. The torque due to gravity about any point in the vertical line containing the particle vanishes and therefore the angular momentum about that point is conserved. For the same system, consider a point belonging to another vertical line which does not contain the particle. The torque is non zero so the angular momentum is not conserved.

• Consider a simpler system: That of the earth orbiting the sun. The reason why people choose to take the angular momentum about the sun itself is because the torque about that point is zero always. Making an angluar momentum calculation for the earth east. Take it about any other point and it will be non zero. However in both cases, the angular momentum about any arbitrary point for the earth-sun system is always a constant. – Russell Yang Aug 10 '17 at 6:17
• @RussellYang The angular momentum for the earth-sun system is always constant because the external torque to that system is always zero. If you consider the system as being only the earth, then there are reference points giving a non constant angular momentum . Consider for example a circular trajectory: at some instant, the angular moment about any point along the line containing the velocity vector is zero. But in the next instant, the angular momentum about that point is different from zero. – Diracology Aug 10 '17 at 11:51