# Conservation of Momentum not universal?

## Main Question or Discussion Point

So I calculate the momentum of a body moving with a constant speed along a circular path with mass m, tangential velocity v and radius r. Its angular momentum is mvr.kk. Good. Now what if I calculate the angular momentum from a point on the path of the circle. A simple calculation shows that the angular momentum about a point vertically below the center of the circle and which is also on the path of the circle is different for the particle at two different points. e.g. at the the point where the radius of the circle makes an angle with the positive x axis and the point where the radius of the circle makes an angle zero with the x axis. at the 90 degree point it is 2mvr and at the 0 degree point it is mvr. So does this mean that angular momentum is not conserved in every reference frame?

Related Classical Physics News on Phys.org
For circular motion there must be a constant force of $\frac{mv^2}{r}$ towards the center of the circle. When you take your reference frame as the center of the circle then there is no net torque since the force vector is parallel to the position vector, however when you move your reference frame to any other point there will be net torques over parts of the motion.
The key then is to try to pick a reference frame with the least torques involved.

"The key then is to try to pick a reference frame with the least torques involved." so what ur saying is that indeed I did not make a mistake and the momentum is not conserved in all inertial reference reference frame. But I thought the laws of physics were meant to be the same in all inertial refrence frame. So what this means is that in one frame of reference angular momentum is conserved and in another frame of reference angular momentum is not conserved. Or perhaps I am missing the theory. Ok can we say that the laws of physics are universal in that the actual law in analysis should have been that in the absence of a torque, angular momentum is conserved. So since torque was present angular momentum would not be conserved. So is that what it means? You know this is one clear way in which angular momentum differs from linear momentum. In linear momentum, momentum is always conserved in all reference frame.

Ken G
Gold Member
Angular momentum is only conserved for systems with no net torque on them. That's why if you choose the center point, the angular momentum is conserved, because the force goes through that point and the torque is zero. But if you choose a point on the circle, the force doesn't go through that point, so the torque is not zero. Nonzero torque causes a change in angular momentum. The conservation is only reestablished when you look at the larger system that includes whatever is supplying that torque. A closed system (one with no external forces on it) must have no net torques on it either, so a closed system will always conserve angular momentum. Open systems only do if they are open in such a way that does not experience any net torque, and that's the only issue that is frame-dependent-- the external torque is frame dependent on an open system like something going in a circle.