I have seen that when a person is rotating while sitting on a spinning chair, his angular momentum is conserved. What I'm not getting is through what point I am to calculate the angular momentum: is it any point on the axis or any point of choice?

I tried it this way that when a body is in uniform circular motion, its angular momentum is conserved only at the center and not any other point as the perpendicular distance between point and $v$ will change,but I'm not able to find the point when a person is spinning or when a collision is taking place.


For a closed system (one in which all the forces are between elements of the system) angular momentum is conserved about every point. In fact, if the center of mass of the system isn't moving, the angular momentum is the same about every point.

However, most often, you want to consider a system which does interact with things outside of itself. A point mass undergoing uniform circular motion, for example, is not a closed system: something external must be providing the force to accelerate the mass. This force always acts toward the center of the circle, so that is the one point about which the mass experiences no torque, and therefore the only point about which angular momentum is conserved.

That is generally the way that the principle of conservation of angular momentum is most useful: if you can identify a point through which forces act during some process, then calculating angular momentum about that point generally simplifies things.

  • $\begingroup$ can u give example of a closed system,where the angular momentum is conserved about any point,by any point i believe u mean any point with in the system,thanks. $\endgroup$ – sachinrath123 Jan 28 '18 at 15:40
  • $\begingroup$ About any point whatsoever. Take your rotating person on a chair. To make it truly a closed system, put the person and chair in outer space. The angular momentum in any inertial reference frame, about any point (call it $A$) in that reference frame, is the sum of the angular momentum of the person/chair about their center of mass, and the angular momentum due to the motion of the person/chair center of mass relative to $A.$ This sum never changes. $\endgroup$ – Ben51 Jan 28 '18 at 16:14
  • $\begingroup$ so can i conclude that if the linear momentum of a system is conserved,the angular momentum of the system is conserved through any point,and if linear momentum is not conserved then angular momentum may or may not get conserved. $\endgroup$ – sachinrath123 Jan 28 '18 at 18:40
  • $\begingroup$ If linear momentum is conserved because no external forces act then angular momentum is also conserved. However, it possible for linear momentum to remain constant while angular momentum changes if an external torque acts but net external force is zero. But in spirit, yes, angular momentum conservation is often useful when linear momentum conservation is not because in the case of angular momentum, the influence of the external force can be neutralized by choosing the point appropriately $\endgroup$ – Ben51 Jan 28 '18 at 19:25
  • $\begingroup$ one more thing if the person and chair system is taken to space,the angular momentum will remain conserved,my worry is each particle is moving in circular motion,is the centripetal force now becomes internal,can we conclude that a body can move in circular motion without application of external forces. $\endgroup$ – sachinrath123 Jan 28 '18 at 20:11

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