Angular momentum in different points












1














I have a question about angular momentum:
Is it possible to have a system where angular momentum is conserved relative to 1 point,but not conserved relative to another?






classical-mechanics angular-momentum







share|cite|improve this question



























    1














    I have a question about angular momentum:
    Is it possible to have a system where angular momentum is conserved relative to 1 point,but not conserved relative to another?






    classical-mechanics angular-momentum







    share|cite|improve this question

























      1












      1








      1







      I have a question about angular momentum:
      Is it possible to have a system where angular momentum is conserved relative to 1 point,but not conserved relative to another?






      classical-mechanics angular-momentum







      share|cite|improve this question













      I have a question about angular momentum:
      Is it possible to have a system where angular momentum is conserved relative to 1 point,but not conserved relative to another?






      classical-mechanics angular-momentum




      classical-mechanics angular-momentum






      share|cite|improve this question













      share|cite|improve this question











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      share|cite|improve this question










      asked 3 hours ago









      Frogfire

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          3 Answers
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          Consider central-force motion, such as a planet moving around a (very massive) star. The angular momentum of such a planet is constant if we take the origin as the center of the star. It is not constant if we take the origin to be any other point.






          share|cite|improve this answer





















          • But "constant" is different from "conserved." In the new system, there is a torque on the planet about any other point, so the torque is providing the change of the angular momentum. That torque-time integral is part of the conservation law.
            – Bill N
            1 hour ago










          • @BillN: If you're defining angular momentum to be conserved whenever $Delta mathbf{L} = int pmb{tau} , dt$, then I'm pretty sure that the statement "angular momentum is conserved" is tautological.
            – Michael Seifert
            37 mins ago












          • @BillN How do you define "conserved"?
            – FGSUZ
            9 mins ago



















          1














          Angular momentum relative to an origin ${mathcal O_1}$



          $$ mathbf{L_{mathcal O_1}} = mathbf{r_{mathcal O_1} times p_{mathcal O_1}}$$



          where $mathbf r_{mathcal O_1}$ is the position vector to the particle relative to some origin ${mathcal O_1}$.
          Now suppose that angular momentum is conserved in ${mathcal O_1}$. Then



          $$ frac{d mathbf L_1}{dt} = mathbf{dot{r_1} times p_1} + mathbf{r_1 times dot{p_1}} = frac{1}{m} mathbf{p_1 times p_1} + mathbf{r_1 times dot{p_1}} =0 $$



          but since the direction of momentum is frame-independent, the first term vanishes (that is, $mathbf{p_1} = mathbf{p}$). It then follows that



          $$ mathbf{r_1 times F_1} =0 . $$



          Now, let's look at some other origin $mathcal{O}_2$, given that $L$ is conserved in $mathcal O_1$. Well the first term much vanish again, that's fine but what about the second term? Does



          $$mathbf{r_2 times F_2} stackrel{?}{=}0. $$



          Well, no not necessarily. Namely, just choose an origin in which the force is perpendicular to your position vector.






          share|cite|improve this answer































            0















            Is it possible to have a system where angular momentum is conserved relative to 1 point,but not conserved relative to another?




            Total angular momentum will be conserved but the angular momentum of any part of the system will have a value dependent on where you take your base point.






            share|cite|improve this answer





















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              3 Answers
              3






              active

              oldest

              votes








              3 Answers
              3






              active

              oldest

              votes









              active

              oldest

              votes






              active

              oldest

              votes









              3














              Consider central-force motion, such as a planet moving around a (very massive) star. The angular momentum of such a planet is constant if we take the origin as the center of the star. It is not constant if we take the origin to be any other point.






              share|cite|improve this answer





















              • But "constant" is different from "conserved." In the new system, there is a torque on the planet about any other point, so the torque is providing the change of the angular momentum. That torque-time integral is part of the conservation law.
                – Bill N
                1 hour ago










              • @BillN: If you're defining angular momentum to be conserved whenever $Delta mathbf{L} = int pmb{tau} , dt$, then I'm pretty sure that the statement "angular momentum is conserved" is tautological.
                – Michael Seifert
                37 mins ago












              • @BillN How do you define "conserved"?
                – FGSUZ
                9 mins ago
















              3














              Consider central-force motion, such as a planet moving around a (very massive) star. The angular momentum of such a planet is constant if we take the origin as the center of the star. It is not constant if we take the origin to be any other point.






              share|cite|improve this answer





















              • But "constant" is different from "conserved." In the new system, there is a torque on the planet about any other point, so the torque is providing the change of the angular momentum. That torque-time integral is part of the conservation law.
                – Bill N
                1 hour ago










              • @BillN: If you're defining angular momentum to be conserved whenever $Delta mathbf{L} = int pmb{tau} , dt$, then I'm pretty sure that the statement "angular momentum is conserved" is tautological.
                – Michael Seifert
                37 mins ago












              • @BillN How do you define "conserved"?
                – FGSUZ
                9 mins ago














              3












              3








              3






              Consider central-force motion, such as a planet moving around a (very massive) star. The angular momentum of such a planet is constant if we take the origin as the center of the star. It is not constant if we take the origin to be any other point.






              share|cite|improve this answer












              Consider central-force motion, such as a planet moving around a (very massive) star. The angular momentum of such a planet is constant if we take the origin as the center of the star. It is not constant if we take the origin to be any other point.







              share|cite|improve this answer












              share|cite|improve this answer



              share|cite|improve this answer










              answered 2 hours ago









              Michael Seifert

              14.7k22752




              14.7k22752












              • But "constant" is different from "conserved." In the new system, there is a torque on the planet about any other point, so the torque is providing the change of the angular momentum. That torque-time integral is part of the conservation law.
                – Bill N
                1 hour ago










              • @BillN: If you're defining angular momentum to be conserved whenever $Delta mathbf{L} = int pmb{tau} , dt$, then I'm pretty sure that the statement "angular momentum is conserved" is tautological.
                – Michael Seifert
                37 mins ago












              • @BillN How do you define "conserved"?
                – FGSUZ
                9 mins ago


















              • But "constant" is different from "conserved." In the new system, there is a torque on the planet about any other point, so the torque is providing the change of the angular momentum. That torque-time integral is part of the conservation law.
                – Bill N
                1 hour ago










              • @BillN: If you're defining angular momentum to be conserved whenever $Delta mathbf{L} = int pmb{tau} , dt$, then I'm pretty sure that the statement "angular momentum is conserved" is tautological.
                – Michael Seifert
                37 mins ago












              • @BillN How do you define "conserved"?
                – FGSUZ
                9 mins ago
















              But "constant" is different from "conserved." In the new system, there is a torque on the planet about any other point, so the torque is providing the change of the angular momentum. That torque-time integral is part of the conservation law.
              – Bill N
              1 hour ago




              But "constant" is different from "conserved." In the new system, there is a torque on the planet about any other point, so the torque is providing the change of the angular momentum. That torque-time integral is part of the conservation law.
              – Bill N
              1 hour ago












              @BillN: If you're defining angular momentum to be conserved whenever $Delta mathbf{L} = int pmb{tau} , dt$, then I'm pretty sure that the statement "angular momentum is conserved" is tautological.
              – Michael Seifert
              37 mins ago






              @BillN: If you're defining angular momentum to be conserved whenever $Delta mathbf{L} = int pmb{tau} , dt$, then I'm pretty sure that the statement "angular momentum is conserved" is tautological.
              – Michael Seifert
              37 mins ago














              @BillN How do you define "conserved"?
              – FGSUZ
              9 mins ago




              @BillN How do you define "conserved"?
              – FGSUZ
              9 mins ago











              1














              Angular momentum relative to an origin ${mathcal O_1}$



              $$ mathbf{L_{mathcal O_1}} = mathbf{r_{mathcal O_1} times p_{mathcal O_1}}$$



              where $mathbf r_{mathcal O_1}$ is the position vector to the particle relative to some origin ${mathcal O_1}$.
              Now suppose that angular momentum is conserved in ${mathcal O_1}$. Then



              $$ frac{d mathbf L_1}{dt} = mathbf{dot{r_1} times p_1} + mathbf{r_1 times dot{p_1}} = frac{1}{m} mathbf{p_1 times p_1} + mathbf{r_1 times dot{p_1}} =0 $$



              but since the direction of momentum is frame-independent, the first term vanishes (that is, $mathbf{p_1} = mathbf{p}$). It then follows that



              $$ mathbf{r_1 times F_1} =0 . $$



              Now, let's look at some other origin $mathcal{O}_2$, given that $L$ is conserved in $mathcal O_1$. Well the first term much vanish again, that's fine but what about the second term? Does



              $$mathbf{r_2 times F_2} stackrel{?}{=}0. $$



              Well, no not necessarily. Namely, just choose an origin in which the force is perpendicular to your position vector.






              share|cite|improve this answer




























                1














                Angular momentum relative to an origin ${mathcal O_1}$



                $$ mathbf{L_{mathcal O_1}} = mathbf{r_{mathcal O_1} times p_{mathcal O_1}}$$



                where $mathbf r_{mathcal O_1}$ is the position vector to the particle relative to some origin ${mathcal O_1}$.
                Now suppose that angular momentum is conserved in ${mathcal O_1}$. Then



                $$ frac{d mathbf L_1}{dt} = mathbf{dot{r_1} times p_1} + mathbf{r_1 times dot{p_1}} = frac{1}{m} mathbf{p_1 times p_1} + mathbf{r_1 times dot{p_1}} =0 $$



                but since the direction of momentum is frame-independent, the first term vanishes (that is, $mathbf{p_1} = mathbf{p}$). It then follows that



                $$ mathbf{r_1 times F_1} =0 . $$



                Now, let's look at some other origin $mathcal{O}_2$, given that $L$ is conserved in $mathcal O_1$. Well the first term much vanish again, that's fine but what about the second term? Does



                $$mathbf{r_2 times F_2} stackrel{?}{=}0. $$



                Well, no not necessarily. Namely, just choose an origin in which the force is perpendicular to your position vector.






                share|cite|improve this answer


























                  1












                  1








                  1






                  Angular momentum relative to an origin ${mathcal O_1}$



                  $$ mathbf{L_{mathcal O_1}} = mathbf{r_{mathcal O_1} times p_{mathcal O_1}}$$



                  where $mathbf r_{mathcal O_1}$ is the position vector to the particle relative to some origin ${mathcal O_1}$.
                  Now suppose that angular momentum is conserved in ${mathcal O_1}$. Then



                  $$ frac{d mathbf L_1}{dt} = mathbf{dot{r_1} times p_1} + mathbf{r_1 times dot{p_1}} = frac{1}{m} mathbf{p_1 times p_1} + mathbf{r_1 times dot{p_1}} =0 $$



                  but since the direction of momentum is frame-independent, the first term vanishes (that is, $mathbf{p_1} = mathbf{p}$). It then follows that



                  $$ mathbf{r_1 times F_1} =0 . $$



                  Now, let's look at some other origin $mathcal{O}_2$, given that $L$ is conserved in $mathcal O_1$. Well the first term much vanish again, that's fine but what about the second term? Does



                  $$mathbf{r_2 times F_2} stackrel{?}{=}0. $$



                  Well, no not necessarily. Namely, just choose an origin in which the force is perpendicular to your position vector.






                  share|cite|improve this answer














                  Angular momentum relative to an origin ${mathcal O_1}$



                  $$ mathbf{L_{mathcal O_1}} = mathbf{r_{mathcal O_1} times p_{mathcal O_1}}$$



                  where $mathbf r_{mathcal O_1}$ is the position vector to the particle relative to some origin ${mathcal O_1}$.
                  Now suppose that angular momentum is conserved in ${mathcal O_1}$. Then



                  $$ frac{d mathbf L_1}{dt} = mathbf{dot{r_1} times p_1} + mathbf{r_1 times dot{p_1}} = frac{1}{m} mathbf{p_1 times p_1} + mathbf{r_1 times dot{p_1}} =0 $$



                  but since the direction of momentum is frame-independent, the first term vanishes (that is, $mathbf{p_1} = mathbf{p}$). It then follows that



                  $$ mathbf{r_1 times F_1} =0 . $$



                  Now, let's look at some other origin $mathcal{O}_2$, given that $L$ is conserved in $mathcal O_1$. Well the first term much vanish again, that's fine but what about the second term? Does



                  $$mathbf{r_2 times F_2} stackrel{?}{=}0. $$



                  Well, no not necessarily. Namely, just choose an origin in which the force is perpendicular to your position vector.







                  share|cite|improve this answer














                  share|cite|improve this answer



                  share|cite|improve this answer








                  edited 2 hours ago

























                  answered 2 hours ago









                  InertialObserver

                  1,042515




                  1,042515























                      0















                      Is it possible to have a system where angular momentum is conserved relative to 1 point,but not conserved relative to another?




                      Total angular momentum will be conserved but the angular momentum of any part of the system will have a value dependent on where you take your base point.






                      share|cite|improve this answer


























                        0















                        Is it possible to have a system where angular momentum is conserved relative to 1 point,but not conserved relative to another?




                        Total angular momentum will be conserved but the angular momentum of any part of the system will have a value dependent on where you take your base point.






                        share|cite|improve this answer
























                          0












                          0








                          0







                          Is it possible to have a system where angular momentum is conserved relative to 1 point,but not conserved relative to another?




                          Total angular momentum will be conserved but the angular momentum of any part of the system will have a value dependent on where you take your base point.






                          share|cite|improve this answer













                          Is it possible to have a system where angular momentum is conserved relative to 1 point,but not conserved relative to another?




                          Total angular momentum will be conserved but the angular momentum of any part of the system will have a value dependent on where you take your base point.







                          share|cite|improve this answer












                          share|cite|improve this answer



                          share|cite|improve this answer










                          answered 2 hours ago









                          Mozibur Ullah

                          4,59322249




                          4,59322249






























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