Questions on classical mechanics

[Gavroy]

Hi
Question 1
i was wondering if there is any method to find the point from which the angular momentum is a conserved quantity. let me e.g. choose the case of a planet moving in an orbit around the sun. In this case, the angular momentum measured from the center of mass as the point of reference is conserved. But if i choose a different point, that is not exactly on the line connecting the planet and the sun, then the angular momentum is varying with time. so how do i found out how to choose this point, if the system is more complex?

Question 2
if F is a conservative force field, then the energy is conserved. is the converse, the energy is conserved, therefore we have a conservative force field also true?

 

[Simon Bridge]

Hi
Question 1
i was wondering if there is any method to find the point from which the angular momentum is a conserved quantity. let me e.g. choose the case of a planet moving in an orbit around the sun.

To be more precise: the sun and the planet each orbit their common center of mass.

In this case, the angular momentum measured from the center of mass as the point of reference is conserved. But if i choose a different point, that is not exactly on the line connecting the planet and the sun, then the angular momentum is varying with time.

But it is still conserved.

so how do i found out how to choose this point, if the system is more complex?

You mean you want to find a reference frame in which a particular bodies angular momentum is a constant?

Is it not always the center of mass for gravitating systems?

Question 2
if F is a conservative force field, then the energy is conserved. is the converse, the energy is conserved, therefore we have a conservative force field also true?

Kinetic energy is conserved in an elastic collision: is the collision an example of a conservative force field?

 

[Gavroy]

Thank you for your answer, but is this a question or an answer?

Is it not always the center of mass for gravitating systems?

 

[Simon Bridge]

Thank you for your answer, but is this a question or an answer?

That's up to you :) Both - I hope.

It can be hard to tell if a statement followed by a question mark is an actual question or a rhetorical question.
All the questions in post #2 can be safely treated as actual questions. I am posing them as a way to help you clarify your thinking and so find the answers you seek.

 

[PJC01]

Question 1:
There is a general principle in classical mechanics known as the conservation of angular momentum, which states that in a closed system, the total angular momentum remains constant. This means that the point from which the angular momentum is measured does not affect its conservation. In the case of a planet orbiting the sun, the center of mass is often chosen as the reference point because it simplifies the calculations, but any point can be chosen as long as it remains consistent throughout the analysis. In more complex systems, it may be helpful to choose a reference point that simplifies the equations of motion or is physically meaningful.

Question 2:
Yes, the converse statement is also true. If the energy is conserved in a system, then the force field must be conservative. This is because a conservative force field is one in which the total mechanical energy (kinetic + potential) of a system remains constant. So, if the energy is conserved, it means that the work done by the force is zero, which is a characteristic of a conservative force. However, it is important to note that the converse statement is not always true, as there are non-conservative forces that do not conserve energy (such as friction).