Noether's Theorem & Conservation of Angular Momentum

Thread starter Saraphysics123
Start date Apr 18, 2017

In summary, Noether's Theorem is a fundamental principle in physics that states that for every continuous symmetry in a physical system, there is a corresponding conservation law. It relates to the conservation of angular momentum by stating that for every continuous rotational symmetry, there is a corresponding conservation of angular momentum. An example of Noether's Theorem in action is seen in planetary motion, where the laws of motion and gravitation exhibit rotational symmetry and thus conserve angular momentum. This conservation is useful in practical applications such as understanding the stability and control of objects in motion and is applicable to all physical systems that exhibit continuous symmetries.

Apr 18, 2017

Saraphysics123

Homework Statement

What is the realashinship between the Noether s therom and conservation of angular momentum and how I can get it from lagranian?

Homework Equations

The Attempt at a Solution

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Apr 18, 2017

stevendaryl

Staff Emeritus

Science Advisor

Insights Author

The rules here are that you need to show an attempt at a solution. You also don't have any relevant equations. Could you start by writing down what Noether's theorem says? Do you know how to use LaTex?

FAQ: Noether's Theorem & Conservation of Angular Momentum

1. What is Noether's Theorem?

Noether's Theorem is a fundamental principle in physics that states that for every continuous symmetry in a physical system, there is a corresponding conservation law. It was discovered by mathematician Emmy Noether in 1915 and has since been applied to various branches of physics, including classical mechanics, quantum mechanics, and general relativity.

2. How does Noether's Theorem relate to conservation of angular momentum?

Noether's Theorem states that for every continuous rotational symmetry in a physical system, there is a corresponding conservation of angular momentum. This means that if a physical system remains unchanged under rotation, then its angular momentum will be conserved.

3. Can you give an example of Noether's Theorem in action?

One example of Noether's Theorem in action is in planetary motion. The laws of motion and gravitation that govern the motion of planets around the sun are symmetric under rotations, which leads to the conservation of angular momentum. This explains why planets continue to orbit the sun without losing or gaining angular momentum.

4. How is conservation of angular momentum useful in practical applications?

Conservation of angular momentum has many practical applications. For example, it is essential in understanding the stability and control of objects in motion, such as satellites and spacecraft. It is also used in fields such as robotics, where the conservation of angular momentum is crucial in balancing and controlling movements.

5. Is Noether's Theorem applicable to all physical systems?

Yes, Noether's Theorem is applicable to all physical systems that exhibit continuous symmetries. This includes classical mechanics, quantum mechanics, and general relativity. It is a fundamental principle that has been proven to hold true in a wide range of physical systems, making it an essential tool in understanding the laws of nature.