Potential conserved quantities

In summary, the conversation discusses the conservation of angular momentum and energy in a system with a potential U(x) = -Gm1m2/(x^2+y^2+(kz)^2 )^1/2. It is mentioned that the z component of angular momentum is conserved, but the other two components are not unless k = 1. The possibility of other conserved quantities is also mentioned, with a suggestion to use Lagrangian mechanics and Noether's Theorem to calculate them. The conversation concludes with the confirmation that the z component of angular momentum and the energy are conserved, and the mention of the speaker's plan to learn Lagrangian mechanics in the future.
  • #1
madking153
37
0
hi,

if i have mass possesses potential U(x)=-Gm1m2/(x^2+y^2+(kz)^2 )^1/2 , i said angular momentum of z is conserved but not angular momentum of x , y .. is it correct ?

what else is conserved ? energy ?
 
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  • #2
Yes, the z component of angular momentum is conserved, but the other two are not unless k = 1. As for other conserved quantities, what do you think? You have a potential ...
 
  • #3
Are you familliar with Lagrangian mechanics? If so you can use Noether's Theorem to calculate conserved quantities:

http://www.mathpages.com/home/kmath564/kmath564.htm

It may very well be quicker to just use your physical intuition though.
 
  • #4
My thought : angular momentum of z component and the energy of the system is conserved ... Pls tell me if there are more quantities are conserved
thanks
 
Last edited:
  • #5
no i am not familiar to Langrage mechanics - will learn next 2 months
 
  • #6
So i am correct ?? angular momentum of z and energy are conserved ?
 

1. What are potential conserved quantities?

Potential conserved quantities are physical quantities that remain constant in a system throughout a certain process or transformation. They are important in physics as they provide a way to understand and predict the behavior of a system.

2. What are some examples of potential conserved quantities?

Some examples of potential conserved quantities include energy, momentum, and angular momentum. These quantities are often conserved in closed systems, meaning that they do not change in value over time.

3. How do potential conserved quantities relate to the laws of thermodynamics?

The laws of thermodynamics, specifically the first law which states that energy cannot be created or destroyed, are closely related to potential conserved quantities. In a closed system, the total energy is conserved, and this includes potential energy as well.

4. Can potential conserved quantities be converted into each other?

Yes, potential conserved quantities can be converted into each other through different processes. For example, potential energy can be converted into kinetic energy, and momentum can be converted into angular momentum. However, the total amount of conserved quantity remains constant.

5. How are potential conserved quantities useful in practical applications?

Potential conserved quantities are useful in practical applications as they allow us to make predictions and calculations about the behavior of systems. For example, the conservation of energy can be used to calculate the speed of an object at a certain height, or the conservation of momentum can be used to predict the trajectory of a projectile.

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