L = 0 in the equation for effective potential energy?

In summary, L can be set to zero in an equation for zero angular momentum. This corresponds to radial infall and can be studied in both the Newtonian and general relativistic cases. It is recommended to first study the Kepler problem in Newtonian physics before delving into the relativistic treatment.
  • #1
sqljunkey
181
8
Hi,

What would happen if I set L in this equation to zero? I can have an L that is zero right?
 
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  • #2
Sure. That would be zero angular momentum. What do you expect to happen?

(EDIT: Which equation, exactly? There are many on that page.)
 
  • #3
L can be zero. From context, L is just the angular momentum, and L=0 corresponds to a radial infall. This is the GR forum, so I'd guess you are most likely interested in the GR case, though it's possible you are interested in the Newtonian case as well.
 
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Likes vanhees71
  • #4
Start with a thorough study of the Kepler problem in Newtonian physics. There (almost) everything can be solved in analytical form with standard elementary functions. After that it's easier to understand the general-relativsitic treatment (test particle in a Schwarzschild spacetime).
 

Related to L = 0 in the equation for effective potential energy?

1. What does L = 0 mean in the equation for effective potential energy?

When L = 0, it means that the angular momentum of the system is equal to zero. This can occur in situations where there is no rotation or angular motion present.

2. How does L = 0 affect the effective potential energy?

When L = 0, the effective potential energy simplifies to just the radial potential energy term. This means that the potential energy is only dependent on the distance between the two interacting objects and not on their angular motion.

3. Can L = 0 ever be negative in the equation for effective potential energy?

No, L = 0 is always a positive value. This is because angular momentum is defined as the cross product of an object's linear momentum and its position vector, and both of these quantities are always positive.

4. What happens if L = 0 is not satisfied in the equation for effective potential energy?

If L = 0 is not satisfied, then the effective potential energy will not accurately describe the motion of the system. This is because the equation assumes that there is no angular motion present, so any non-zero value for L will result in incorrect predictions.

5. How does L = 0 relate to the conservation of angular momentum?

When L = 0, it means that there is no change in the angular momentum of the system. This is consistent with the principle of conservation of angular momentum, which states that the total angular momentum of a system remains constant unless acted upon by an external torque.

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