# neutral and stable equilibrium

Discussion in 'Physics & Math' started by perfectionist, Oct 25, 2006.

1. ### perfectionistRegistered Senior Member

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In some of the questions in electrostatics, I came across 2 terms namely neutral equilibrium and stable equilibrium. Is there a difference between these 2?

3. ### D HSome other guyValued Senior Member

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There is a third class as well -- metastable equilibrium points. Suppose a system is very close to but not at some equilibrium point. The equilibrium point is
• Stable if forces act on the system to move it toward the equilibrium point
• Metastable (or unstable) if forces act on the system to move away from the equilibrium point
• Neutral if no dispersive or restoring forces act on the system.

For example, a broomstick held by the end of the handle has two equilibrium points in a gravity field. The business end pointing along the gravity force vector (i.e., straight down) is a stable equilibrium point, while straight up is a metastable equilibrium point.

5. ### funkstarratsknufValued Senior Member

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In a stable equilibrium, a slight change will lead to the system returning to its prior state. For instance, if you strectch a spring slightly, it will oscillate back to its still state.

In a neutral equilibrium, a slight change won't necessarily lead to the system returning to the prior state, but it won't begin to diverge, either. Say, a sphere on a table. Push it slightly, and it will roll a bit and settle on another spot on the table. The disturbance affected the position, but not the stability.

7. ### SarkusHippomonstrosesquippedalo phobeValued Senior Member

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And unstable is, for example, a ball at the top of a hill. In its current position it is stable - but a slight push in any direction and it rolls downhill - diverging from the equilibrium point.

8. ### perfectionistRegistered Senior Member

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That's cool! Thanks.

9. ### catoless hate, more scienceRegistered Senior Member

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heh, boomstick...