Equality between centrifugal force and V

[soul]

Hi everyone,

Today in a question I saw an equality like this but I couldn't figure out how they are equal? Can anyonu help me please?

mv^2/ r = | dV/dr |

 

[JimChampion]

What do the various symbols in this equality represent?

 

[Topher925]

I can't figure it out either, probably because they are not equal. If the equation was: m*v^2/r = dv/dr*m then they would be equal.

 

[soul]

In the left side of the equation is the known centrifugal force. m--mass,v--velocity,r--radius,on the right side V is the potential,r--radius

 

[JimChampion]

Are you working at a level where you can relate forces to gradients of potential?

 

[tiny-tim]

Hi everyone,

Today in a question I saw an equality like this but I couldn't figure out how they are equal? Can anyonu help me please?

mv^2/ r = | dV/dr |

Hi soul!

Could that be mv^2/ r = | dU/dr |, where U is the gravitational or electric potential?

 

[soul]

Yes, tiny-tim.it is. I think I am not good enough to express myself. Thank you.

 

[JimChampion]

Writing mv^2/ r = | dV/dr | is like writing ma=F (which you might be more familiar with?). Does this help?

 

[soul]

Could you explain it in a more detailed way, please,JimChampion?

 

[JimChampion]

F=ma is a common way of expressing Newton's second law of motion for an object with constant mass m.

The mv^2/ r = | dV/dr | is equivalent to writing ma=F because

v^2/r is the centripetal acceleration

|dV/dr| is the magnitude of the centripetal force (given by the gradient of the potential V)

 

[JimChampion]

I don't really know what level of explanation you're after!

When I did A-level physics (in the UK, 1994) knowing about potential and how it relates to force was part of the course. I now teach A-level physics, and this is no longer part of the course: anything with calculus is avoided and probably wouldn't be encountered unless you studied an undergraduate physics course.