Equality between centrifugal force and V

In summary, the conversation discusses an equality involving mv^2/ r = | dV/dr | and what the various symbols represent. The participants also mention the relationship between this equality and Newton's second law of motion, as well as the role of potential and force in physics. One person expresses difficulty in understanding the concept and receives assistance from others.
  • #1
soul
62
0
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 |
 
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  • #2
What do the various symbols in this equality represent?
 
  • #3
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.
 
  • #4
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
 
  • #5
Are you working at a level where you can relate forces to gradients of potential?
 
  • #6
soul said:
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! :smile:

Could that be mv^2/ r = | dU/dr |, where U is the gravitational or electric potential?
 
  • #7
Yes, tiny-tim.it is. I think I am not good enough to express myself. Thank you.
 
  • #8
Writing mv^2/ r = | dV/dr | is like writing ma=F (which you might be more familiar with?). Does this help?
 
  • #9
Could you explain it in a more detailed way, please,JimChampion?
 
  • #10
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)
 
  • #11
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.
 

FAQ: Equality between centrifugal force and V

What is the concept of "Equality between centrifugal force and V"?

The concept of "Equality between centrifugal force and V" refers to the principle that the centrifugal force acting on an object is equal in magnitude but opposite in direction to the centripetal force, which is the force that keeps the object moving in a circular path. This principle is based on Newton's first law of motion, which states that an object will continue moving in a straight line unless acted upon by a force.

How is this principle applied in real-life situations?

This principle can be observed in various real-life situations, such as the motion of a satellite around the Earth, the spinning of a merry-go-round, or the motion of a car around a curve. In all of these cases, the centrifugal force and the centripetal force are in equilibrium, resulting in a circular motion.

What is the formula for calculating centrifugal force?

The formula for calculating centrifugal force is F = m * V^2 / r, where F is the centrifugal force in Newtons, m is the mass of the object in kilograms, V is the velocity of the object in meters per second, and r is the radius of the circular path in meters.

Can centrifugal force be greater than centripetal force?

No, according to Newton's third law of motion, for every action, there is an equal and opposite reaction. This means that the centrifugal force and the centripetal force must be equal in magnitude but opposite in direction to each other. Therefore, one cannot be greater than the other.

How does the concept of "Equality between centrifugal force and V" relate to the principle of inertia?

The principle of inertia states that an object will continue to move with a constant velocity unless acted upon by a force. This principle is closely related to the concept of "Equality between centrifugal force and V" because the centrifugal force is the force that keeps an object moving in a circular path, while the velocity remains constant due to the object's inertia.

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