Arc Length In Polar Cordinates

In summary, a high school student is researching arc length in polar coordinates for a project and is struggling to find real life applications for it. They are seeking help to better understand the topic and its practical uses, such as in the calculation of work done by a force or in designing roller coasters.
  • #1
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Hello,
i am a high school student currently taking ap calculus. i am currently working on a research project on arc length in polar coordinates. through all of my research thus far the one thing that has eluded my grasp so far that is really frustrating is the applications in real life for arc length. :rofl:

if you know anything about this topic or applications of it i would be greatfull for your help because it would allow me to make sure that i have got this topic down pat. :rolleyes:


Gracias :biggrin: :biggrin: :biggrin:
 
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  • #2
What would you consider as an "application of arc length" in real life?
The following might be considered as such:

The work done by a force acting on an object satisfies the inequality:

0<=W<=F*l,

where W is the the (absolute) value of the work done, F is the magnitude of the force, and l is the arc length of the distance traversed by the object.
 
  • #3
what i mean by applications, is something that you would actually use arc length for in real life business industry designing something :smile:
i was thinking along the lines of roller coasters :surprise:
 

1. What is arc length in polar coordinates?

Arc length in polar coordinates is the distance along a curve in polar coordinates, measured from one point to another. It is represented by the symbol "s" and is typically measured in radians.

2. How is arc length calculated in polar coordinates?

Arc length in polar coordinates can be calculated by using the formula: s = ∫√(r² + (dr/dθ)²) dθ where r is the function that defines the curve and dr/dθ is the derivative of r with respect to θ.

3. What is the difference between arc length and arc measure in polar coordinates?

Arc length is the actual distance along a curve, while arc measure is the angle between the initial and terminal points of an arc. Arc length is measured in units of distance, while arc measure is measured in units of degrees or radians.

4. Can arc length be negative in polar coordinates?

No, arc length cannot be negative in polar coordinates. It is always a positive value, as it represents the distance along a curve.

5. How is arc length used in real-life applications?

Arc length in polar coordinates is commonly used in fields such as physics, engineering, and astronomy to calculate the distance traveled by an object along a curved path. It is also used in the design and construction of circular objects, such as bridges and roller coasters.

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