Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

nadia_g

  • 3 years ago

can some one give me the concept of arc and curvature( related to calculus 3)

  • This Question is Closed
  1. elica85
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    curvature is the rate where the unit vector T turns per unit of length. it is calculated \[k=|dT/ds|\]

  2. elica85
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    if you are given a position, you can find T by dividing the derivative of position over the absolute value of it. it can be looked at as velocity over speed\[r'(t)/|r'(t)|\]

  3. elica85
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ds refers to arc length parameter for a curve. if you're given a curve r(t)=x(t)i+y(t)j+z(t)k, \[s(t)= \int\limits_{t _{0}}^{t} (dx/dt)^{2}+(dy/dt)^{2}+(dz/dt)^{2} dt\]

  4. elica85
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    now, k can be re written as \[k=|(dT/dt)(dt/ds)|\]

  5. nadia_g
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hmm.........ok thanx

  6. nadia_g
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    elica?

  7. elica85
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the purpose of finding an arc length can be thought of as wanting to know how sharp a curve is turning

  8. elica85
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i just finished this class so my explanation might not be detailed enough since i need to understand more but i shared what i can

  9. nadia_g
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    in which class u r?

  10. elica85
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    calc III just had the finals on monday

  11. Not the answer you are looking for?
    Search for more explanations.

    Search OpenStudy
    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.