Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Physics teacher wanted me to understand how to derive

  1. Dec 19, 2003 #1

    jimmy p

    User Avatar
    Gold Member

    My Physics teacher wanted me to understand how to derive [tex]a=v^2/r[/tex] using the equations [tex]v=d/t[/tex], [tex]\omega=\theta/t[/tex] and [tex]arc length=r\theta[/tex] but when it came down to it, i had brain freeze..and when my teacher looked at it, he had brain freeze. This isnt part of my syllabus but i was wondering how you derive the equation (so it isnt homework!)

    oh yeah, i was given the hint to work it first into the equation [tex]v=r\omega[/tex] and then work from there.

    Cool, i just used that LaTex stuff! that was quite challenging!

    thanx

    Jimmy P
     
    Last edited: Dec 19, 2003
  2. jcsd
  3. Dec 19, 2003 #2

    Doc Al

    User Avatar

    Staff: Mentor

  4. Dec 19, 2003 #3

    jimmy p

    User Avatar
    Gold Member

    OK unfortuantely i didnt find that too useful. That is kind of what we tried to do but it failed miserably, because we ended up getting T on both sides of the equation. i could get to [tex]v=r\omega[/tex] (if that is even helpful) and couldnt get any further
     
  5. Dec 19, 2003 #4

    FZ+

    User Avatar

    Can you use calculus?
     
  6. Dec 19, 2003 #5

    Doc Al

    User Avatar

    Staff: Mentor

    Well, those two threads show how to derive the formula for centripetal acceleration. I know of no other way.

    Using the equations you started with, you can certainly get to [tex]v=r\omega[/tex]. But you won't get any further without using the strategy explained in those threads. The "trick" is to find [tex]\Delta V[/tex]---the difference in the velocity vectors---between two points on the circle separated by [tex]\Delta\theta[/tex].

    Why don't you show what you've done and perhaps we can fix it.
     
  7. Dec 20, 2003 #6

    krab

    User Avatar
    Science Advisor

    You have everything EXCEPT a formula for [tex]\inline{\Delta v}[/tex]. This is the real physics; you have to think about it. The rest is just formula manipulation. I remember when I was in highschool, I thought about this very thing for days, because I had difficulty coming to terms with how vectors add; I did not understand [tex]\inline{a=\Delta v/\Delta t}[/tex] as a VECTOR equation. But I put in the effort and was rewarded with a career in physics.
     
  8. Dec 20, 2003 #7
    I haven't looked at either of those links, but I remember first deriving the formula by creating a proportion between the triangle the velocity and acceleration vectors created, and the triangle that the 2 radii and the chord created.
     
  9. Dec 20, 2003 #8

    jimmy p

    User Avatar
    Gold Member

    cant anyone actually give the answer? i promise that it isnt homework and that i have tried!!
     
  10. Dec 20, 2003 #9
    Try this.
    Draw a vector for r with a vector for v on the end (will be 90 degrees from this), then a little time later examine what would happen. The arclength s= r theta is an approximation from geometry.

    I havent done this yet myself, but i am working on it
     
  11. Dec 20, 2003 #10
    for the algebraic way you are looking for you go from v = d/t and find d from the other eqns and get v = r omega
    Then with acceleration, a = v / t, substitue the v and you get r omega / t, v=r/t so a = v omega, the trick is a = v^2 omega / v = v^2 omega / ( r omega ) and cancel.

    BUT this gives you nothing (not exactly true). Calculus method and geometry - what i siad to do in last post, work the same and give you a good in sight in to what happend.
    This is related to how Feynman got to grips with QED.
     
  12. Dec 20, 2003 #11
    Although with the geometrical method i cant avoid the final 'trick' bit to go from a = r omega^ 2 to v^2 / r
    Doh
     
  13. Dec 21, 2003 #12

    Doc Al

    User Avatar

    Staff: Mentor

    We have. Several times over. You just don't seem to want to accept it! :smile:
     
  14. Dec 21, 2003 #13

    jimmy p

    User Avatar
    Gold Member

    lol sorry, i wasnt concentrating the other night when i wrote that, thanx guys!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?