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UCM - Derive speed, of a body moving, radius r, and the frequency f.

  1. Mar 17, 2012 #1
    1. The problem statement, all variables and given/known data
    Derive a relationship between the speed v, of a body moving in a circle of radius r, and the frequency f, of the revolutions.

    2. Relevant equations
    v=2πr/T
    T=1/F

    3. The attempt at a solution

    Well, I thought this would be as simple as solving for F in the second equations and substituting into the original formula.
    Eg:

    v=2πr/T
    T=1/F
    F=1/T

    v=2πr/1/F

    v=2πr/F

    Is the above correct? Could I expand it into more steps, like how one would derive F = 1/T, I already know how to derive v=2πr/T.

    Thanks!
     
  2. jcsd
  3. Mar 17, 2012 #2

    PeterO

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    Homework Helper

    Does not the T = 1/f follow from the way they are defined?

    Centripetal acceleration is given alternately by mv2/R or 4∏2R/T2 which means 4∏2Rf2
    by equating the first and last form I think the answer falls out.
     
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