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Circular motion from a central force

  1. Mar 20, 2012 #1
    1. The problem statement, all variables and given/known data

    A particle moves under the influence of a central force, F_r(r) = − α r^−3. At time t = 0, the radius = r0 and the velocity = v0 as shown in the figure.
    (A) Determine the potential energy function U(r).
    (B) Determine the velocity vc such that the particle will move on the circle.
    (C) Now suppose v0 = vc /2. The particle will spiral into the origin. Calculate the time it will take the particle to reach r = 0.



    2. Relevant equations
    U(r) = - integral F(r) dr


    3. The attempt at a solution
    I got U(r).

    For my Part B) I don't know how to get velocity and Part C) how to get time. I think I might have to set ma=− α r^−3 but that doesn't seem right
     
  2. jcsd
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