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A particle that feels an angular force only

  1. Oct 2, 2012 #1
    1. The problem statement, all variables and given/known data

    "Consider a particle that feels an angular force only, of the form F=2mvw(theta direction). Show that r=Ae^theta + Be^-theta, where A and B are constants of integration."
    v=dr/dt
    w=d(theta)/dt


    2. Relevant equations

    F(radial)= 0 = m((dv/dt)-r*w^2)
    F(theta)= 2mvw = m(r*(dw/dt)+2vw)

    3. The attempt at a solution

    So I can solve the F(theta) equation to find that r*(dw/dt)=0, hence dw/dt=0
    and I can also solve the F(radial) equation to find that dv/dt=r*w^2
    I also know that this question involves a separation of variables and then integrating
    However the problem is that I don't know substitutions I can make to put the equations I have into a form that makes that possible. Any hints or ideas are appreciated ^-^
     
  2. jcsd
  3. Oct 2, 2012 #2
    dw/dt = 0 means w = W = const. So the first equation is then dv/dt = Cr, where C = W^2 = const. Are you saying you don't know how to solve this equation?
     
  4. Oct 2, 2012 #3
    Oh, thanks for pointing that out
    dv/dt can written as v(dv/dr)
    So 0.5v^2=0.5c*r^2+D ;where D is the constant of integration
    v=sqrt(cr^2 +2D)=dr/dt
    I end up with: t+E=intg[dr/sqrt(cr^2 +2D)] ;where E is the constant of integration
    Wolfram Alpha can't even solve this integral :O
    What am I missing?
     
  5. Oct 2, 2012 #4
    That integral can be converted to [tex] \int \frac {adx} {\sqrt {x^2 + 1}} [/tex].
     
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