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Circular Motion using polar coordinates - Mechanics

  1. Feb 1, 2010 #1
    1. The problem statement, all variables and given/known data

    A particle of mass m is constrained to slide on the inside of a vertical smooth semi- circular ring of radius r. The position of the particle is described by a polar coordinate system whose origin is at the centre of the circle with axes along the orthogonal unit vectors r(hat) and θ(hat) where θ is the angle

    Write down the resultant force acting on the particle as a function of θ.

    2. Relevant equations

    F=ma

    3. The attempt at a solution

    I have used the expression v = rθ(dot) to find that acceleration, a= rθ(double dot)θ(hat) −
    v^2/r (rhat)
    I'm having a problem getting the 'r' component of the accelration in terms of theta though, so that I can do F=ma(theta) to find resultant force.

    Any help would be appreciated
     
  2. jcsd
  3. Feb 1, 2010 #2

    ehild

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    Homework Helper
    Gold Member

    The particle moves along a smooth vertical ring, so there is gravity, but no friction. You can use conservation of energy to get v2 in terms of theta.

    ehild
     
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