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

Homework Help: 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


    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


    User Avatar
    Homework Helper

    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.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook