Circular Motion using polar coordinates - Mechanics

  • Thread starter Keano16
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  • #1
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Homework Statement



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.

Homework Equations



F=ma

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
 

Answers and Replies

  • #2
ehild
Homework Helper
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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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