Circular Motion using polar coordinates - Mechanics

[Keano16]

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

 

[ehild]

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