Particle on a Circle Homework: Solving with Newton's Law

[faen]

Homework Statement

Homework Equations

I suppose Newtons third and second law.

centripetal acceleration = v^2 /R

The Attempt at a Solution

I'm thinking that the force due to weight, should be exceeded by the centripetal acceleration?

I couldn't get the calculations to add up though. Anyone know how to solve it or if I'm on the right track at all? Thanks for any help! :)

 

[ehild]

What forces act on the particle when sliding on the big sphere, and in what directions?

ehild

 

[faen]

The weight acts perpendicular to the circle, and movement acts parallel to the circle.

 

[barryj]

I think you are on the right track. "I'm thinking that the force due to weight, should be exceeded by the centripetal acceleration?"
Consider the forces acting normal to the surface of the sphere where the particle leaves the sphere.

 

[haruspex]

The weight acts perpendicular to the circle, and movement acts parallel to the circle.

No, weight is due to gravity, so always acts vertically, and movement is not a force.
There is a force perpendicular to the arc of the circle. What is it usually called and where does it come from?
You need a variable to denote the particle's position at an arbitrary point. You could use the height it has descended so far, but the angle of arc it has traveled will be more convenient. What will be its speed when at angle theta? What will be its acceleration if it is remaining in contact with the circle?