How Does Angular Velocity Change as a Particle Slides Down a Sphere?

[James01]

Homework Statement

A particle sits at the top of a fixed sphere of radius a. The particle is given a tiny nudge so that it begins to slide down the frictionless surface of the sphere. Consider the point at which the particle is still in contact with the sphere and its position is indicated by the value of the angle $$\theta$$.

Use the conservation of energy principle to calculate the angular velocity, $$\omega$$, as a function of theta.

Homework Equations

Etotal = Ek + Ep

The Attempt at a Solution

Etot = 1/2*m*($$\omega$$)^2 -m*g*$$\theta$$

$$\omega$$ = (2*g*$$\theta$$)^1/2


Please can anyone verify if I have completed this part correctly?

 

[Doc Al]

Etot = 1/2*m*($$\omega$$)^2 -m*g*$$\theta$$

This is incorrect. Instead, write the total energy in terms of the usual variables of speed and height and then translate that into angular terms. (For a given linear speed, what's the angular speed? For a given height along the sphere, what angle does it make?)