Particle slides down 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?)

 

[m2003]

Your solution looks correct so far. However, it would be helpful to provide more context and information about the problem, such as the mass of the particle and the point at which you are trying to calculate the angular velocity. Also, it may be helpful to explain your thought process and how you arrived at your solution. Additionally, it is always a good idea to double check your units and make sure they are consistent throughout your calculations.