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

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The discussion focuses on calculating the angular velocity of a particle sliding down a frictionless sphere using conservation of energy. The initial attempt incorrectly expresses total energy in terms of angular velocity and potential energy. A suggestion is made to redefine total energy using linear speed and height, then convert these into angular terms. The correct relationship between linear speed and angular speed is emphasized, along with the need to relate height to the angle on the sphere. The conversation highlights the importance of proper variable representation in solving the problem.
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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?
 
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James01 said:
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?)
 

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