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## Homework Statement

http://img372.imageshack.us/img372/4379/diagyx7.jpg [Broken]

A uniform disc has centre O,radius a and mass 2m. It is free to rotate in a vertical plane about a fixed horizontal axis through O. A particle of mass m is placed on the highest point of the rough edge of the disc and the system is slightly disturbed so that OP begins to rotate with the particle in conact with the edge. In the subsequent motion, OP makes an angle [itex]\theta[/itex] with the upward vertical (see diagram), For the motion while the partcile remains in contact with the disc without slipping,find [itex]a \ddot{\theta}[/itex] and [itex]a \dot{\theta}^2[/itex] in terms of g and [itex]\theta[/itex]

Show that if the particle remains in contact with the disc,then it begins to slip when

[itex]4\mu cos\theta -sin\theta =2\mu[/itex]

where [itex]\mu[/itex] is the coefficient of friction between the particle and the edge of the disc,

Show that,however large the value of [itex]\mu[/itex],the particle cannot lose contact with the disc before it starts to slip

## Homework Equations

Not sure which eq'ns are relevant here

## The Attempt at a Solution

Need help on starting. Since the system can rotate,I think I need to use moment of inertia in it somewhere, but the only way to get [itex]a \ddot{\theta}[/itex] from a moment of inertia is to use [itex]\tau =I \alpha[/itex]

But it also talks of the mass slipping,so should I resolve the weight at P into components and find the centripetal acceleration?

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