Angular Momentum (Not the usual Turntable Question)

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SUMMARY

The discussion centers on a physics problem involving a dog walking on a stationary horizontal turntable, analyzing the conservation of angular momentum. The key conclusion is that the turntable rotates in the opposite direction to the dog's motion, maintaining the total angular momentum at zero. The solution requires understanding the relationship between the dog's angular momentum and the turntable's angular momentum, specifically in terms of mass (m), rotational inertia (I), and radius (R). The hint provided emphasizes considering the torque about the center of the turntable to solve the problem effectively.

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divineyang
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Homework Statement



A dog of mass m is standing on the edge of a stationary horizontal turntable of totational inertia I and radius R. The dog walks once around the circumference of the turntable.

What fraction of a full circle does the dog's motion make with respect to the ground? Express your answer in terms of m, I and R. Ignore friction at the axle of the turntable.

Homework Equations



Conservation of angular momentum

The Attempt at a Solution



The turntable will rotate in the opposite direction as motion of the dog. Hence initial angular momentum = final angular momentum = zero.

Final angular momentum = Angular momentum of the dog wrt the ground - angular momentum of the table wrt the ground = 0

Is it correct so far?

I'm not sure as to how to proceed after that. Can anyone help me on this? Thanks!
 
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I don't think that will lead you to the right answer. We don't need to find any final velocities (so I think no use of applying COAM).
I will give you a hint.
Consider the torque acting about the point of hinge (centre of the table) by the force-pair which causes the dog to move forward.
 

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