Uncertainty Principle problem

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Joined Sep 25, 2007
It is a homework question and I solved it in the following way:
To Prove that (∆θ)(∆L)~(ћ/2) ;For what uncertainty of L will the angular position of the particle would be indeterminate?

I considered a particle of mass m moving in a circle of constant radius r at speed v.Then,classically,L=mvr.

Clearly,from uncertainty principle, ∆s ∆p~(ћ/2)
=> (∆s/r)[(∆p)r]~(ћ/2)
=> (∆θ)(∆L)~(ћ/2)
What I am worried if this particular case of a circle will do;and the second question.I think it is ∆L=0 which makes ∆θ indeterminate...But I am not sure...

Please check if this is correct and rectify if I am wrong