# Lagrangian problem

Q. A block of mass m1 is connected to a second block of mass m2 by a light string that passes over a frictionless pulley. Mass m2 is connected to a light spring of spring constant s, as displayed below. Develop an expression for the Lagrangian of the system, assuming that the moment of inertia of the pulley $$I=\fraction{1/2}Mr^2$$ (ie it has mass M and radius r), and hence determine the natural frequency of vibration of the system.

http://img229.imageshack.us/img229/6502/lagrange2rs.png [Broken]

I can do the question without having to consider the moment of inertia. What I did is use the coordinate z, where z is the position of m2 relative to the pulley.
Now that works out just fine when neglecting the moment of inertia. However, I don't see how you can consider a moment of inertia for this problem?? I just don't see how the pulley is rotating about an axis if it is frictionless? Can someone tell me want I'm missing here please.

Thanks for any help

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