Work and Rotational Kinetic Energy

[peaceandlove]

1. The problem statement, all variables and given/known data
A uniform spherical shell of mass M = 7.70 kg and radius R = 0.670 m can rotate about a vertical axis on frictionless bearings. A massless cord passes around the equator of the shell, over a pulley of rotational inertia I = 0.0880 kg·m2 and radius r = 0.0790 m, and is attached to a small object of mass m = 2.00 kg. There is no friction on the pulley's axle; the cord does not slip on the pulley. What is the speed of the object when it has fallen a distance 0.610 m after being released from rest? Use energy considerations.


2. Relevant equations
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3. The attempt at a solution
I don't even know where to begin.

[Dr.D]

The spherical shell is simply a rigid body for which you can find the mass moment of inertia with out too much trouble. It and the pulley are both driven by a falling weight with a mass of 2.0 kg.

Draw some FBDs, write the relevant equations of motion and the kinematic relations, and then write down the conservation of kinetic and potential energy for this system.

It is really a simple problem, even though the wording sounds formidable.

[peaceandlove]

2mgh=((2/3)M+(I/r^2)+m)v^2

Thank you so much!