Calculating Speed of Object in Rotational System with Frictionless Bearings

[phychal]

Homework Statement

A uniform spherical shell of mass M = 4.5kg and radius - 8.5 cm can rotate about a vertical axis on frictionless bearings. Rotational inertia formula for this object = 2/3 *m*r^3 A massless cord passes around the equator of the shell, over a pulley of rotational inertia I = 3.0 x 10^-3 kg * m^2 and radius = 5.0 cm, and is attached to a small object of mass m = .6kg. 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 82 cm after being released from rest?

Homework Equations

W = delta ke + delta pe
pe(gravitational)
pe(elastic)
work(linear/angular)
ke(angular/linear)

The Attempt at a Solution

I'm not even sure where to start...

 

[kuruman]

... Rotational inertia formula for this object = 2/3 *m*r^3 ...

You probably mean r² here or the dimensions don't work.

Homework Equations

W = delta ke + delta pe
pe(gravitational)
pe(elastic)
work(linear/angular)
ke(angular/linear)

Start by finding expressions for each of the terms that you have listed above. Specifically, you have three objects that move, what is ΔKE and what is ΔPE for each of them? How is the linear speed of the descending mass related to the angular speed of the rotating objects?