Calculating Speed of Object in Rotational System with Frictionless Bearings

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In summary, a uniform spherical shell of mass 4.5 kg and radius 8.5 cm can rotate on a vertical axis with no friction. The shell has a rotational inertia formula of 2/3 * m * r^3. A massless cord connected to a small object of mass 0.6 kg passes around a pulley with a rotational inertia of 3.0 x 10^-3 kg * m^2 and radius 5.0 cm. The object is released from rest and falls 82 cm. The problem involves finding the speed of the object using the equations W = ΔKE + ΔPE and considering the gravitational and elastic potential energies, as well as linear and angular work and kinetic energies.
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phychal
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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...
 
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  • #2
phychal said:
... 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?
 

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