A uniform spherical shell of mass M = 17.0 kg and radius R = 0.900 m can rotate

Question

A uniform spherical shell of mass M = 17.0 kg and radius R = 0.900 m can rotate about a vertical axis on frictionless bearings (see the figure). A massless cord passes around the equator of the shell, over a pulley of rotational inertia I = 0.0840 kg

A uniform spherical shell of mass M = 17.0 kg and radius R = 0.900 m can rotate about a vertical axis on frictionless bearings (see the figure). A massless cord passes around the equator of the shell, over a pulley of rotational inertia I = 0.0840 kgm^2 and radius r = 0.0560 m, and is attached to a small object of mass m = 3.10 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 0.847 m after being released from rest? Use energy considerations.

Explanation / Answer

The sum of the kinetic energies in the 2 rotating items will equal the loss in PE of the mass - the KE of the mass:

Is = (2/3)*17*.900

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