What is the speed of an object falling from a rotating spherical shell setup?

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The discussion centers on calculating the speed of a mass falling from a rotating spherical shell using energy considerations. The setup includes a spherical shell with a mass of 4.5 kg and a radius of 8.5 cm, a massless cord, and a pulley with a rotational inertia of 3.0 x 10^-3 kg m². Key factors to consider include the changes in gravitational potential energy, rotational kinetic energy of the shell, and linear kinetic energy of the falling mass. Participants are seeking guidance on applying these energy principles to find the speed of the object after it has fallen 82 cm. The conversation emphasizes the importance of understanding energy transformations in this mechanical system.
ekram
moved from general forum so homework template is missing
Hello everyone,

I am having trouble finding the solution to this problem shown below:-
  1. A uniform spherical shell of mass M = 4,5kg and radius R = 8,5cm can rotate around a vertical axis on frictionless bearings. A massless cord passes around the equator of the shell over a pulley of rotational inertia I = 3,0 10- 3kg m2 and radius r = 5,0cm, and is attached to a small object of mass m = 0,60kg. There is no friction on the pulley’s axel; the cord does not slip on the pulley. What is the speed of the object when it has fallen 82cm after being released from rest? Use energy considerations.
can anyone kindly guide me to the solution to this problem.
 
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Consider the changes in the following;
-Gravitational potential energy
-Rotational kinetic energy
-Linear kinetic energy
 

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