Vertical Atwood machine with a heavy pulley, solved using energy conservation (including rotational)

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We calculate the final velocities of the masses in a vertical Atwood machine/block and pulley system by using energy conservation. Note that the relationship v=r*omega holds for the disk because the string is not slipping and must move at the same rate as the masses. Finally, we compute the amount of rotational kinetic energy in the disk at the end of the process.