Atwood machine with a heavy pulley, energy conservation with rotational energy.

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We compute the final speed of a falling mass in an Atwood machine with one cart on a horizontal track, one mass pulling the system down, and a heavy pulley whose moment of inertia cannot be ignored. In this Atwood machine with a heavy pulley, we use energy conservation with rotational energy included to set up the conservation of energy equation. The initial energy is only the gravitational potential energy of the hanging mass, and the final energy includes the kinetic energy of both masses and the rotational energy of the pulley itself.