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Derive a function for the acceleration of an Atwood machine on a horizontal surface that includes pulley mass as well as friction. The rotational inertia of the pulley can be a challenge because a force must act tangent to the pulley to make it accelerate. The force on the pulley is the result of a difference in tensions on the string. The atwood machine is a pretty typical physics problem seen in high school physics, college physics and AP Physics 1 as well as AP Physics C Mechanics. This problem also comes up on the JEE. This version of the problem covers most of what you see in just about any introductory physics class regardless of what 'level' it is. There are two assumptions in this problem, the first being that the pulley rotates on a frictionless axle the second being that friction is sufficient between the string and pulley such that the string does not slip on the pulley. Note: even though there is friction between the string and pulley, and that friction is responsible for doing work on the pulley, that work by friction is conserved within the 'system' consisting of both blocks and the pulley.