Every university introductory physics course considers the problem ofAtwood's machine taking into account the mass of the pulley. In the usualtreatment the tensions at the two ends of the string are offhandedly taken toact on the pulley and be responsible for its rotation. However such a free-bodydiagram of the forces on the pulley is not {\it a priori} justified, inducingstudents to construct wrong hypotheses such as that the string transfers itstension to the pulley or that some symmetry is in operation. We reexamine thisproblem by integrating the contact forces between each element of the stringand the pulley and show that although the pulley does behave as if the tensionswere acting on it, this comes only as the end result of a detailed analysis. Wealso address the question of how much friction is needed to prevent the stringfrom slipping over the pulley. Finally, we deal with the case in which thestring is on the verge of sliding and show that this will never happen unlesscertain conditions are met by the coefficient of friction and the massesinvolved.
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