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70.33 An adapted moment of inertia

Problem. A circular disc of mass M and radius a is free to turn about a horizontal axis through its centre. A light string passes over the disc and masses M and \M hang at its ends. The free portions of the string are vertical and there is no slipping of the string over the disc. Find the acceleration of the masses. Instead of tackling this in the traditional way of considering the motion of the two masses and the disc separately, three of my students, Lisa Mellor, Paul Drew and Timothy Must, produced the following interesting and quicker solution. Initially the system is equivalent to the one illustrated. This has moment of inertia, about the horizontal axis through the centre of the disc, equal to