I was doing some pulley block problems in rotational mechanics and almost everywhere when the pulley is rotating and some masses are connected by a light rope(for example I am taking a two block and 1 pulley system connected by light rope) the acceleration of the blocks are made equal to the tangential acceleration of the rim of the pulley//after which the problem is easily solved but I am not able to understand how is this result derived and how or why are we saying that the accelerations of the block are equal to the tangential accelertaion of the rim of the wheel.
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$\begingroup$ The rope is attached to the block, so the acceleration of the rope is the same as the acceleration of the block. The rope is fixed relative to the pulley (assuming the rope doesn't slip on the pulley) so the magnitude of the acceleration of the pulley rim is the same as the rope, which is in turn the same as the block. $\endgroup$– John RennieCommented Oct 8, 2015 at 7:22
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The rope is tangent to the wheel. Assuming that the rope doesn't slide, this means that the acceleration of the block is equal to the acceleration of the rope. As the rope is pulled tight, is has to be travelling at the same speed at all points. As the rope is tangent to the wheel, the tangential acceleration of the wheel has to match the acceleration of the rope. As a matter of interest, the force that keeps the rope from sliding is static friction. Anyway, I hope this helped answer your question.