# Massive Pulley Dilemma

by dkb12085
Tags: dilemma, massive, pulley
 P: 1,478 If you consider the string to be massless then the tension at the pulley end will be the same as at the block end. For real strings, if short or lightweight, you can make the assumption that the string mass is negligable in comparison the the block. If the string length is longer or more massive, then the mass of the string and the mass of the block both contribute in the acceleration of the pulley. As one moves up the string, starting from the block, the mass below a particular position increases due to the addition of the incremental mass of the string below. For that reason, the tension as one moves up the string, where the mass of the string is not negligable, also increases. Like you said, the block, the string, and the contact of string at the pulley all have the same linear acceleration. While the block has translational inertia, as evident by the formula F=ma ( a more massive object requires more of a force for the same acceleration as a less massive object ), the pulley has a corresponding rotational inertia designated as moment of inertia ( mass moment of inertia ) about the axis of rotation. http://en.wikipedia.org/wiki/List_of_moments_of_inertia The corresponding rotational equation is T = I $\alpha$, ( $\alpha$ is Greek alpha symbol lower case ) where T = torque, I = mass moment of inertia, a = angular acceleration http://theory.uwinnipeg.ca/physics/rot/node5.html