Question

A string is wound around the outside of a uniform disc of mass M and radius R. If the disc is released from rest, calculate the acceleration of the disc as the string unwinds from the disc in terms of Ag.

Answer 1

What method have you chosen to solve this? (forces, energy?)

Answer 2

equation of motions are
\[Ma = Mg - T ~~~~(1)\]
\[\frac{1}{2}MR^2 \frac{d \omega}{dt}=RT~~~~(2)\]
\[a=R \frac{d \omega }{dt}~~~~~~(3)\]
(1)+(2)/R and (3)
We get
\[\frac{3}{2}Ma=Mg\]
therefore
\[a=\frac{2}{3}g\]