Question:
A string is wrapped over the edge of a uniform disc and the free end is fixed with the ceiling. The disc moves down, unwinding the string. Find the downward acceleration of the disc.
Solution:
$\mathrm{mg}-\mathrm{T}=\mathrm{ma}-(\mathrm{i})$
$\mathrm{T}=\mid \alpha$
$T \cdot R=\frac{m R^{2}}{2}\left(\frac{a}{R}\right)$
From (i) and (ii)
$a=\frac{2 g}{3}$