Question

A disc of mass $m$, radius $r$ wrapped over by a light and inextensible string is pulled by force $F$ at the free end of the string. If it moves on a smooth horizontal surface, find linear and angular acceleration of the disc.

Answer 1

The force translates the $C.M$ of the disc with an acceleration
$a$ given as

$F=ma\Rightarrow a=\frac{F}{m}$

The force $F$ develops a torque $\tau$ about $O$; consequently the disc rotates with an angular acceleration $\alpha$ about an axis passing through $O$, given as $\tau =l_0\alpha$
$\because \tau =FR$ & $I_0=\frac{1}{2}m{R}^2$
$\Rightarrow \alpha =\frac{\tau }{I_0}=\frac{FR}{\left(1/2\right)m{R}^2}=\frac{2F}{mR}$