A flat disc of mass m=1.8kg, radius r=0.2m lies on a frictionless horizontal table. A string wound around the cylindrical surface of the disc exerts a force of 3N in the northly direction (Fig.) Find the angular acceleration (in  $rad/s^2$ ) (nearest integer) about the centre of mass.

the equations of motion are : $F=ma, Fr=I\alpha$

Where $I=m{r}^2/2,giving, a=\frac{F}{m}=1.7m/s^2, \alpha =\frac{2F}{mr}=17rad/s^2$

The direction of a is same as that of f. It is seen that $a\ne \alpha r$ . This is because as the disc lies on its flat surface the two motions are not related even through they are due to the same force.