Question

A rope of negligible mass is wound around a hollow cylinder of mass 3 kg and radius 40 cm , what is the angular acceleration of the of the cylinder , if rope is pulled with a force of 30N ? What is the linear acceleration of the rope ? Assume there is no slipping .

Answer 1

The only external force being applied on the cylinder is that of $30N$
$\therefore F_{ext}=30N=m{a}_{C}M$ where $a_{CM}$ is the linear accelertaion of the centre of mass.
$\therefore a_{CM}=\frac{30}{3}=10m/se{c}^2$
Angulae acceleration ${\alpha }_{CM}=\frac{\tau }{l}=\frac{30\times r}{m{r}^2}$
=$\frac{30}{mr}=\frac{30}{3\times \left(0.4\right)}=25rad/se{c}^2$