Question

A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N? What is the linear acceleration of the rope?

Answer 1

Mass of the hollow cylinder, m = 3 kg
Radius of the hollow cylinder, r = 40 cm = 0.4 m
Applied force, F = 30 N
The moment of inertia of the hollow cylinder about its geometric axis:
$I=m{r}^2=3\times (0.4{)}^2=0.48kg{m}^2$
Torque, $\tau =Fr=30\times 0.4=12Nm$
For angular acceleration $\alpha$, torque is also given by the relation:
$\tau =I\alpha \alpha =\frac{\tau }{I}=\frac{12}{0.48}=25rad{s}^{-2}$
Linear acceleration $=r\alpha =0.4\times 25=10m{s}^{-2}$