Question

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

Answer 1

The moment of inertia of the hollow cylinder about its geometric axis:

$I=m{r}^2=3\times {0.4}^{2}kg{m}^2$

The Torque developed is given by:

$\tau =rF=0.4\times 30Nm=12Nm$

We know that the relation between the torque and angular acceleration is:

$\tau =I\alpha$

$⟹\alpha =25rad{s}^{-2}$

Thus linear acceleration$\left(a\right)=r\alpha =0.4\times 25m/s^2=10m/s^2$