Question

A rope of negligible mass is wound round a hollow cylinder of mass $3kg$ and radius $40cm$. What is angular acceleration (in $rad/s^2$ ) of the cylinder if the rope is pulled with a force of $30N$ ? Assume that there is no slipping.

Answer 1

Answer: 25

Here $M=3kg,R=40cm=0.40m,F=30N$
Torque, $\tau =F\times R=30\times 0.40=12Nm$
M.I. of the hollow cylinder about it own axis,
$I=M{R}^2=3\times (0.40{)}^2=0.48kg{m}^2$
Angular acceleration,
$\alpha =\frac{\tau }{I}=\frac{12}{0.48}=25rad{s}^{-2}$