Question

A rope is wound around 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 $30N$.

• A. $5m/s^2$
• B. $25m/s^2$
• C. $0.25rad/s^2$
• D. $25rad/s^2$

Answer 1

The correct option is D $25rad/s^2$

For hollow cylinder moment of inertia
$I=M{R}^2=3\times {0.4}^2$
Torque, $\begin{array}{}\tau =I\alpha & \text{(1)}\end{array}$

Torque about centre line of cylinder
$\begin{array}{}\tau =F\times R& \text{(2)}\end{array}$
From equation 1 and 2
$F\times R=I\alpha$
Angular acceleration $=\frac{F\times R}{M{R}^2}=\frac{30\times 0.4}{3\times (0.4{)}^2}$
$=\frac{100}{4}rad/s^2$
$=25rad/s^2$