Question 598: Centre of Mass and Rotational Motion

Question

A rope is wound around a solid cylinder of mass 1 kg and radius 0.4 m . What is the angular acceleration of cylinder, if the rope is pulled with a force of 25 N ? (Cylinder is rotating about its own axis.)

Accepted Answer

Consider the free body diagram shown below,
,
The torque about centre of cylinder,
$$	au=F 	imes r=25 	imes 0.4=10 \mathrm{Nm}$$
The relation between angular acceleration ( $\alpha$ ) and torque $(	au)$ is given as
$$\begin{aligned}
	au & =l \alpha \
& =\frac{M r^2}{2} \alpha \quad(	ext { for solid cylinder, } I=\frac{M R^2}{2}) \
10 & =\frac{1 	imes(0.4)^2}{2} \alpha \Rightarrow \alpha=125 \mathrm{rad} / \mathrm{s}^2
\end{aligned}$$

Answer

$125 \mathrm{~rad} / \mathrm{s}^2$

Answer

$10 \mathrm{~rad} / \mathrm{s}^2$

Answer

$1 \mathrm{~rad} / \mathrm{s}^2$

Answer

$50 \mathrm{~rad} / \mathrm{s}^2$

Centre of Mass and Rotational Motion

A rope is wound around a solid cylinder of mass 1 kg and radius 0.4 m . What is the angular acceleration of cylinder, if the rope is pulled with a force of 25 N ? (Cylinder is rotating about its own axis.)

Choose the correct answer: