Question

A cord is wound over the rim of a flywheel of mass $20kg$ and radius $25cm$ . A mass $2.5kg$ attached to the cord is allowed to fall under gravity. Calculate the angular acceleration of the flywheel.

• A. $25rad/s^2$
• B. $20rad/s^2$
• C. $10rad/s^2$
• D. $5rad/s^2$

Answer 1

Answer: (C)

Given $M=20kg$
$R=0.25cm$
$R=\frac{1}{4}m$
$F=mg$
$=2.5\times 10=25N$
Torque $=F\times R$
$=25\times \frac{1}{4}$
$=\frac{25}{4}$
Moment of inertia $=\frac{1}{2}M{R}^2$
$=\frac{1}{2}\times 20\times (\frac{1}{4}{)}^2$
$=\frac{5}{8}$
We have $\tau =I\alpha$
$\therefore$ Angular acceleration of flywheel
$\alpha =\frac{\tau }{I}$
$=\frac{25/4}{5/8}$
$\alpha =10rad/s^2$