Question

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

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

Answer 1

The correct option is C $10$ $rad/s^2$

$\tau =1\alpha$
$\therefore r\times F=\frac{M{r}^2}{2}\alpha$
$\frac{2F}{Mr}=\alpha (F=mgr=radius)$
$\Rightarrow \frac{2\times 25}{20\times 1/4}=\alpha$
$\Rightarrow \alpha =10$ $rad/s^2$