Question

A wheel of mass $10kg$ and radius $0.2m$ is rotating at an angular speed of $100rpm,$ when the motion is turned off. Neglecting the friction at the axis, the force that must be applied tangentially to the wheel to bring it to rest in $10$ rev is approximately $o.xN$. Find $x$. Assume wheel to be a disc.

Answer 1

${\omega }^2={\omega }_0^2-2\alpha \theta$
$0=(\frac{100}{60}\times 2\pi {)}^2-2\alpha (10\times 2\pi )$
$\therefore \alpha =0.87N$
$=\frac{\tau }{I}$
$=\frac{F.R}{\frac{1}{2}m{R}^2}$
$F=\left(0.87\right)\left(0.5mR\right)$
$=\left(0.87\right)\left(0.5\right)\left(10\right)\left(0.2\right)$
$=0.87N$