Question

Consider a $20\,\,kg$ uniform circular disk of radius $0.2\,\,m$. It is pin supported at its center and is at rest initially. The disk is acted upon by a constant force $F =20\,\,N$ through a massless string wrapped around its periphery as shown in the figure.

Suppose the disk makes n number of revolutions to attain an angular speed of $50 \,rad\,s ^{-1}$. The value of $n$, to the nearest integer, is_____ [Given : In one complete revolution, the disk rotates by $6.28\,\,rad\,]$

Answer 1

$\alpha=\frac{\tau}{ I }=\frac{ F \cdot R .}{ mR ^{2} / 2}=\frac{2 F }{ mR }$
$\alpha=\frac{2 \times 200}{20 \times(0.2)}=10 rad / s ^{2}$
$\omega^{2}=\omega_{0}^{2}+2 \alpha \Delta \theta$
$(50)^{2}=0^{2}+2(10) \Delta \theta\,\Rightarrow \,\Delta \theta=\frac{2500}{20}$
$\Delta \theta=125\,\,rad$
No. of revolution $=\frac{125}{2 \pi} \approx 20$ revolution