Physics - Rotation Question with Solution | TestHub

During the motion of the object, there is only one force tension which is acting towards a fixed point (centre of the table - disc). So that motion is under the effect to central force and thus, angular momentum will be conserved. At any radial distance,$\mathrm{r}$is$\mathrm{L}={\mathrm{m\omega r}}^2$

$\frac{\mathrm{dL}}{\mathrm{dr}}={\mathrm{mr}}^2\frac{\mathrm{d\omega }}{\mathrm{dr}}+\mathrm{m\omega }\left(2\mathrm{r}\right)=0$

So,$\frac{\mathrm{d\omega }}{\mathrm{dr}}=\mathrm{ }-\frac{2\mathrm{\omega }}{\mathrm{r}}$