A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is…
A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc:
continuously decreases
continuously increases
first increases and then decreases
remains unchanged
Solution
$
\tau=0
$
Angular momentum is conserve
$
\mathrm{I}_1 \omega_1=\mathrm{I}_2 \omega_2 \Rightarrow \omega_2=\frac{\mathrm{I}_1 \omega_1}{\mathrm{I}_2}
$
$\mathrm{I}_2$ first decreases and then increases
$\therefore \omega$ first increases and then decreases