Question

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 with constant speed $v$ along a diameter of the disc to reach it's other end. During the journey of the insect, the angular speed of the disc will

• A. Remains unchanged
• B. Continously decreases
• C. Continously increases
• D. First increase and then decrease.

Answer 1

The correct option is D First increase and then decrease.

$\Rightarrow$The external force on system is weight of disc, which passes through it's centre and weight of insect $mg$ is parallel to axis of rotation, so ${\tau }_{\text{ext}}=0$, hence angular momentum will be conserved for system.
$L_i=L_f$
From the shown figure, as the insect crawl on the diameteric line towards the axis of rotation, it's distance from axis decreases and in next half as it crosses then distance from centre ($r$) increases

The angular momentum of insect is given by $L$;
$L=I\omega$
$L=m{r}^2\omega$
Since, $r$ first decreases then increases.
$\Rightarrow$ For insect, $L$ decreases first, then increases.
$\therefore$ To conserve system's angular momentum, angular speed of disc ($\omega$) will increase first, then decreases.