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  4. 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

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Q. 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

NTA AbhyasNTA Abhyas 2020System of Particles and Rotational Motion

Solution:

Moment of inertia $=\frac{1}{2} \, MR^{2}+mx^{2}$
Where $m=$ mass of insect,
and $x=$ distance of insect from centre.
Clearly, as the insect moves along the diameter of the disc, MI first decreases, then increases.
By conservation of angular momentum, angular speed first increases, then decreases.