A circular platform is free to rotate in a horizontal plane about a vertical axis passing through its centre. A tortoise is sitting at the edge of the platform. Now the platform is given an angular velocity $ω_{0}$ When the tortoise moves along a chord of platform with a constant velocity (with respect to the platform), the angular velocity of the platform $ω$ (t) will vary with time t as

Moderate

Solution

Since no external torque is acting on the system , its angular momentum remains conserved . So I $ω = c o n s \tan t .$ During motion along chord, the distance of tortoise from centre decreases initially and then increases' So, the moment of inertia first decreases and then increases. Hence $ω$ initially increase and then decrease. Also variation in $ω$ is non-linear.

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