A circular platform is free to rotate in a horizontal plane about a vertical axis passing through its center. 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 the 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

The angular momentum (Z) of the system is conserved, i.e. L= I $ω$ = constant
When the tortoise walks along a chord, it first moves closer to the center and then away from the center. Hence, M.I. first decreases and then increases. As a result, $ω$ will first increase and then decrease. Also the change in $ω$ will be non-linear function of time.

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