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 ω₀. 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
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Question

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 ω₀. 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

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G1 Physics · Accepted Answer

No external torque acts about the vertical axis, so angular momentum is conserved: I(t)ω(t)=constant. As the tortoise moves from the rim toward the interior along the chord, its distance from the axis first decreases and then increases, so total I first decreases and then increases. Hence ω first increases and then decreases symmetrically, matching Image 2 (option B).