A circular platform is free to rotate in a ho | vedclass

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(B) The angular momentum $(L)$ of the system is conserved because there are no external torques acting on the system about the axis of rotation. Thus,

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(B) The angular momentum $(L)$ of the system is conserved because there are no external torques acting on the system about the axis of rotation. Thus, $L = I\omega = 	ext{constant}$.As the tortoise moves along a chord of the circular platform, its distance $(r)$ from the center of rotation changes. Specifically, the tortoise starts at the edge, moves towards the center (decreasing $r$), reaches the point on the chord closest to the center, and then moves back towards the edge (increasing $r$).The moment of inertia $(I)$ of the system is given by $I = I_{	ext{platform}} + m r^2$, where $m$ is the mass of the tortoise. As the tortoise moves towards the center, $r$ decreases, so $I$ decreases. As it moves away, $r$ increases, so $I$ increases.Since $L = I\omega$ is constant, $\omega = L/I$. When $I$ decreases, $\omega$ increases, and when $I$ increases, $\omega$ decreases. Therefore, the angular velocity $\omega(t)$ will first increase and then decrease. The relationship between $r$ and time $t$ is $r^2 = r_{	ext{min}}^2 + (vt)^2$, making $I$ a quadratic function of time, which implies that $\omega(t) = L / (I_0 + m(r_{	ext{min}}^2 + v^2t^2))$ is a non-linear function of time. This corresponds to a smooth, curved graph.

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