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(D) The system consists of the circular stage and the tortoise. Since there are no external torques acting on the system about the axis of rotation,th

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(D) The system consists of the circular stage and the tortoise. Since there are no external torques acting on the system about the axis of rotation,the total angular momentum $J$ of the system is conserved.$J = I \omega = 	ext{constant}$,where $I$ is the moment of inertia of the system and $\omega$ is the angular velocity.The moment of inertia $I$ of the system is given by $I = I_{	ext{stage}} + I_{	ext{tortoise}} = I_{	ext{stage}} + m r^2$,where $m$ is the mass of the tortoise and $r$ is its perpendicular distance from the axis of rotation.As the tortoise moves along a chord of the circular stage,its distance $r$ from the centre (axis of rotation) first decreases until it reaches the point on the chord closest to the centre,and then it increases as it moves towards the other end of the chord.Since $I = I_{	ext{stage}} + m r^2$,the moment of inertia $I$ first decreases as $r$ decreases,and then increases as $r$ increases.From the conservation of angular momentum,$\omega = J / I$. Since $J$ is constant,$\omega$ is inversely proportional to $I$. Therefore,as $I$ decreases,$\omega$ increases,and as $I$ increases,$\omega$ decreases.Thus,the angular velocity $\omega(t)$ first increases and then decreases. This corresponds to the behavior shown in graph $D$.

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