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AP Physics C: Mechanics
6.2 Torque and Work
6.1 Rotational Kinetic Energy
IntermediateMCQMathematical19k
A shape-focused graph with bare axes showing net torque \(\tau\) on the vertical axis versus angular displacement \(\theta\) on the horizontal axis. The horizontal axis has a tick mark at \(0\) at the origin and a tick mark at \(1\) at the right. The vertical axis has a tick mark at \(0\) at the origin and a tick mark at \(\tau_0\) near the top. Three distinct curves span from \(\theta = 0\) to \(\theta = 1\). The first curve is a horizontal solid line at height \(\tau_0\) running from \(\theta = 0\) to \(\theta = 1\), labeled 1. The second curve is a straight dashed line from the origin \((0,0)\) to the point \((1, \tau_0)\), labeled 2. The third curve is a dotted line starting at \((0,0)\) that curves upward concavely downward to meet the point \((1, \tau_0)\) with zero slope, labeled 3. No other labels, lines, text, or axes appear.
Net torque as a function of angular displacement for three separate trials.
A rigid rotor with rotational inertia \(I\) is initially at rest at angular position \(\theta = 0\). In three separate trials, the rotor is turned from \(\theta = 0\) to \(\theta = 1\text{ rad}\) by a single applied torque: Trial 1 uses constant torque \(\tau_1(\theta) = \tau_0\), Trial 2 uses linearly increasing torque \(\tau_2(\theta) = \tau_0\theta\), and Trial 3 uses sinusoidal torque \(\tau_3(\theta) = \tau_0\sin\left(\dfrac{\pi}{2}\theta\right)\). Which row in the table correctly identifies the work delivered in Trial 2 (\(W_2\)), the work delivered in Trial 3 (\(W_3\)), and the ranking of the final rotational kinetic energies \(K_1, K_2, K_3\) of the rotor at \(\theta = 1\text{ rad}\)?

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