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AP Physics C: Mechanics
6.2 Torque and Work
6.1 Rotational Kinetic Energy
IntermediateMCQMathematicalProportional Analysis21.8k
A perspective view of a circular disk of uniform thickness mounted vertically on a horizontal central axle. The central axle is represented by a thin cylinder passing perpendicularly through the center of the circular face of the disk and supported at its ends by two small rectangular stands. The disk is labeled with rotational inertia \(I\). A curved arrow is drawn along the outer circumference of the disk indicating the direction of angular acceleration, labeled \(\tau(\theta)\). A horizontal dashed line extends radially from the center of the disk to its rim, and a solid radial line extends from the center at an angle above the dashed line, with the arc between them labeled \(\theta\). No other labels, lines, text, or axes appear.
A wheel of rotational inertia \(I\) driven by an angle-dependent torque \(\tau(\theta)\).
A uniform wheel of known rotational inertia \(I\) is mounted on a frictionless horizontal axle and is initially at rest at angular position \(\theta = 0\). A motor exerts a variable net torque on the wheel given by \(\tau(\theta) = C\theta^2\), where \(C\) is a positive constant and \(\theta\) is the angular displacement in radians. An experimenter measures the angular speed \(\omega\) of the wheel at various values of \(\theta\). To determine the value of \(C\) from the slope \(S\) of a linear graph, which quantities should be plotted on the vertical and horizontal axes, and what is the relationship between \(C\) and \(S\)?

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