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AP Physics C: Mechanics
7.5 Simple and Physical Pendulums
5.4 Rotational Inertia
Multi-Unit
AdvancedMCQMathematical13.8k
A vertical rectangular bar representing a uniform rod of length \(L\) and mass \(M\). The center of mass is indicated by a black dot at the vertical midpoint of the bar, labeled \(\text{CM}\). Above the center of mass, three small circles along the centerline represent pivot points: the first circle is located at distance \(d_1\) above \(\text{CM}\), the second circle is located at distance \(d_2\) above \(\text{CM}\), and the third circle is at the top end of the bar at distance \(d_3\) above \(\text{CM}\). Vertical double-headed dimension arrows extend from the horizontal level of \(\text{CM}\) to each pivot point, labeled \(d_1 = \dfrac{L}{6}\), \(d_2 = \dfrac{L}{3}\), and \(d_3 = \dfrac{L}{2}\). A dashed vertical line marks the central longitudinal axis of the rod. No other labels, lines, text, or axes appear.
A uniform rod with three pivot locations at distances \(d_1\), \(d_2\), and \(d_3\) from its center of mass.
A thin, uniform rod of mass \(M\) and length \(L\) is suspended from a horizontal frictionless axle perpendicular to the rod and allowed to oscillate with small angular amplitude. Three different pivot locations along the rod are tested, located at distances \(d_1 = \dfrac{L}{6}\), \(d_2 = \dfrac{L}{3}\), and \(d_3 = \dfrac{L}{2}\) from the center of mass of the rod, resulting in oscillation periods \(T_1\), \(T_2\), and \(T_3\), respectively. Which of the following correctly ranks the periods of oscillation?

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