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AP Physics C: Mechanics
7.5 Simple and Physical Pendulums
AdvancedMCQMathematical18.1k
A vertical diagram showing a slender rectangular rod of total length \(L\). The rod is oriented vertically. A small solid circular dot representing the center of mass is located at the geometric center of the rod and labeled \(\text{CM}\). Above the center of mass, a small open circle representing a horizontal pivot axis passes through the rod at a distance \(d\) from the center of mass. A vertical two-headed dimension arrow spans between the center of mass and the pivot, labeled \(d\). A full-length vertical dimension line spans the entire height of the rod on the right, labeled \(L\). A dashed vertical reference line extends along the center line of the rod. No other labels, lines, text, or axes appear.
Uniform rod suspended from a pivot at distance \(d\) from its center of mass.
A uniform thin rod of mass \(M\) and length \(L\) is suspended from a frictionless horizontal pivot located a distance \(d\) from the center of mass of the rod, where \(0 < d < \dfrac{L}{2}\). When displaced by a small angle and released from rest, the rod oscillates as a physical pendulum. In terms of \(L\), at what distance \(d\) from the center of mass is the period of oscillation minimized?

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