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AP Physics C: Mechanics
2.10 Circular Motion
2.5 Newton’s Second Law
AdvancedMCQMathematicalConceptual16.3k
A schematic diagram showing a pendulum swinging in a vertical plane. At the top center, a small horizontal hatched support attaches to a pivot point. A straight solid line of length \(L\) extends downward and to the right at an angle \(\theta_0\) to the vertical dashed line, terminating in a solid circular bob of mass \(m\). A curved arrow indicates the swing path toward the lowest point directly below the pivot, where a second circular bob is drawn with a dashed outline. At this lowest position, a vertical solid line connects the dashed bob to the pivot. A single upward arrow labeled \(T\) originates from the center of the dashed bob along the string, and a single downward arrow labeled \(mg\) originates from the center of the dashed bob. No other labels, lines, text, or axes appear.
Pendulum released from rest at angle \(\theta_0\).
A simple pendulum consisting of a small bob of mass \(m\) attached to a light string of length \(L\) is released from rest at an angle \(\theta_0\) from the vertical, where \(0 < \theta_0 < 90^\circ\). The tension in the string at the lowest point of the swing can be separated into a static component \(T_{\text{stat}}\) that balances the component of gravity along the string, and a dynamic component \(T_{\text{dyn}}\) that provides the centripetal acceleration. In a second trial, the pendulum is released from rest from a larger initial angle \(\theta_0' > \theta_0\) (where \(\theta_0' < 90^\circ\)). Which row in the table correctly describes how \(T_{\text{stat}}\), \(T_{\text{dyn}}\), and the magnitude of the time rate of change of tension \(\left|\dfrac{dT}{dt}\right|\) at the lowest point compare to their values in the initial trial?

Static Component \(T_{\text{stat}}\)Dynamic Component \(T_{\text{dyn}}\)Magnitude of Rate of Change \(\left|\dfrac{dT}{dt}\right|\)
(A)IncreasesRemains the sameIncreases
(B)IncreasesIncreasesIncreases
(C)Remains the sameRemains the sameRemains the same
(D)Remains the sameIncreasesRemains the same

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