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AP Physics C: Mechanics
2.10 Circular Motion
2.7 Kinetic and Static Friction
2.5 Newton’s Second Law
AdvancedMCQProportional AnalysisConceptual18.6k
A side cross-sectional schematic diagram of a vertical hollow cylinder. A vertical dashed line indicates the central rotation axis. A curved arrow labeled \(\omega\) loops around the top of the axis to show rotation. The cylinder has two vertical solid side walls and a horizontal floor outline. A horizontal double-headed arrow extends from the central axis to the right vertical wall, labeled \(R\). On the inner surface of the right vertical wall, a solid rectangular block represents the person of mass \(m\). A horizontal arrow originates at the wall-block interface and points left toward the central axis, labeled \(F_N\). A vertical arrow originates at the center of the block and points vertically upward, labeled \(f_s\). A second vertical arrow originates at the center of the block and points vertically downward, labeled \(mg\). No other labels, lines, text, or axes appear.
Cross-sectional schematic of a rider against the vertical wall of a rotating cylinder.
In an amusement park rotor ride, a person of mass \(m\) stands against the rough, vertical interior wall of a hollow cylinder of radius \(R\) that rotates about its central vertical axis at a constant angular speed \(\omega\). When the floor beneath the person drops away, the person remains pinned at a constant height along the wall due to static friction with coefficient \(\mu_s\). Applying Newton's second law in the radial and vertical directions yields the minimum angular speed required to prevent downward slipping as \(\omega_{\text{min}} = \sqrt{\dfrac{g}{\mu_s R}}\). Which of the following statements correctly describes the behavior of the system in the theoretical limit where wall friction drops to zero (\(\mu_s \to 0\)), and provides the correct physical justification?

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