---
title: "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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url: "https://nerd-notes.com/ubq/124057/"
date_modified: "2026-09-28T13:30:17+00:00"
---

# 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?

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?

![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.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790602216-YxdqGJ.jpg)

- **A.** In the limit \(\mu_s \to 0\), \(\omega_{\text{min}} \to \infty\), meaning that the person can remain stationary relative to the wall at an arbitrarily high angular speed because the immensely large normal force provides an upward reaction force that balances the person's weight.
- **B.** In the limit \(\mu_s \to 0\), the normal force \(F_N \to 0\) for any finite \(\omega\) because static friction is required to press the person against the wall; consequently, centripetal acceleration cannot be maintained and the person leaves the wall tangentially.
- **C.** In the limit \(\mu_s \to 0\), \(\omega_{\text{min}} \to \infty\), indicating that no finite angular speed can prevent downward sliding because the normal force acts strictly perpendicular to the vertical wall and cannot provide an upward vertical force component to counteract gravity.
- **D.** In the limit \(\mu_s \to 0\), the person remains suspended at any angular speed where the centripetal force exceeds the person's weight (\(m R \omega^2 > mg\)), because the net contact force tilts upward to support the person against gravity.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124057/*