---
title: "An amusement park ride consists of a vertical hollow cylinder of radius \\(R\\) that rotates about a central vertical axis with a constant angular speed \\(\\omega\\). A rider of mass \\(m\\) stands against the interior vertical wall, and when the floor drops away, the rider remains pinned to the wall without sliding downward. If a second rider of mass \\(2m\\) enters the same cylinder, which of the following statements correctly compares the minimum angular speed \\(\\omega_{\\text{min}}\\) required to prevent the second rider from sliding down to that of the first rider, and provides the correct physical justification?"
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url: "https://nerd-notes.com/ubq/120597/"
date_modified: "2026-08-23T04:41:51+00:00"
---

# An amusement park ride consists of a vertical hollow cylinder of radius \(R\) that rotates about a central vertical axis with a constant angular speed \(\omega\). A rider of mass \(m\) stands against the interior vertical wall, and when the floor drops away, the rider remains pinned to the wall without sliding downward. If a second rider of mass \(2m\) enters the same cylinder, which of the following statements correctly compares the minimum angular speed \(\omega_{\text{min}}\) required to prevent the second rider from sliding down to that of the first rider, and provides the correct physical justification?

An amusement park ride consists of a vertical hollow cylinder of radius \(R\) that rotates about a central vertical axis with a constant angular speed \(\omega\). A rider of mass \(m\) stands against the interior vertical wall, and when the floor drops away, the rider remains pinned to the wall without sliding downward. If a second rider of mass \(2m\) enters the same cylinder, which of the following statements correctly compares the minimum angular speed \(\omega_{\text{min}}\) required to prevent the second rider from sliding down to that of the first rider, and provides the correct physical justification?

![A vertical cylinder with an open top, shown in a cutaway perspective view. A vertical dashed line passes through the center of the cylinder, representing the axis of rotation. A curved arrow at the top of the dashed axis indicates rotation with angular speed \(\omega\). A horizontal line segment extends from the central axis to the right wall of the cylinder, labeled \(R\). A small rectangular block representing a rider of mass \(m\) rests flush against the right interior vertical wall of the cylinder. No floor is present beneath the block. No force vectors, coordinate axes, or additional labels appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460111-sWWbju.jpg)

- **A.** The minimum angular speed \(\omega_{\text{min}}\) is greater for the second rider because the downward gravitational force is doubled, while the normal force provided by the wall is independent of the rider's mass.
- **B.** The minimum angular speed \(\omega_{\text{min}}\) is less for the second rider because the greater mass doubles the normal force at any given rotation rate, providing excess static friction to counteract gravity at lower speeds.
- **C.** The minimum angular speed \(\omega_{\text{min}}\) is the same for both riders because the coefficient of static friction \(\mu_s\) between the wall and the rider increases proportionally with the rider's weight.
- **D.** The minimum angular speed \(\omega_{\text{min}}\) is the same for both riders because both the downward gravitational force and the radial normal force scale linearly with the rider's mass.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120597/*