---
title: "A rigid cylinder of mass \\(M\\) and radius \\(R\\) has an internal mass distribution that yields a rotational inertia \\(I = \\beta M R^2\\) about its central axis, where \\(\\beta > 0\\) is a dimensionless parameter. The cylinder is released from rest on a plane inclined at an angle \\(\\theta\\) above the horizontal and rolls down the incline without slipping. Which of the following correctly describes the magnitude of the linear acceleration \\(a\\) of the cylinder’s center of mass and the magnitude of the static friction force \\(f_s\\) exerted on the cylinder in the theoretical limit as \\(\\beta \\to \\infty\\)?"
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url: "https://nerd-notes.com/ubq/120904/"
date_modified: "2026-08-23T04:44:12+00:00"
---

# A rigid cylinder of mass \(M\) and radius \(R\) has an internal mass distribution that yields a rotational inertia \(I = \beta M R^2\) about its central axis, where \(\beta > 0\) is a dimensionless parameter. The cylinder is released from rest on a plane inclined at an angle \(\theta\) above the horizontal and rolls down the incline without slipping. Which of the following correctly describes the magnitude of the linear acceleration \(a\) of the cylinder’s center of mass and the magnitude of the static friction force \(f_s\) exerted on the cylinder in the theoretical limit as \(\beta \to \infty\)?

A rigid cylinder of mass \(M\) and radius \(R\) has an internal mass distribution that yields a rotational inertia \(I = \beta M R^2\) about its central axis, where \(\beta > 0\) is a dimensionless parameter. The cylinder is released from rest on a plane inclined at an angle \(\theta\) above the horizontal and rolls down the incline without slipping. Which of the following correctly describes the magnitude of the linear acceleration \(a\) of the cylinder's center of mass and the magnitude of the static friction force \(f_s\) exerted on the cylinder in the theoretical limit as \(\beta \to \infty\)?

![A right-triangular inclined plane resting on a flat horizontal line. The incline rises to the left at an angle labeled \(\theta\) relative to the horizontal base. A solid circular cylinder of radius \(R\) and mass \(M\) rests on the inclined surface. A radial dashed line extends from the center of the circle to its upper edge, labeled \(R\). The center of mass of the circle is marked with a small solid black dot labeled \(M\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460252-k2y0it.jpg)

- **A.** \(a \to g\sin\theta\) and \(f_s \to 0\)
- **B.** \(a \to 0\) and \(f_s \to 0\)
- **C.** \(a \to g\sin\theta\) and \(f_s \to Mg\sin\theta\)
- **D.** \(a \to 0\) and \(f_s \to Mg\sin\theta\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120904/*