---
title: "A uniform slender rod of mass \\(M\\) and length \\(L\\) is pivoted at its top end about a frictionless horizontal axle attached to a ceiling. The rod is displaced to the right by an angle \\(\\theta_0\\) from the vertical, where \\(0 < \\theta_0 < \\dfrac{\\pi}{2}\\), and released from rest. Immediately after release, which of the following correctly indicates the direction of the horizontal force exerted by the pivot on the rod and compares the magnitude of the tangential acceleration of the free end of the rod, \\(a_{\\text{end}}\\), to \\(g \\sin\\theta_0\\)?"
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url: "https://nerd-notes.com/ubq/124423/"
date_modified: "2026-09-28T14:05:18+00:00"
---

# A uniform slender rod of mass \(M\) and length \(L\) is pivoted at its top end about a frictionless horizontal axle attached to a ceiling. The rod is displaced to the right by an angle \(\theta_0\) from the vertical, where \(0 < \theta_0 < \dfrac{\pi}{2}\), and released from rest. Immediately after release, which of the following correctly indicates the direction of the horizontal force exerted by the pivot on the rod and compares the magnitude of the tangential acceleration of the free end of the rod, \(a_{\text{end}}\), to \(g \sin\theta_0\)?

A uniform slender rod of mass \(M\) and length \(L\) is pivoted at its top end about a frictionless horizontal axle attached to a ceiling. The rod is displaced to the right by an angle \(\theta_0\) from the vertical, where \(0 < \theta_0 < \dfrac{\pi}{2}\), and released from rest. Immediately after release, which of the following correctly indicates the direction of the horizontal force exerted by the pivot on the rod and compares the magnitude of the tangential acceleration of the free end of the rod, \(a_{\text{end}}\), to \(g \sin\theta_0\)?

![A horizontal ceiling line is drawn at the top with short diagonal hatching marks along its upper surface. A small circular pivot is fixed directly beneath the center of the ceiling line. A straight, slender rod of length \(L\) is attached at its top end to the pivot and extends downward and to the right at an angle \(\theta_0\) relative to the vertical. A vertical dashed reference line extends downward from the pivot. An arc with an arrow indicates the angle \(\theta_0\) between the vertical dashed line and the rod. The center of mass of the rod is marked with a small dot at the midpoint along its length. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604318-zHYETP.jpg)

- **A.** Horizontal force: To the right ; Tangential acceleration: Less than \(g \sin\theta_0\)
- **B.** Horizontal force: To the right ; Tangential acceleration: Greater than \(g \sin\theta_0\)
- **C.** Horizontal force: To the left ; Tangential acceleration: Greater than \(g \sin\theta_0\)
- **D.** Horizontal force: To the left ; Tangential acceleration: Less than \(g \sin\theta_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124423/*