---
title: "A uniform slender rod of mass \\(M\\) and length \\(L\\) is pivoted at one end about a frictionless, horizontal axle. The rod is released from rest in a horizontal position and swings downward in a vertical plane. Let \\(\\theta\\) represent the angle through which the rod has rotated below the horizontal, such that \\(\\theta = 0\\) at release and \\(\\theta = \\pi/2\\) when the rod is vertical. Which of the following graphs best represents the magnitudes of the radial force \\(F_r\\) (directed along the rod toward the pivot) and tangential force \\(F_t\\) (directed perpendicular to the rod) exerted by the pivot on the rod as functions of \\(\\theta\\)?"
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url: "https://nerd-notes.com/ubq/120888/"
date_modified: "2026-08-23T04:44:10+00:00"
---

# A uniform slender rod of mass \(M\) and length \(L\) is pivoted at one end about a frictionless, horizontal axle. The rod is released from rest in a horizontal position and swings downward in a vertical plane. Let \(\theta\) represent the angle through which the rod has rotated below the horizontal, such that \(\theta = 0\) at release and \(\theta = \pi/2\) when the rod is vertical. Which of the following graphs best represents the magnitudes of the radial force \(F_r\) (directed along the rod toward the pivot) and tangential force \(F_t\) (directed perpendicular to the rod) exerted by the pivot on the rod as functions of \(\theta\)?

A uniform slender rod of mass \(M\) and length \(L\) is pivoted at one end about a frictionless, horizontal axle. The rod is released from rest in a horizontal position and swings downward in a vertical plane. Let \(\theta\) represent the angle through which the rod has rotated below the horizontal, such that \(\theta = 0\) at release and \(\theta = \pi/2\) when the rod is vertical. Which of the following graphs best represents the magnitudes of the radial force \(F_r\) (directed along the rod toward the pivot) and tangential force \(F_t\) (directed perpendicular to the rod) exerted by the pivot on the rod as functions of \(\theta\)?

![A schematic diagram showing a uniform rod of length \(L\) and mass \(M\) attached to a fixed pivot at its left end. A horizontal dashed reference line extends to the right from the pivot. The rod is tilted downward below the horizontal reference line at an angle \(\theta\). An arc with an arrow indicates the angle \(\theta\) between the horizontal dashed line and the rod. A solid dot marks the center of mass of the rod at a distance \(L/2\) from the pivot. A small circular pin represents the frictionless pivot at the top left. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460249-9yTvNF.jpg)

- **A.** Graph A
- **B.** Graph B
- **C.** Graph C
- **D.** Graph D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120888/*