---
title: "A physical pendulum consists of a uniform thin rod of mass \\(M\\) and length \\(L\\) pivoted frictionlessly at one end. The rod is held at an angle \\(\\theta_0\\) relative to the downward vertical and released from rest. What is the magnitude of the vertical force exerted by the pivot on the rod as the rod passes through the vertical equilibrium position?"
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url: "https://nerd-notes.com/ubq/121011/"
date_modified: "2026-08-23T04:45:11+00:00"
---

# A physical pendulum consists of a uniform thin rod of mass \(M\) and length \(L\) pivoted frictionlessly at one end. The rod is held at an angle \(\theta_0\) relative to the downward vertical and released from rest. What is the magnitude of the vertical force exerted by the pivot on the rod as the rod passes through the vertical equilibrium position?

A physical pendulum consists of a uniform thin rod of mass \(M\) and length \(L\) pivoted frictionlessly at one end. The rod is held at an angle \(\theta_0\) relative to the downward vertical and released from rest. What is the magnitude of the vertical force exerted by the pivot on the rod as the rod passes through the vertical equilibrium position?

![A schematic diagram showing a physical pendulum. A small dark circular pivot is fixed to a horizontal support line at the top center. A straight, narrow uniform rod of length \(L\) extends downward and to the right at an angle \(\theta_0\) from a vertical dashed reference line that extends straight down from the pivot. The angle between the vertical dashed reference line and the rod is labeled \(\theta_0\) with a curved arc. A small dot at the geometric midpoint of the rod represents its center of mass. A curved dashed arrow near the lower end of the rod indicates the direction of motion toward the vertical dashed line. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460311-1cPWF4.jpg)

- **A.** \(Mg\left(\dfrac{5}{2} - \dfrac{3}{2}\cos\theta_0\right)\)
- **B.** \(Mg\left(3 - 2\cos\theta_0\right)\)
- **C.** \(Mg\left(4 - 3\cos\theta_0\right)\)
- **D.** \(\dfrac{3}{2}Mg\left(1 - \cos\theta_0\right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121011/*