---
title: "A uniform rod of length \\( L \\) and mass \\( M \\) is free to rotate about one end, as shown in the diagram. The free end is released from rest at a horizontal position, as shown. The pivot point is supported by a stand so that only the free end can move. The moment of inertia of a rod about its end is \\(\\tfrac{1}{3} M L^{2}\\)."
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url: "https://nerd-notes.com/ubq/103999/"
date_modified: "2025-10-28T03:49:47+00:00"
---

# A uniform rod of length \( L \) and mass \( M \) is free to rotate about one end, as shown in the diagram. The free end is released from rest at a horizontal position, as shown. The pivot point is supported by a stand so that only the free end can move. The moment of inertia of a rod about its end is \(\tfrac{1}{3} M L^{2}\).

A uniform rod of length \( L \) and mass \( M \) is free to rotate about one end, as shown in the diagram. The free end is released from rest at a horizontal position, as shown. The pivot point is supported by a stand so that only the free end can move. The moment of inertia of a rod about its end is \(\tfrac{1}{3} M L^{2}\).

![nerd notes ubq 103999](https://nerd-notes.com/wp-content/uploads/2025/10/rotating-bar-angular-speed-derivation-problem-nerd-notes.png)

**Part a)** Draw a Free Body Diagram for the rod immediately after the free end is released. *(3 points)*

**Part b)** Derive expressions for the angular and tangential accelerations of the center of mass of the rod immediately after the free end is released. Express your answers in terms of \( M \), \( L \), and \( g \). *(3 points)*

**Part c)** Describe qualitatively how the angular acceleration of the rod changes as the rod rotates, from its starting position until it is vertical (assume there is a hole in the floor so the rod does not hit anything). Justify your answer. *(3 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/103999/*