---
title: "A uniform thin rod of mass \\(M\\) and length \\(L\\) is pivoted at one end about a frictionless vertical axle so that it can rotate freely in a horizontal plane. The rod is initially at rest. A lump of clay of mass \\(m\\) travels horizontally with speed \\(v_0\\) perpendicular to the rod and strikes the rod at its free end, sticking to it. Which of the following expressions represents the angular speed \\(\\omega\\) of the rod-clay system immediately after the collision?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/120894/"
date_modified: "2026-08-23T04:44:11+00:00"
---

# A uniform thin rod of mass \(M\) and length \(L\) is pivoted at one end about a frictionless vertical axle so that it can rotate freely in a horizontal plane. The rod is initially at rest. A lump of clay of mass \(m\) travels horizontally with speed \(v_0\) perpendicular to the rod and strikes the rod at its free end, sticking to it. Which of the following expressions represents the angular speed \(\omega\) of the rod-clay system immediately after the collision?

A uniform thin rod of mass \(M\) and length \(L\) is pivoted at one end about a frictionless vertical axle so that it can rotate freely in a horizontal plane. The rod is initially at rest. A lump of clay of mass \(m\) travels horizontally with speed \(v_0\) perpendicular to the rod and strikes the rod at its free end, sticking to it. Which of the following expressions represents the angular speed \(\omega\) of the rod-clay system immediately after the collision?

![A top-down schematic view showing a thin rectangular uniform bar of length \(L\) and mass \(M\) oriented vertically. At the top end of the bar, a small solid circular dot represents a fixed pivot. At the bottom end of the bar, a small circular object representing a clay lump of mass \(m\) has a horizontal vector arrow of length 2 cm labeled \(v_0\) pointing directly toward the right, perpendicular to the bottom tip of the rod. A vertical dimension line with boundary ticks spans from the pivot at the top end to the bottom end and is labeled \(L\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460250-2qgnwG.jpg)

- **A.** \(\dfrac{m v_0}{(M + m)L}\)
- **B.** \(\dfrac{3m v_0}{ML}\)
- **C.** \(\dfrac{3m v_0}{(M + 3m)L}\)
- **D.** \(\dfrac{12m v_0}{(M + 12m)L}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120894/*