---
title: "A uniform thin rod of mass \\(M\\) and length \\(L\\) lies at rest on a frictionless horizontal table and is attached to a frictionless vertical pivot at one end. A small projectile of mass \\(m\\) moves horizontally across the table with constant speed \\(v_0\\) along a path perpendicular to the rod and strikes the free end, becoming permanently embedded in it. In the limit where the projectile is extremely massive compared to the rod (\\(m \\gg M\\)), what is the angular speed of the system immediately after the collision?"
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url: "https://nerd-notes.com/ubq/120937/"
date_modified: "2026-08-23T04:44:25+00:00"
---

# A uniform thin rod of mass \(M\) and length \(L\) lies at rest on a frictionless horizontal table and is attached to a frictionless vertical pivot at one end. A small projectile of mass \(m\) moves horizontally across the table with constant speed \(v_0\) along a path perpendicular to the rod and strikes the free end, becoming permanently embedded in it. In the limit where the projectile is extremely massive compared to the rod (\(m \gg M\)), what is the angular speed of the system immediately after the collision?

A uniform thin rod of mass \(M\) and length \(L\) lies at rest on a frictionless horizontal table and is attached to a frictionless vertical pivot at one end. A small projectile of mass \(m\) moves horizontally across the table with constant speed \(v_0\) along a path perpendicular to the rod and strikes the free end, becoming permanently embedded in it. In the limit where the projectile is extremely massive compared to the rod (\(m \gg M\)), what is the angular speed of the system immediately after the collision?

![A schematic overhead diagram showing a horizontal uniform thin rod of length \(L\) and mass \(M\). The left end of the rod is attached to a small fixed circular pivot labeled Pivot. A dimension line with arrows spans the length of the rod and is labeled \(L\). Near the right free end of the rod, a small solid circle representing a projectile of mass \(m\) has a straight arrow pointing perpendicularly upward toward the rod tip, labeled \(v_0\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460264-idiHbQ.jpg)

- **A.** \(0\)
- **B.** \(\dfrac{v_0}{3L}\)
- **C.** \(\dfrac{v_0}{L}\)
- **D.** \(\dfrac{3v_0}{L}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120937/*