---
title: "A uniform thin rod of mass \\(M\\) and length \\(L\\) lies at rest on a frictionless horizontal table and is free to rotate about a frictionless vertical axis fixed at one end. In Scenario 1, a small lump of sticky clay of mass \\(M\\) moving perpendicularly to the rod with speed \\(v_0\\) strikes and sticks to the free end of the rod, resulting in a post-collision angular velocity \\(\\omega_1\\). In Scenario 2, an identical lump of clay moving with the same speed \\(v_0\\) strikes and sticks to the rod at its midpoint, resulting in a post-collision angular velocity \\(\\omega_2\\). What is the ratio \\(\\dfrac{\\omega_1}{\\omega_2}\\)?"
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url: "https://nerd-notes.com/ubq/124259/"
date_modified: "2026-09-28T14:04:33+00:00"
---

# A uniform thin rod of mass \(M\) and length \(L\) lies at rest on a frictionless horizontal table and is free to rotate about a frictionless vertical axis fixed at one end. In Scenario 1, a small lump of sticky clay of mass \(M\) moving perpendicularly to the rod with speed \(v_0\) strikes and sticks to the free end of the rod, resulting in a post-collision angular velocity \(\omega_1\). In Scenario 2, an identical lump of clay moving with the same speed \(v_0\) strikes and sticks to the rod at its midpoint, resulting in a post-collision angular velocity \(\omega_2\). What is the ratio \(\dfrac{\omega_1}{\omega_2}\)?

A uniform thin rod of mass \(M\) and length \(L\) lies at rest on a frictionless horizontal table and is free to rotate about a frictionless vertical axis fixed at one end. In Scenario 1, a small lump of sticky clay of mass \(M\) moving perpendicularly to the rod with speed \(v_0\) strikes and sticks to the free end of the rod, resulting in a post-collision angular velocity \(\omega_1\). In Scenario 2, an identical lump of clay moving with the same speed \(v_0\) strikes and sticks to the rod at its midpoint, resulting in a post-collision angular velocity \(\omega_2\). What is the ratio \(\dfrac{\omega_1}{\omega_2}\)?

![A top-down view shows a thin horizontal rectangular bar representing a rod of length \(L\) and mass \(M\). The left end of the rod is attached to a small solid circle representing a fixed vertical pivot. Two incoming identical small solid circles, each representing clay of mass \(M\), are shown below the rod with upward vertical arrows labeled \(v_0\). The first mass is aligned with the right end of the rod at distance \(L\) from the pivot, labeled Scenario 1. The second mass is aligned with the center of the rod at distance \(L/2\) from the pivot, labeled Scenario 2. A dimension line beneath the rod indicates the full length \(L\) and marks the midpoint \(L/2\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604273-dGRhOr.jpg)

- **A.** \(\dfrac{7}{8}\)
- **B.** \(1\)
- **C.** \(\dfrac{8}{7}\)
- **D.** \(2\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124259/*