---
title: "A uniform thin rod of length \\(L\\) and mass \\(M\\) lies at rest on a frictionless horizontal tabletop and is pivoted at one end about a fixed vertical axis. A small sphere of mass \\(m\\) slides across the tabletop with speed \\(v_0\\) perpendicular to the rod and strikes the rod at its free end. In Case 1, the collision is elastic, and the sphere rebounds backward along its initial line of motion; in Case 2, the collision is perfectly inelastic, and the sphere sticks to the tip of the rod. Which of the following correctly compares the magnitude of the angular impulse delivered to the rod about the pivot and the angular speed of the rod immediately after the collision for the two cases?"
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url: "https://nerd-notes.com/ubq/124477/"
date_modified: "2026-09-28T14:06:02+00:00"
---

# A uniform thin rod of length \(L\) and mass \(M\) lies at rest on a frictionless horizontal tabletop and is pivoted at one end about a fixed vertical axis. A small sphere of mass \(m\) slides across the tabletop with speed \(v_0\) perpendicular to the rod and strikes the rod at its free end. In Case 1, the collision is elastic, and the sphere rebounds backward along its initial line of motion; in Case 2, the collision is perfectly inelastic, and the sphere sticks to the tip of the rod. Which of the following correctly compares the magnitude of the angular impulse delivered to the rod about the pivot and the angular speed of the rod immediately after the collision for the two cases?

A uniform thin rod of length \(L\) and mass \(M\) lies at rest on a frictionless horizontal tabletop and is pivoted at one end about a fixed vertical axis. A small sphere of mass \(m\) slides across the tabletop with speed \(v_0\) perpendicular to the rod and strikes the rod at its free end. In Case 1, the collision is elastic, and the sphere rebounds backward along its initial line of motion; in Case 2, the collision is perfectly inelastic, and the sphere sticks to the tip of the rod. Which of the following correctly compares the magnitude of the angular impulse delivered to the rod about the pivot and the angular speed of the rod immediately after the collision for the two cases?

![A top-down view showing a uniform thin rod and a small sphere on a horizontal surface. A vertical fixed pivot is represented as a small black filled circle at the top end of the rod. The rod is drawn as a long, slender vertical rectangle of length \(L\) extending downward from the pivot. The rod is labeled with mass \(M\). A small gray filled circle representing a sphere of mass \(m\) is positioned below and to the left of the bottom tip of the rod. A single horizontal straight arrow originates at the center of the sphere, points horizontally to the right toward the bottom tip of the rod perpendicular to the rod length, and is labeled \(v_0\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604362-WcAkRP.jpg)

- **A.** Angular impulse: Greater in Case 1 ; Angular speed: Greater in Case 2
- **B.** Angular impulse: Greater in Case 2 ; Angular speed: Greater in Case 1
- **C.** Angular impulse: Greater in Case 1 ; Angular speed: Greater in Case 1
- **D.** Angular impulse: Greater in Case 2 ; Angular speed: Greater in Case 2

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124477/*